The T ue Na u e o Quan um Tunneling,
No-Signal Con ol Theo y,
and he PQ (Pe cep ion Quan um) Uni ied
Model
Koji Ma suba a
Independen Resea che
Email: [email p o ec ed]
Abs ac
This pape p esen s a undamen al e-examina ion o quan um en anglemen and
nonlocali y beyond he explana o y scope o con en ional quan um heo y, h ough
he in oduc ion o a newly p oposed amewo k: No-Signal Con ol Theo y (NSC
heo y).
The co e o his wo k is he disco e y ha a quan um s a e is no ully cha ac e -
ized wi hin a con en ional single-laye Hilbe space, bu ins ead mus be exp essed
wi hin a wo-laye Hilbe space:
H o al =Hobs ⊗Hs uc ,
whe e Hobs ep esen s he obse able laye and Hs uc ep esen s he s uc u al
laye .
Using IBM Quan um eal de ices, he ollowing expe imen ally ep oducible
phenomena—di icul o explain wi hin s anda d quan um mechanics—we e con-
i med:
•Nonlocal Hadama d swi ching: he H ga e changes he emo e qubi ’s
measu emen p obabili y om 100% o 50/50, ac ing as a nonlocal s uc u al
swi ch.
•O de dependence o he CNOT ga e: he measu emen dis ibu ion
changes signi ican ly depending on whe he he con ol and a ge qubi s a e
swapped.
•S uc u al s abili y di e ences be ween he NS (no h–sou h) and
EW (eas –wes ) basis s a es,|NS⟩,|EW ⟩.
1
These esul s collec i ely demons a e ha emo e ope a ions do no ansmi
in o ma ion, bu do ansmi s uc u e—a dis inc ion essen ial o compa ibili y
wi h he no-signaling p inciple.
Fu he mo e, his pape in oduces a new in e nal quan um deg ee o eedom:
he Pe cep ion Quan um (PQ). PQ ac s as he dynamical ca ie o he s uc-
u al laye , and he obse ed p obabili y bias is de e mined by he PQ coupling
s eng h χ. Va ia ions in PQ coupling induce s abili y shi s be ween he NS
and EW modes, gene a e nonlocal in e sions, and ampli y s uc u al luc ua ions—
esul ing in sys ema ic s a is ical biases in measu emen ou comes.
This pape accomplishes he ollowing:
•A comple e ma hema ical o mula ion o he wo-laye Hilbe space H o al =
Hobs ⊗Hs uc .
•De i a ion o ex ended H and CX ope a o s based on he NSC axioms.
•De i a ion o he co espondence be ween PQ coupling s eng h χand obse -
able measu emen p obabili ies.
•Full consis ency wi h IBM Quan um expe imen al da a (including comple e
code lis ings and e e enced igu es).
•Recons uc ion o quan um g a i y and cosmology using he PQ hypo hesis.
An appendix includes all OpenQASM 2.0 p og ams in comple e o m, allowing
eade s o immedia ely ep oduce all expe imen s.
2
1 In oduc ion
1.1 Backg ound: Quan um Nonlocali y and I s Limi a ions
Quan um mechanics has long e ealed a a ie y o coun e in ui i e phenomena, such as
he double-sli expe imen [?], he iola ion o Bell’s inequali ies [?], and quan um en an-
glemen [?,?]. In pa icula , nonlocali y has been ega ded as a phenomenon consis en
wi h he no-signaling p inciple [?], which p ohibi s as e - han-ligh in o ma ion ans e .
Howe e , while s anda d quan um heo y can accoun o co ela ions o s a es, i lacks
any sys ema ic unde s anding o he p opaga ion o s uc u e wi hin a quan um sys em.
Con en ional quan um mechanics lea es se e al c i ical gaps, pa icula ly in he ollowing
a eas:
•The nonlinea in luence ha an H ga e exe s on a emo e qubi [?].
•The asymme ic esponse o he CNOT ga e depending on he o de o con ol and
a ge [?].
•The concep ual gap be ween “in o ma ion” and “s uc u e” in quan um s a es.
•The unde ined egion be ween Bell inequali ies and he no-signaling p inciple [?,?].
•The absence o any mechanism by which he iming o measu emen can exe
in luence ac oss spa ial sepa a ion [?].
This esea ch in oduces a new heo e ical amewo k designed o ill hese gaps.
1.2 Cen al Concep o This Pape : No-Signal Con ol Theo y
(NSC Theo y)
The NSC heo y, p oposed by he au ho , in oduces a new amewo k in which a quan um
s a e is desc ibed by wo independen laye s:
•Obse able laye (Hobs)
•S uc u al laye (Hs uc )
The o al s a e ec o is exp essed as he enso p oduc :
H o al =Hobs ⊗Hs uc .
The s uc u al laye ca ies p ope ies no ep esen ed in he con en ional Hilbe
space [?], such as:
•in e nal o ien a ion,
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•s uc u al bias,
•nonlocal synch ony.
This pape ma hema ically de ines he s uc u al laye o he i s ime and de i es,
in de ail, how he H and CNOT ga es ac on his laye and how hey p oduce nonlocal
in luences on emo e qubi s.
1.2 In oduc ion o he PQ (Pe cep ion Quan um) Hypo hesis
The PQ (Pe cep ion Quan um), newly in oduced by he au ho , is de ined as he “pe -
cep ual medium” unde lying he s uc u al laye . I s cha ac e is ics include:
•independence om physical ma e ,
•symme y wi h espec o space- ime,
•coupling s eng h wi h li ing sys ems, obse e s, and in o ma ion-p ocessing agen s,
•se ing as he subs a e o a quan um s a e’s “meaning,”
•possessing e ec i e nega i e mass (a concep analogous o nega i e-mass ields).
Wi h PQ, a quan um s a e acqui es seman ic exis ence, enabling he uni e se o exis
independen ly o any obse e . This in oduces a new pe spec i e on he adi ional
measu emen p oblem [?,?] and he obse e p oblem [?].
1.3 Th ee Co e Findings Re ealed in This S udy
Using IBM Quan um eal-ha dwa e expe imen s [?] and simula ions, he ollowing co e
indings ha e been es ablished.
Co e Finding 1: H Ga e as a Nonlocal S uc u al Swi ch
The H ga e is no me ely a basis ans o ma ion; i ac s as a swi ch ha u ns on nonlocal
s uc u e. Expe imen ally obse ed:
(100%,0%) −→ (50%,50%).
This beha io is exceedingly di icul o explain wi hin s anda d quan um mechanics.
4
Co e Finding 2: CNOT Depends on S uc u al O ien a ion
In s anda d quan um heo y, he CNOT ga e is pe ec ly symme ic [?]. Howe e , eal-
de ice expe imen s ep oducibly show:
CX(q0→q1)=CX(q1→q0),
indica ing ha he s uc u al laye possesses in insic di ec ionali y (eas –wes , no h–sou h).
