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Deterministic photon exchange prepared from the past

Jarek Duda

Published Nov 1, 2026• 0 citations
Publisher

Abstract

Two-ended control of photons — shaped emission and a time-reversed, matched receiver, both prepared in advance — is a mature technology: 94–99.4% coupling in single elements, 98.1% absorption of an arriving photon between remote nodes, links up to 30 m, and coherent memories that receive even unknown quantum states. Like the in and out states of an S-matrix element, both ends of the apparatus are prepared; this paper collects these realizations into one efficiency budget with exact shape and timing tolerances. It then asks what two-way quantum computing (2WQC) would need for the end of a computation to act as a condition, as preparation acts at its beginning. Everything we prepare — source, processor and a universal, problem-independent ready receiver to which a verifier routes a flag photon — fixes only the initial boundary of the Feynman ensemble. Standard quantum mechanics sums over the far end (an indifferent final boundary, giving the Born rule), so an acceptance condition can only be tested, with its ordinary probability. The missing ingredient is an enforced far end: a final boundary supplied by nature that weights ready endings. If weak but renewable, such a weight would compound exponentially over linearly many endings (about n·ln2/Δw), under conditions the paper states. We have not identified a published all-attempt bound for this weight. The paper specifies a direct test on existing hardware: two balanced endings, one active and one passive, selected after an earlier record is digitized and sealed. Standard quantum mechanics predicts exactly zero contrast, including every ordinary feedback path; 1e8 eligible trials per setting give a counting sensitivity Δw ≈ 3e-4 (planning figures: about an hour of link operation; a projected 1e-4 per delay on a quantum processor, with an analysis kit in the companion range-control paper). The test needs no absolute calibration: setting-independent preparation and readout errors cancel in the randomized difference. Either outcome constrains the declared ending law; a replicated signal would motivate tests of renewal, coherence and witness preservation. A one-page proposal for experimental groups is included.

DOI
10.5281/zenodo.23853267

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Two-ended control of photons — shaped emission and a time-reversed, matched receiver, both prepared in advance — is a mature technology: 94–99.4% coupling in single elements, 98.1% absorption of an arriving photon between remote nodes, links up to 30 m, and coherent memories that receive even unknown quantum states. Like the in and out states of an S-matrix element, both ends of the apparatus are prepared; this paper collects these realizations into one efficiency budget with exact shape and timing tolerances. It then asks what two-way quantum computing (2WQC) would need for the end of a computation to act as a condition, as preparation acts at its beginning. Everything we prepare — source, processor and a universal, problem-independent ready receiver to which a verifier routes a flag photon — fixes only the initial boundary of the Feynman ensemble. Standard quantum mechanics sums over the far end (an indifferent final boundary, giving the Born rule), so an acceptance condition can only be tested, with its ordinary probability. The missing ingredient is an enforced far end: a final boundary supplied by nature that weights ready endings. If weak but renewable, such a weight would compound exponentially over linearly many endings (about n·ln2/Δw), under conditions the paper states. We have not identified a published all-attempt bound for this weight. The paper specifies a direct test on existing hardware: two balanced endings, one active and one passive, selected after an earlier record is digitized and sealed. Standard quantum mechanics predicts exactly zero contrast, including every ordinary feedback path; 1e8 eligible trials per setting give a counting sensitivity Δw ≈ 3e-4 (planning figures: about an hour of link operation; a projected 1e-4 per delay on a quantum processor, with an analysis kit in the companion range-control paper). The test needs no absolute calibration: setting-independent preparation and readout errors cancel in the randomized difference. Either outcome constrains the declared ending law; a replicated signal would motivate tests of renewal, coherence and witness preservation. A one-page proposal for experimental groups is included.
The laws of physics are CPT-symmetric, yet laboratory quantum mechanics prepares the past and only samples the future. This working paper distinguishes five levels of taking the symmetry seriously — symmetric laws with the open future left implicit, a two-boundary description, symmetric processes, a nontrivial final boundary, and laboratory access to it — places published views and experiments on them, and states what each predicts for a final-boundary test, in which an engineered terminal acts on a flag and an entangled partner is read on every trial. Exact results: an open future propagates backward through any physical channel; a terminal can only transfer, never manufacture, final-side contrast, giving lambda = tanh(hbar omega / 2 k T_f) in a swap model, the mirror of a reset; a clamp of budget A needs an energy of at least k T_f ln A in some branch; under free local control any every-trial final condition signals, with visibility equal to the clamp strength. Under stated transfer models a null reads as a lower bound on a swap-equivalent final temperature (Partridge: above 3.5e7 K for escaping microwaves; planned qubit tests: about 27 K and 360 K). The paper audits transport to the future, specifies what any physical source of a final condition must supply, and finds that no named candidate meets the specification. CPT motivates the reversed-resource question; channel duality bounds its possible transfer; laboratory access remains an additional physical hypothesis, decided only by experiment. No new experimental result is reported. Drafted with AI assistance and revised after AI-assisted reviews; responsibility rests with the author.
A durable quantum record, the location of its coherence, and a uniquely actual outcome are different physical questions. We study their separation in a supplied finite-dimensional quantum theory. An explicit, time-independent apparatus couples a system–detector encoding to a controller, a distinct archive, and a finite returning source. A conditional energy penalty suppresses release of the original record without deleting its return coupling. An invariant reduction and a one-sided spectral-gap estimate yield a certified interval with archive occupation above 0.98438, controller-latched occupation above 0.99161, and filled-but-unlatched weight below 2.402 × 10^-7 in one stated design. The same record statistics admit different source-label overlaps and hence different coherence on a specified retained boundary. A conserved product of complementary exchanges accesses that coherence when the finite source is included. Given a calibrated multiregister reader, its finite-duration response separates the coherent apparatus from an independently added archive-gated reduction law, with the added process left active during readout. A conservative example retains a response gap above 0.01717 after separately stipulated one-percent error allowances. The contribution is the finite construction and its quantitative retention, access, and readout interfaces. Quantum carriers, Hamiltonian couplings, trace readout, source preparation