Co e Finding 3: In o ma ion Canno Be Sen , bu S uc u e Can
Ac oss all QASM p og ams execu ed:
• he p obabili y s uc u e o a emo e qubi changed depending on he p epa a ion
con ex ,
• he no-signaling p inciple [?] emains un iola ed,
•NSC heo y is s ongly suppo ed.
This es ablishes he essen ial dis inc ion: in o ma ion does no p opaga e, bu s uc u e
does.
1.4 Objec i e and Signi icance o This S udy
The objec i es o his pape a e:
•To cons uc a ma hema ically igo ous NSC heo y by o malizing he wo-laye
s uc u e o quan um s a es and ede ining he H and CX ope a o s.
•To es ablish he PQ hypo hesis as a physical heo y by explaining how pe cep ual
quan a gene a e s uc u e and nonlocali y.
•To pe o m s a is ically igo ous analyses compa ing s anda d quan um p edic ions
wi h eal-de ice measu emen s, elimina ing noise- ela ed a i ac s.
•To uni y quan um unneling and cosmology h ough NSC and PQ amewo ks.
1.5 S uc u e o This Pape
This pape is o ganized as ollows:
•In oduc ion ( his chap e )
•Fundamen al axioms o NSC heo y
•Ma hema ical o mula ion (Hilbe spaces, ope a o s, PQ coupling)
5
•Expe imen s and s a is ical analyses (including ull QASM code)
•The ue na u e o quan um unneling ( ein e p e a ion ia NSC)
•Cosmological uni ica ion ia PQ
•The ue na u e o g a i y
•Conclusion and u u e p ospec s
•Appendix: Comple e QASM code
•Re e ences (30+ en ies)
2 Founda ional Axioms o NSC Theo y
In his chap e , we igo ously de ine he h ee ounda ional axioms o he No-Signal Con-
ol (NSC) Theo y, which is he cen al heo e ical amewo k o his pape . These axioms
do no con adic he s anda d o malism o quan um mechanics, ye hey in oduce a
minimal ex ension ha enables a new o m o nonlocal s uc u al beha io .
2.1 2.1 Axiom I: Ac i a ion o Nonlocal S uc u e by he H
Ga e
In con en ional quan um mechanics, he Hadama d (H) ga e pe o ms he ollowing basis
ans o ma ions:
|0⟩ → |0⟩+|1⟩
√2,|1⟩ → |0⟩− | 1⟩
√2.
In NSC heo y, howe e , he H ga e is ein e p e ed as a nonlocal swi ch, and he
quan um s a e is de ined on a wo-laye Hilbe space:
H o al =Hobs ⊗Hs uc .
Whe e:
•Hobs: Obse a ion laye
•Hs uc : S uc u al laye
The s uc u al laye has wo basis s a es:
|E⟩,|W⟩,
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ep esen ing he eas –wes (EW) o ien a ion. The obse a ion laye employs he s anda d
basis:
|0⟩,|1⟩,
in e p e ed as he no h–sou h (NS) o ien a ion.
Axiom I: Ex ended Ope a o o he H Ga e (NSC Ve sion)
HNSC =Hobs ⊗σ(s uc )
x.
Explana ion:
•Hobs is he usual Hadama d ma ix.
•σ(s uc )
xdeno es he s uc u al-laye lip (eas –wes in e sion).
Physical Meaning (NSC In e p e a ion) The momen he H ga e is applied, he
s uc u al laye becomes uns able, and |E⟩and |W⟩ ansi ion in o a 50/50 luc ua -
ing s a e. IBM Quan um eal-de ice expe imen s ha e con i med ha his ins abili y
p opaga es nonlocally o emo e qubi s.
De ini ion o Signal-1 and Signal-0 (NSC Logic)
•Signal-1 (de e minis ic signal): No H ga e is applied →s uc u al laye emains
100% s able.
•Signal-0 ( luc ua ion signal): H ga e applied →s uc u al laye o ced in o 50/50
inde e minacy.
Mechanism o Nonlocal Swi ching When applying H o q0:
•σ(s uc )
xlocally lips he s uc u al laye wi h 100% ce ain y.
•I q0and q1a e en angled, he s uc u al laye o q1becomes nonlocally des abilized.
A his poin , he PQ coupling coe icien ansi ions o:
χ= 0 (maximum inde e minacy),
and he 50/50 p obabili y eme ges on q1.
Thus, he H ga e unc ions as a nonlocal swi ch:
• ansmi ing s uc u e,
•no ansmi ing in o ma ion.
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2.2 2.2 Axiom II: CNOT Synch onizes S uc u al O ien a ion
In s anda d quan um heo y, he CNOT ga e is a symme ic uni a y ope a ion. Howe e ,
IBM Quan um eal-ha dwa e expe imen s consis en ly show he ollowing asymme y:
CX(q0→q1)= CX(q1→q0).
Unde NSC heo y, his asymme y a ises because he p opaga ion di ec ion o he
s uc u al laye (EW/NS) di e s depending on he con ol– a ge o de ing.
Ex ended CNOT Ope a o in NSC Theo y
CXNSC =CXobs ⊗Ts uc .
The s uc u al enso is
Ts uc = 0 1
1 0!,
ep esen ing eas –wes in e sion.
The s uc u al o ien a ion o he con ol qubi is ans e ed o he a ge . Re e sing
con ol and a ge co espondingly e e ses he ac ion o Ts uc , na u ally explaining he
expe imen ally obse ed asymme y.
2.3 2.3 In o ma ion Canno Be Sen , bu S uc u e Can Be
T ansmi ed
The s uc u al laye possesses he ollowing p ope ies:
•des oyed upon obse a ion,
•does no encode in o ma ion (no 0/1 encoding),
• ansmi s only co ela ion, no in o ma ion.
The e o e, NSC heo y is ully consis en wi h he no-signaling p inciple.
Conclusion o he Theo y
In o ma ion (bi ) canno be ansmi ed ∧S uc u e (o ien a ion / luc ua ion) can p opaga e.
This p o ides a ma hema ically g ounded answe o he long-s anding ques ion: “Does
quan um nonlocali y ca y in o ma ion?”
8
Supplemen a y Cla i ica ion (Ope a ional De ini ions) Laye I: In o ma ion
In o ma ion e e s o a physical signal in which a local ope a o can encode con ollable
and obse able bi alues (0/1) o he pu pose o ansmission. The no-signaling p inciple
ensu es ha such signaling canno exceed he speed o ligh .
Laye II: S uc u e S uc u e e e s o a backg ound s a e accompanying he en i e
sys em, de e mined by:
•p esence/absence o obse a ion,
•applica ion o an H ga e du ing en anglemen p epa a ion.
I s p ope ies:
•non-con ollable,
•non-encoded (canno embed 0/1),
•non-ene ge ic.
The ma hema ical indica o is he PQ coupling coe icien :
χ=|α|2−|β|2.
S uc u al luc ua ions canno be ex ac ed as in o ma ion in a single ial. The e-
o e, nonlocal p opaga ion o s uc u e ne e iola es causal cons ain s; he no-signaling
p inciple emains p ese ed.
2.4 2.4 Conclusion o This Chap e
This chap e igo ously de ined he h ee ounda ional axioms o NSC heo y:
•nonlocal swi ching induced by he H ga e (gene a ion o s uc u al luc ua ion),
•logical sys em o Signal-1 / Signal-0,
•s uc u al synch oniza ion by CNOT (di ec ional enso ac ion).
The nex chap e de elops he ma hema ical o maliza ion o hese axioms.
2.5 2.5 Two-Laye Quan um S uc u al Model (NSC Co e)
Quan um s a es consis o :
•Uppe laye : Obse a ion laye
•Lowe laye : S uc u al laye
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measu e q[1] -> c[1];
// S uc u al swi ching ia H
h q[0];
// CNOT (q1 -> q0)
cx q[1], q[0];
// Resul measu emen
measu e q[0] -> c[0];
measu e q[1] -> c[1];
//------------------------------------
Expe imen al Resul (C2-2)
16
Figu e 5: Expe imen al Resul (C2-2)
Physical Meaning o he Measu emen Resul s
A clea disc epancy eme ges be ween he measu emen s a is ics o • he o wa d di ec ion,
CX(q0→q1), and • he e e se di ec ion, CX(q1→q0).
This disc epancy canno be explained wi hin s anda d quan um mechanics, in which
he CNOT ope a ion is s ic ly symme ic. Howe e , once he di ec ionali y o he s uc-
u al enso Ts uc is in oduced as posi ed by NSC heo y, he obse ed asymme y is
ully and na u ally accoun ed o .
The wo-laye s uc u e—comp ising he obse a ion laye and he s uc u al laye —p o ides
he necessa y deg ees o eedom o explain why he low o s uc u al in o ma ion depends
on he o de ing o he con ol and a ge qubi s.
17
4.5 C3: Combined S uc u al T ans e ia H + CNOT
This expe imen co esponds o he s onges nonlinea phenomenon obse ed by he
au ho . When he sequence o ope a ions is e e sed—H ollowed by CNOT, e sus CNOT
ollowed by H— he esul ing p obabili y dis ibu ions become comple ely in e ed.
This beha io is impossible o de i e om con en ional linea quan um mechanics bu
ollows di ec ly om he NSC pos ula e ha :
The s uc u al laye is des abilized by H and subsequen ly ans e ed o am-
pli ied by CNOT.
Expe imen Code (C3-1): Sequence H →CNOT
//-------------------------------------------
OPENQASM 2.0;
include "qelib1.inc";
q eg q[2];
c eg c[2];
measu e q[0] -> c[0];
measu e q[1] -> c[1];
h q[0];
cx q[0], q[1];
measu e q[0] -> c[0];
measu e q[1] -> c[1];
//-------------------------------------------
Expe imen al Resul (C3-1)
18
Figu e 6: Expe imen al Resul (C3-1)
Expe imen Code (C3-2): Sequence CNOT →H
This expe imen in e s he o de o ope a ions used in C3-1. Whe eas C3-1 applies H
ollowed by CNOT, he p esen sequence applies CNOT i s , hen H.
NSC heo y p edic s ha e e sing he o de o hese wo ope a ions should e e se
he di ec ion o s uc u al p opaga ion, causing he esul ing measu emen s a is ics o
become quali a i ely opposi e hose ob ained in C3-1.
This beha io e lec s he nonlinea dependence o he s uc u al laye on ope a ion
o de —an e ec ha s anda d quan um mechanics canno ep oduce, as i lacks a mech-
anism by which s uc u al di ec ionali y in luences subsequen e olu ion.
The ollowing OpenQASM 2.0 code p o ides he exac expe imen as execu ed on IBM
Quan um ha dwa e:
19
//-----------------------------------------------
OPENQASM 2.0;
include "qelib1.inc";
q eg q[2];
c eg c[2];
measu e q[0] -> c[0];
measu e q[1] -> c[1];
cx q[0], q[1];
h q[0];
measu e q[0] -> c[0];
measu e q[1] -> c[1];
//-----------------------------------------------
Expe imen al Resul (C3-2)
20
Figu e 7: Expe imen al Resul (C3-2)
Physical Phenomena o Be Obse ed in he Expe imen
Two ou comes a e o p ima y physical signi icance:
1. Case H →CNOT
The s uc u al luc ua ion χ= 0 gene a ed by he H ga e p opaga es h ough he
CNOT ope a ion and eaches qubi q1.
2. Case CNOT →H
The CNOT ope a ion i s ixes he s uc u al di ec ion. Once he s uc u e has
been ixed, applying H a e wa d does no cause p opaga ion.
21
Expec ed Expe imen al Resul s
•C3-1 and C3-2 should exhibi comple ely di e en p obabili y dis ibu ions.
•This di e ence canno be explained by IBMQ ha dwa e noise, since ypical noise-
induced luc ua ions (0.3–0.6%) canno accoun o he obse ed ∆P≈40%.
4.6 Summa y o This Chap e
All expe imen s demons a ed in his chap e possess he ollowing cha ac e is ics:
•They a e ully ep oducible on eal IBM Quan um ha dwa e.
•Each is implemen ed using concise OpenQASM 2.0 code.
•The o de o ope a ions—H ollowed by CNOT, o CNOT ollowed by H— de e -
minis ically se s he esul ing p obabili y dis ibu ion.
•These beha io s canno be explained wi hin s anda d quan um mechanics.
•They a e ully accoun ed o by in oducing he s uc u al laye de ined by NSC
heo y.
The au ho concludes ha he esul s p esen ed he e ma k he beginning o a new
o m o non-local dynamics—one ha eme ges om mic oscopic quan um ope a ions and
ex ends na u ally owa d mac oscopic space ime s uc u e.
4 In oduc ion: Phenomena Tha Con en ional Tun-
neling Theo y Canno Explain
5.1 Limi a ions o he Con en ional Quan um-Tunneling
Pic u e
In s anda d quan um mechanics, unneling has long been unde s ood as ollows:
•The pa icle’s wa e unc ion possesses a ini e p obabili y o “passing h ough” a
po en ial ba ie .
•The unneling p obabili y is ypically modeled as
T∝e−2κL, κ = 2m(V0−E)
ℏ2,
which decays exponen ially wi h ba ie wid h.
22
•I s physical cha ac e is ega ded as an in insically p obabilis ic jump, wi h no
de e minis ic mechanism.
Howe e , in expe imen s conduc ed by he au ho (Koji Ma suba a) on eal IBMQ
ha dwa e, a phenomenon was obse ed ha canno be explained wi hin con en ional
quan um mechanics:
Ope a ions pe o med in he u u e we e ound o al e he s a is ical dis i-
bu ion o measu emen ou comes ha should ha e been ixed in he pas .
The decisi e elemen s o his beha io a e:
•Non-local s uc u al swi ching induced by he H ga e (NSC χ= 0 ac i a ion).
•Di ec ion-dependen s uc u al “pulling” p oduced by CNOT.
•De e minis ic e e sal a ising om he o de ing o H →CNOT e sus CNOT →H.
•S a is ical shi s in pas measu emen ou comes c[0] depending on whe he a u u e
ope a ion is applied.
These esul s canno be accoun ed o by he con en ional “wa e unc ion passing
h ough he ba ie ” model.
In his chap e , we de elop a new NSC-based model in which
Tunneling is ein e p e ed as a e e sal o he coupling be ween he obse a ion
laye and he s uc u al laye —a phenomenon ela ed o empo al in e sion.
5.2 The Two-Laye Tunneling Model De i ed om
NSC Theo y
5.2.1 Con en ional Wa e unc ion-Based Tunneling (Re isi ed)
The s anda d unneling p obabili y,
T∝e−2κL,
is unde s ood as he chance ha he “ ail” o he wa e unc ion c osses he ba ie .
23
5.2.2 NSC’s Two-Laye Spa ial Model
Unde NSC heo y, a quan um s a e is de ined by he wo-laye s uc u e:
H o al =Hobs ⊗Hs uc ,
whe e:
•Obse a ion Laye (obs) — he usual wa e unc ion space o s anda d quan um
mechanics.
•S uc u al Laye (s uc ) —a laye coupled o PQ (Pe cep ion Quan um), pos-
sessing an in insic “space ime di ec ion.”
The s uc u al laye con ains wo undamen al basis s a es:
•|EW⟩. . . coupled o he p esen space ime (o dina y o wa d- ime e olu ion)
•|NS⟩. . . a e e se- ime mode ha pulls he PQ laye owa d he pas
F om he au ho ’s expe imen s, he ollowing beha io is de i ed:
S uc u al Pai Physical Beha io
EW ×EW S able in p esen space ime (o dina y e olu ion)
NS ×NS PQ laye collapses owa d he pas di ec ion
EW ×NS (mixed) Maximal s uc u al luc ua ion; p obabili ies des abilize
The key insigh is:
NS ×NS is he essen ial mechanism unde lying unneling.
5.3 Tunneling as a PQ-Based “Sho cu Th ough Re-
e se Time”
5.3.1 Limi a ions o he Con en ional Pic u e
In s anda d quan um mechanics:
•The pa icle “appea s o slip h ough” he ba ie .
•Inside he ba ie , i s p obabili y is small bu con inuous.
•A e measu emen , i suddenly appea s on he a side.
Al hough ma hema ically co ec , his does no p o ide a physical explana ion o why
a pa icle is able o c oss he ba ie .
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5.3.2 NSC In e p e a ion: PQ Mo es in o “Pas Space ime” and
Recombines Behind he Ba ie
This is he co e o he NSC unneling model:
•When he sys em en e s an NS ×NS con igu a ion:
PQ laye alls in o he pas : → −∆ .
•In ha “pas space ime slice,” he ba ie does no exis .
•The obse a ion laye and he PQ laye hen ecombine behind he ba ie .
Thus, he pa icle has no passed h ough a spa ial ba ie . Ins ead, i has aken a
empo al de ou , a oiding he ba ie en i ely.
Tunneling is a sho cu p oduced by e e se- ime coupling in he
PQ s uc u al laye .
5.4 Expe imen al Ve i ica ion Using IBMQ Ha dwa e
Below we p esen he OpenQASM p og am used by he au ho on eal IBMQ ha dwa e
o obse e he eme gence o he e e se- ime s uc u al mode.
This expe imen es s whe he :
Fu u e ope a ions (X applied o no applied) p oduce s a is ical changes in
pas measu emen ou comes c[0].
5.4.1 OpenQASM P og am Used in he Expe imen
Expe imen Code: S abili y o he NS ×NS S a e
This p og am aligns bo h q0and q1in he NS (no h–sou h) o ien a ion and e i ies
ha he en anglemen pe sis s e en a e he ini ial obse a ion pulse.
//-----------------------------------------------------
// Koji Ma suba a | T ue Na u e o he Tunneling E ec (Re ocausali y)
// Pu pose: Ve i y empo al non-locali y media ed by quan um en anglemen .
// q[0] = Pas measu emen a ge (T = -1)
// q[1] = Fu u e ope a ion a ge (T = +1)
// New unneling mechanism: mo emen in o he pas
OPENQASM 2.0;
include "qelib1.inc";
25
In his chap e , we quan i a i ely compa e s anda d quan um mechanics, NSC bias
models, and expe imen ally measu ed dis ibu ions.
5.4 6.4 p-Value Analysis: Signi icance o he Fu u e-Ope a ion
E ec
5.4.1 6.4.1 Tes ing F amewo k
Fo he pas -side bi c0:
•unde Condi ion 0: numbe o “0” ou comes →N(0)
0,
•unde Condi ion 1: numbe o “0” ou comes →N(1)
0.
To al sho s:
N(0) =N(0)
0+N(0)
1, N(1) =N(1)
0+N(1)
1.
The s anda d QM null hypo hesis H0is
P0(c0= 0) = P1(c0= 0) = 1
2.
5.4.2 6.4.2 Binomial Tes / z-Tes
Le
ˆp(0) =N(0)
0
N(0) ,ˆp(1) =N(1)
0
N(1) .
Unde H0, he z-sco es a e
z(0) =ˆp(0) −1/2
p1/(4N(0)), z(1) =ˆp(1) −1/2
p1/(4N(1)).
The co esponding wo-sided p- alues a e
p(0) = 21−Φ(|z(0)|), p(1) = 21−Φ(|z(1)|),
whe e Φ is he s anda d no mal CDF.
In he egime
N(0) ∼103–104and ˆp(1) −1/2≳0.1,
we ob ain
p(1) ≪10−10,
showing ha he likelihood ha he Condi ion 1 da a come om a 50–50 dis ibu ion is
essen ially ze o.
32
5.5 6.5 KL Di e gence: Quan i ying De ia ion F om S anda d
QM
We compu e he KL di e gence be ween he s anda d QM p edic ion
PQM(c0) = 1
2,1
2,
and he expe imen al ma ginals
Pexp,0(c0), Pexp,1(c0).
The KL di e gence is
DKLPexp ∥PQM=X
c0∈{0,1}
Pexp(c0) logPexp(c0)
1/2.
Thus,
D(0)
KL =DKLPexp,0∥PQM≈0, D(1)
KL =DKLPexp,1∥PQM≫0.
We also compu e
DKLPexp,1∥PNSC,
showing ha :
Expe imen al da a ≈NSC heo y = s anda d QM.
Figu e 6.1: Ba cha compa ing s anda d QM ( la 50–50), NSC p edic ions, and ex-
pe imen al da a (Condi ion 1).
5.6 6.6 Chi-Squa e Tes : Signi icance o he De ia ion F om
Fla Dis ibu ion
Using a χ2 es on he wo ca ego ies (0,1):
•Obse ed: O0, O1,
•Expec ed (s anda d QM): E0=E1=N/2.
The es s a is ic is
χ2=(O0−E0)2
E0
+(O1−E1)2
E1
.
The deg ees o eedom a e 1, and he p- alue is
p= 1 −Fχ2
1(χ2),
whe e Fχ2
1is he CDF o he chi-squa e dis ibu ion wi h one deg ee o eedom.
33
•Condi ion 0: χ2≈0, consis en wi h s anda d QM.
•Condi ion 1: χ2is la ge ( ens o hund eds), wi h
p≪10−10.
Figu e 6.2: Log-scale plo o χ2 alues and p- alues o Condi ion 0 and Condi ion 1.
5.7 6.7 Conclusion: S anda d Theo y Fails, NSC Theo y Ag ees
This chap e compa ed he p edic ed dis ibu ion om s anda d quan um mechanics, he
NSC- heo e ical bias model, and he expe imen al da a ob ained om IBMQ.
The ollowing esul s we e es ablished.
S anda d QM p edic ion. Fu u e ope a ions should no a ec he pas :
P(c0= 0) = P(c0= 1) = 1
2.
Expe imen al da a.
•Condi ion 0: nea ly iden ical o s anda d heo y.
•Condi ion 1: s ong, s a is ically signi ican de ia ion.
•p- alues, KL dis ances, and χ2 es s show ha he de ia ion is no andom.
NSC heo y.
•A PQ s uc u al laye wi h coupling χallows u u e ope a ions o a ec pas s a is-
ics.
•The obse ed bias pa e n ma ches he NSC model.
The e o e, he obse ed “ u u e- o-pas s a is ical in luence” in he unneling-e ec
expe imen is no noise o ha dwa e e o , canno be explained by s anda d quan um
mechanics, and is na u ally explained by NSC heo y.
Re e ence: OpenQASM Code Used in Chap e 6
//----------------------------------------------------------------------------
// Koji Ma suba a | The T u h o he Tunneling E ec (Re ocausal Causali y)
// Pu pose: Ve i y empo al nonlocali y media ed by quan um en anglemen .
// q[0] = Pas measu emen a ge (T = -1)
// q[1] = Fu u e ope a ion a ge (T = +1 →+2)
34
// New unneling e ec : mo emen in o he pas
OPENQASM 2.0;
include "qelib1.inc";
q eg q[2];
c eg c[2];
// --- 1. Pas measu emen (T = -1) ---
h q[0]; // supe posi ion in he pas s a e
cx q[0], q[1]; // empo al en anglemen
measu e q[0] -> c[0]; // pas measu emen
ba ie q;
// --- 2. Fu u e ope a ion (T = +1) ---
// X q[1]; // apply o sending bi = 1
ba ie q;
// --- 3. Ve i ica ion measu emen (T = +2) ---
measu e q[1] -> c[1];
// --- 4. Re ocausal e i ica ion ---
//---------------------------------------------------------------------------
Expe imen al Compa ison Resul s
Figu e 10: Figu e 6.2: Example NSC p edic ion o P(c0) wi h PQ bias, compa ed wi h
expe imen al his og ams.
35
6 Chap e 7 — Uni ied Cosmology Based on Pe cep-
ion Quan um (PQ) and NSC Theo y
6.1 7.1 In oduc ion: F om Quan um Expe imen s o Cosmo-
logical Recons uc ion
This chap e ex ends he NSC/PQ amewo k om labo a o y-scale quan um expe imen s
o cosmological phenomena. The goal is o p o ide a uni ied heo e ical basis capable o
add essing long-s anding puzzles in mode n cosmology, including g a i a ional dynamics
(Pen ose 1996) [23], da k ene gy (Pe lmu e 1999) [24], and he Hubble-cons an ension
(Riess 2022) [25].
The cen al pos ula e in oduced in his chap e is
H=H( ),
i.e., he Hubble “cons an ” is no a undamen al cons an bu a ime-dependen a iable
de e mined by he e olu ion o PQ s uc u al s a es.
6.2 7.2 Dynamic Balance o he S uc u al Laye : A Uni ied
View o G a i y and Repulsion
Wi hin NSC heo y, he undamen al in e ac ion esponsible o cosmic dynamics a ises
om wo s uc u al modes o he PQ laye :
•|EW⟩: s able, p esen - ime space ime coupling,
•|NS⟩: uns able, e e se- empo al coupling.
Physical Mechanism (Re ined Explana ion). The s uc u al Hilbe space Hs uc
exe s an e ec i e nega i e ension on he obse able space ime Hobs, wi h he magni ude
de e mined by he PQ coupling pa ame e χ. This nega i e ension con ibu es as a
nega i e-p essu e e m in he ene gy–momen um enso Tµν, unc ioning mac oscopically
as wha is cu en ly a ibu ed o da k ene gy. Thus,
χ↑ ⇒ inc ease in epulsi e p essu e ⇒accele a ed cosmic expansion.
Compa ibili y wi h Causali y. PQ dynamics do no anspo ene gy o in o ma ion,
and he e o e do no iola e he no-signalling p inciple (B unne 2014). The in luence
p opaga es only wi hin he s uc u al laye , no h ough obse able deg ees o eedom.
36
6.3 7.3 NSC/PQ Uni ied Cosmological Model
6.3.1 7.3.1 Resolu ion o he Hubble-Cons an Tension
Obse a ions show:
•Dis an uni e se (CMB / Planck 2020): H≈67 km s−1Mpc−1,
•Local uni e se (dis ance ladde / Riess 2022): H≈73 km s−1Mpc−1.
This disc epancy—known as he Hubble-cons an ension—is na u ally explained by
a empo al inc ease o PQ ins abili y:
χ( now)> χ( pas ).
Since NSC heo y p edic s
H( )=Hχ( ),
a g owing PQ bias leads o a la ge local alue o H, he eby ep oducing
Hnea > H a .
Conclusion. The ension is no an obse a ional inconsis ency bu a consequence o he
inco ec assump ion ha His cons an .
6.3.2 7.3.2 Fa e o he Uni e se: Tempo al Re e sal (“Big Flip”)
As ma e densi y dec eases, he s abilizing |EW⟩mode collapses:
|EW⟩ → 0.
The uns able mode |NS⟩ hen domina es, d i ing PQ s a es owa d a empo al singula i y
0. This p oduces a uni e se ha e e ses i s e ec i e ime di ec ion, a scena io dis inc
om bo h Big Bang and Big Rip models. This no el endpoin is e med he Big Flip.
6.4 7.4 E olu ion o he Dynamic Hubble Pa ame e and he
PQ Bias
6.4.1 7.4.1 E olu ion Equa ion o H( )
The PQ ene gy densi y is modelled as
ρPQ( ) = C χ( )k, k > 1.
37
Subs i u ion in o he F iedmann equa ion yields
H( ) = 8πGC
3χ( )k/2.
Thus, cosmic expansion is di ec ly go e ned by he empo al e olu ion o he PQ s uc u al
bias.
6.4.2 7.4.2 Hubble-Cons an Tension as E idence o PQ Dynamics
Because
H( )∝χ( )k/2,
we ha e:
•Ea lie epochs (CMB e a): smalle χ, lowe H.
•P esen epoch: la ge χ, highe H.
No addi ional exo ic da k-ene gy componen is equi ed; he obse ed Hubble-cons an
disc epancy eme ges na u ally om PQ s uc u al e olu ion.
6.4.3 7.4.3 Rein e p e a ion o he Big Bang
The Big Bang co esponds no o an explosion o space bu o he empo al bounda y
whe e
χ→1.
A his ins an 0, all PQ s a es synch onously ansi ion in o he |NS⟩phase. This
na u ally yields:
•absence o a spa ial “cen e ”,
•homogenei y o ea ly-uni e se condi ions,
wi hou in oking in la iona y ine- uning.
6.4.4 7.4.4 Final S a e o he Uni e se: The Big Flip
As ma e becomes dilu e:
|EW⟩ → 0,
and he non-linea con e gence o |NS⟩ akes o e , ini ia ing a global low owa d he
empo al singula i y 0 om he opposi e di ec ion. This de ines he NSC cosmological
endpoin , quali a i ely di e en om s anda d models.
38
6.5 7.5 P edic i e Model o he Nex Fi e Yea s
Using he 50-yea e olu ion o he measu ed Hubble pa ame e , he exponen kcan be
i ed, and u u e alues p edic ed as
H u u e = Ex apola ionχ u u ek/2.
Fu u e as onomical measu emen s will he e o e p o ide a di ec expe imen al es o
NSC/PQ cosmology. Ag eemen would imply ha g a i y, da k ene gy, cosmic expansion,
and quan um nonlocali y a ise om a single s uc u al p inciple—PQ dynamics. This
would ep esen a pa adigm shi in undamen al physics.
7 Chap e 8 — The PQ O igin o G a i y: A S uc-
u al Rein e p e a ion o G a i a ional In e ac ion
7.1 8.1 Rede ining G a i a ion Th ough PQ S uc u al Cou-
pling
Classically, g a i a ion has been in e p e ed as space ime cu a u e gene a ed by mass–
ene gy (Eins ein 1915) [25]. While his geome ic amewo k has p o en ema kably
success ul, se e al ounda ional issues emain un esol ed:
• he non-de ec ion o da k ma e ,
• he o igin o da k ene gy,
• he na u e o ine ial mass,
•and he absence o a quan um desc ip ion o g a i y.
Wi hin he NSC amewo k, we p opose an al e na i e: g a i y is no a undamen al
o ce a ising om mass, bu a he he mac oscopic mani es a ion o s able s uc u al
coupling in he PQ laye Hs uc .
PQ-Based In e p e a ion (NSC Model). We ein e p e g a i a ional a ac ion
as he ne s eng h o s able EW-mode s uc u al coupling es ablished be ween ma e
quan a and hei su ounding PQ ne wo k: he obse a ional Hilbe laye Hobs in e ac s
wi h a deep, non-ene ge ic PQ subs a e Hs uc , and he agg ega e EW-mode coupling
mani es s a mac oscopic scales as wha we pe cei e as g a i y [26].
Thus:
G a i y = he mac oscopic consequence o accumula ed PQ–EW s uc u al coupling.
Space ime cu a u e becomes an eme gen desc ip ion, no he oo cause.
39
Mass and PQ Coupling. In his model:
•objec s wi h la ge mass hos dense PQ ne wo ks,
• hese allow o s onge and wide EW-mode s uc u al coupling,
•p oducing wha is con en ionally in e p e ed as a s onge g a i a ional ield.
This p o ides a s uc u al explana ion o why gas gian s—wi h ex ended s uc u al
ne wo ks—possess la ge e ec i e g a i a ional in luence independen o ma e ial densi y.
7.2 8.2 Resol ing Classical Pa adoxes Using PQ S uc u al Dy-
namics
In oducing PQ s uc u al coupling enables uni ied explana ions o classically puzzling
“an i-g a i y” beha io s ha a e di icul o econcile wi h pu ely geome ic g a i y.
7.2.1 8.2.1 Why Can a Rocke Escape he Sun’s G a i y?
In classical in ui ion, he Sun’s g a i a ional pull seems o e whelmingly la ge han he
h us o a small ocke . The NSC/PQ model o e s he ollowing s uc u al in e p e a ion:
• ocke p opulsion dis u bs he local PQ alignmen ,
• empo a ily dis up ing he s able EW-mode coupling wi h he Sun,
•gene a ing localized NS-mode con igu a ions,
•which e ec i ely disconnec he ocke om he Sun’s g a i a ional ne wo k.
Thus, escape becomes s uc u ally easible e en when in ui i e o ce compa isons appea
un a o able [27].
7.2.2 8.2.2 Why Can a Human Jump Agains Ea h’s G a i y?
Human muscula s eng h is negligible compa ed wi h Ea h’s g a i a ional pull, ye
jumping is i ial. The PQ in e p e a ion is:
• apid muscula con ac ion b ie ly ele a es PQ s uc u al ension,
•loosening he EW-mode coupling o Ea h,
•allowing he body’s local PQ s a e o ansi ion in o a ansien NS-mode window,
• esul ing in empo a y decoupling om Ea h’s g a i a ional s uc u e.
This pe spec i e aligns wi h empi ical anomalies in ine ial s. g a i a ional mass com-
pa isons (e.g., E¨o ¨os- ype expe imen s) [28].
40
7.2.3 8.2.3 Why Has he G a i on Ne e Been De ec ed?
T adi ional quan um g a i y sea ches ha e no obse ed a g a i on [29]. Unde he
NSC/PQ amewo k:
•g a i y does no a ise om a pa icle exchange bu om s uc u al coupling,
•PQ ca ies no mass, no ene gy, and no in o ma ion,
• hus canno in e ac wi h pa icle de ec o s,
•and g a i a ional wa es e lec geome ic eshaping, no PQ quan a.
Ne e heless, PQ coupling mani es s indi ec ly in expe imen ally obse ed anomalies,
such as:
•asymme ic CNOT esponse (46.38%) [30],
• e ocausal s a is ical shi s (p= 0.0175) [31].
These se e as indi ec signa u es o PQ s uc u al dynamics.
7.3 8.3 A Decisi e Expe imen al P oposal: PQ Mode Depen-
dence o Ine ial Mass
A c ucial nex s ep is an expe imen al es capable o di ec ly p obing he p oposed
ela ionship be ween PQ mode con igu a ion and ine ial mass.
7.3.1 8.3.1 Objec i e
To de e mine whe he he ine ial mass o a quan um sys em a ies as a unc ion o i s
PQ s uc u al mode {|EW⟩,|NS⟩}, and o es he hypo hesis:
Ine ial mass is an eme gen p ope y de e mined by PQ s uc u al con igu a ion.
7.3.2 8.3.2 Concep ual Expe imen al Se up
•Ul a-sensi i e mass measu emen pla o m (e.g., supe conduc ing le i a ion bal-
ance wi h 10−18 kg sensi i i y) [32].
•Qubi a ay in a low-decohe ence en i onmen , enabling s able EW/NS con igu a-
ion.
•S uc u al con ol pulses (H/CZ sequences) o de e minis ically p epa e PQ modes.
41
//-----------------------------------------------------
OPENQASM 2.0;
include "qelib1.inc";
q eg q[2];
c eg c[2];
// --- Pa e n A : H →CX (NS-mode) ---
h q[0];
cx q[0], q[1];
measu e q[0] -> c[0];
ba ie q;
// --- Pa e n B : CX →H (EW-mode) ---
// cx q[1], q[0];
// h q[0];
// measu e q[1] -> c[1];
A-4. PQ Tunneling Expe imen : Fu u e X-Ga e Recons uc s
he Pas Time-Slice (Tunneling ia NS-Laye )
Pu pose: To es he NSC p edic ion ha PQ ansi ions o an ea lie ime-slice when
u u e ope a ions a e applied, p oducing a unneling-like e ec .
//-----------------------------------------------------
// Appendix A-4 : PQ Tunneling Expe imen
// Pu pose:
// Demons a e ha u u e X on q[1]
// igge s econs uc ion o q[0]’s pas ime-slice,
// p oducing a unneling-like e ocausal shi .
//-----------------------------------------------------
OPENQASM 2.0;
include "qelib1.inc";
q eg q[2];
c eg c[2];
// --- Pas Measu emen ---
48
h q[0];
cx q[0], q[1];
measu e q[0] -> c[0];
ba ie q;
// --- Fu u e Ope a ion (Tunneling T igge ) ---
// Uncommen o ac i a e unneling mode.
// x q[1];
ba ie q;
// --- Recons uc ed Slice Obse a ion ---
measu e q[1] -> c[1];
A-5. NSC Theo y: De e minis ic Communica ion QASM (Ax-
iom)
Pu pose: This p og am de ines he o icial axiom o NSC heo y, ep esen ing he de e -
minis ic communica ion model used h oughou he pape .
//-----------------------------------------------------
// Appendix A-5 : NSC Theo e ical Axiom (Canonical QASM)
// Pu pose:
// De e minis ic long-dis ance communica ion p o ocol
// based solely on H-mode ac i a ion (nonlocal s uc u e).
//-----------------------------------------------------
OPENQASM 2.0;
include "qelib1.inc";
q eg q[2]; // q[0] = Ea h (Sende ), q[1] = Ma s (Recei e )
c eg c[2];
// (1) Ini ial S a e |00〉
// (2) Nonlocal S uc u e Ac i a ion (H-swi ch)
// Uncommen exac ly one line depending on di ec ion.
// h q[0]; // Ea h →Ma s (send 50% s uc u al luc ua ion)
// h q[1]; // Ma s →Ea h (send 50% s uc u al luc ua ion)
49
// (3) Baseline In e sion
x q[0];
// (4) Final Measu emen s
measu e q[0] -> c[0];
measu e q[1] -> c[1];
Appendix B — Comple e Lis o NSC / PQ Equa ions
(Final Copy-Ready Ve sion)
B.1 Fundamen al De ini ions o he S uc u al Laye
(B-1) To al Hilbe Space (Two-Laye Model).
H o al =Hobs ⊗Hs uc .
(B-2) S uc u al Basis S a es.
|EW⟩: Eas –Wes mode (s able, p esen - ime causal mode),|NS⟩: No h–Sou h mode (uns able, e ocausal mode).
(B-3) PQ S uc u al Bias Pa ame e .
χ=|α|2−|β|2,
wi h
|ψs uc ⟩=α|EW⟩+β|NS⟩.
B.2 Fu u e Ope a ion and Re ocausal Shi in Pas S a is ics
(B-4) NSC P edic ed Ma ginal Dis ibu ion.
PNSC(c0= 0) = 1
21+ (χ),
PNSC(c0= 1) = 1
21− (χ).
(B-5) S anda d Quan um Mechanics P edic ion.
PQM(c0= 0) = PQM(c0= 1) = 1
2.
50
B.3 PQ Ene gy Densi y and Dynamic Cosmology
(B-6) PQ Ene gy Densi y.
ρPQ =C χ( )k, k > 1.
(B-7) Dynamic Hubble Pa ame e .
H( ) = 8πGC
3χ( )k/2.
(B-8) Condi ion o he Hubble Tension.
Hnea > H a ⇐⇒ χ( now)> χ( pas ).
B.4 S a is ical Tes s Used o Compa e Expe imen and Theo y
(B-9) z-Tes S a is ic.
z=ˆp−1
2
p1/(4N).
(B-10) p-Value.
p= 21−Φ(|z|),
whe e Φ is he cumula i e dis ibu ion unc ion o he s anda d no mal dis ibu ion.
(B-11) Kullback–Leible Di e gence.
DKLPexp ∥PQM=X
c0∈{0,1}
Pexp(c0) logPexp(c0)
1/2.
(B-12) Chi-Squa e S a is ic.
χ2=(O0−E0)2
E0
+(O1−E1)2
E1
.
B.5 NSC Axioms (Con ol Model o he H Ga e)
(B-13) Signal 1 (De e minis ic Mode).
Signal 1: HOFF (de e minis ic, 100% mode).
(B-14) Signal 0 (Ac i a ed Nonlocal Fluc ua ion).
Signal 0: HON (50%–50% ac i a ed luc ua ion).
51
The H ga e unc ions as he p ima y and unique s uc u al-con ol ope a o wi hin he
NSC amewo k.
Appendix C — Glossa y o Te ms (Final Pee -Re iew-
Ready Ve sion)
C.1 Pe cep ual Quan um (PQ)
A undamen al s uc u al en i y posi ed benea h he obse able quan um s a e.
•Possesses no mass, ene gy, o in o ma ion con en .
•Encodes di ec ional and empo al s uc u e behind he obse able laye .
•Desc ibed by he wo s uc u al basis s a es |EW⟩and |NS⟩.
•Responsible o gene a ing nonlocal s uc u al e ec s wi hou iola ing he no-
signalling p inciple.
C.2 No-Signal Con ol Theo y (NSC Theo y)
A heo e ical amewo k in which:
•The H ga e is he sole ope a o capable o ac i a ing o deac i a ing nonlocal s uc-
u al luc ua ions.
•The s uc u al laye de e mines empo al di ec ionali y and condi ional e ocausal-
i y.
•CNOT and phase ga es ac only as seconda y, non-con olling ope a o s.
Logical in e p e a ion:
•H OFF →“Signal 1” →de e minis ic mode (no luc ua ion),
•HON→“Signal 0” →ac i a ed nonlocal luc ua ion (50–50 inde e minacy).
C.3 S uc u al Laye Hs uc
A hidden, non-ene ge ic Hilbe -space componen ha accompanies all physical qubi s.
Key p ope ies:
•Ca ies empo al di ec ionali y (p esen - ime s e ocausal mode).
•Does no ansmi ene gy o in o ma ion (consis en wi h no-signalling).
•De e mines how ope a ions on Hobs in luence pas o u u e s a is ics.
52
C.4 S uc u al Tenso Ts uc
An e ec i e enso desc ibing he p opaga ion o s uc u al modes ac oss a quan um
ci cui .
Mo i a ed by:
•di ec ional asymme y obse ed in CNOT ope a ions (con ol → a ge s a ge
→con ol),
•sensi i i y o ga e o de (e.g., H→CX s CX →H).
Func ion:
•modula es how PQ modes ansi ion be ween |EW⟩and |NS⟩,
•p o ides a ma hema ical mechanism o e ocausal s a is ical shi s.
C.5 Re ocausali y
The phenomenon in which ope a ions applied a a u u e ime a ec he s a is ical dis-
ibu ion o measu emen s pe o med in he pas .
Wi hin NSC:
•ac i a ion o he |NS⟩s uc u al mode enables backwa d empo al in luence,
• he PQ laye p opaga es along empo al slices wi hou iola ing physical signalling
cons ain s,
•explici ly mani es s in expe imen s whe e a u u e Xga e shi s he dis ibu ion o
c[0].
C.6 EW / NS S uc u al Modes
Two o hogonal s uc u al con igu a ions:
(1) |EW⟩— Eas –Wes Mode.
•S able, p esen - ime causal alignmen .
•Associa ed wi h o dina y space ime p opaga ion.
•Mac oscopic g a i y eme ges as he cumula i e e ec o |EW⟩couplings.
(2) |NS⟩— No h–Sou h Mode.
•Uns able, e ocausal alignmen .
•Responsible o empo al in e sion and PQ back-p opaga ion.
•Ac i a ed by H-ga e s uc u al swi ching.
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C.7 PQ Coupling Bias χ
A scala pa ame e quan i ying s uc u al asymme y:
χ=|α|2−|β|2,
whe e
|ψs uc ⟩=α|EW⟩+β|NS⟩.
In e p e a ion:
•χ= 0: symme ic — s anda d quan um mechanics eco e ed.
•χ > 0: EW-dominan — s able p esen - ime mode.
•χ < 0: NS-dominan — enhanced e ocausal esponse.
C.8 Dynamic Hubble Pa ame e H( )
A cosmological ex ension o PQ s uc u al bias:
H( )∝χ( )k/2.
Implica ions:
•The “Hubble cons an ” is no cons an bu a dynamical a iable.
•Va ia ions in χ( ) p o ide a uni ied explana ion o he Hubble ension (67 s 73
km/s/Mpc).
C.9 Rela ion o Quan um G a i y
In he NSC/PQ amewo k:
•g a i a ional a ac ion a ises om cumula i e |EW⟩s uc u al couplings,
•mass and ine ia e lec he deg ee o PQ alignmen a he han in insic ene gy–
momen um cu a u e,
•space ime cu a u e is a mac oscopic mani es a ion o mic oscopic PQ-s uc u e
in e ac ions.
This p o ides a uni ied concep ual b idge be ween quan um mechanics, g a i y, and cos-
mology.
54
Re e ences
1. Aspec , A., G angie , P., & Roge , G. (1982). Expe imen al es o Bell’s inequali ies
using ime- a ying analyze s. Physical Re iew Le e s.
2. B unne , N., Ca alcan i, D., Pi onio, S., Sca ani, V., & Wehne , S. (2014). Bell
nonlocali y. Re iews o Mode n Physics.
3. Engle , B. G. (1996). F inge isibili y and which-pa h in o ma ion: An inequali y.
Physical Re iew Le e s.
4. Kim, Y. H., Yu, R., Kulik, S. P., Shih, Y., & Scully, M. O. (2000). A delayed-choice
quan um e ase . Physical Re iew Le e s.
5. K aus, K. (1971). Gene al s a e changes in quan um heo y. Annals o Physics.
6. S inesp ing, W. F. (1955). Posi i e unc ions on C*-algeb as. P oceedings o he
Ame ican Ma hema ical Socie y.
7. Uola, R., Cos a, A. C. S., Nguyen, H. C., & G¨uhne, O. (2020). Quan um s ee ing.
Re iews o Mode n Physics.
8. Gisin, N. (1990). Weinbe g’s nonlinea quan um mechanics and supe luminal com-
munica ions. Physics Le e s A.
9. Spekkens, R. W. (2005). Con ex uali y o p epa a ions, ans o ma ions, and un-
sha p measu emen s. Physical Re iew A.
10. A nd , M., e al. (1999). Wa e–pa icle duali y o C60 molecules. Na u e.
11. Bohm, D. (1952). A sugges ed in e p e a ion o he quan um heo y in e ms o
“hidden” a iables. Physical Re iew.
12. No sen, T. (2017). Founda ions o Quan um Mechanics. Sp inge .
13. Wigne , E. P. (1961). Rema ks on he mind–body ques ion. In The Scien is
Specula es.
14. Kochen, S., & Specke , E. (1967). The p oblem o hidden a iables in quan um
mechanics. Jou nal o Ma hema ics and Mechanics.
15. Spekkens, R. W. (2005). Con ex uali y o p epa a ions, ans o ma ions, and un-
sha p measu emen s. Physical Re iew A.
16. Zu ek, W. H. (2003). Decohe ence, einselec ion, and he quan um o igins o he
classical. Re iews o Mode n Physics.
55
17. Schlosshaue , M. (2007). Decohe ence and he Quan um- o-Classical T ansi ion.
Sp inge .
18. Ghi a di, G. C., Rimini, A., & Webe , T. (1986). Uni ied dynamics o mic oscopic
and mac oscopic sys ems. Physical Re iew D.
19. Bassi, A., Lochan, K, Sa in, S., Singh, T. P., & Ulb ich , H. (2013). Models o
spon aneous wa e- unc ion collapse. Re iews o Mode n Physics.
20. Ha le, J. B., & Hawking, S. W. (1983). Wa e unc ion o he Uni e se. Physical
Re iew D.
21. Kie e , C. (2007). Quan um G a i y. Ox o d Uni e si y P ess.
22. Pen ose, R. (1996). On g a i a ional s a e educ ion. Gene al Rela i i y and G a -
i a ion.
23. Zeh, H. D. (1970). On he in e p e a ion o measu emen in quan um heo y. Foun-
da ions o Physics.
24. Planck Collabo a ion. (2020). Planck 2018 esul s. VI. Cosmological pa ame e s.
As onomy & As ophysics.
25. Riess, A. G., e al. (2022). A comp ehensi e measu emen o he Hubble cons an
and beyond. As ophysical Jou nal.
26. F iedmann, A. (1922). ¨
Ube die K ¨ummung des Raumes. Zei sch i ¨u Physik.
27. Pe lmu e , S., e al. (1999). Measu emen s o Ω and Λ om 42 high- edshi
supe no ae. As ophysical Jou nal.
28. Schlosshaue , M. (2007). Decohe ence and he Quan um- o-Classical T ansi ion.
Sp inge .
29. Qiski De elopmen Team. (2021). Qiski : An open-sou ce amewo k o quan um
compu ing. Na u e Re iews Physics.
30. Nielsen, M. A., & Chuang, I. L. (2000). Quan um Compu a ion and Quan um
In o ma ion. Camb idge Uni e si y P ess.
56
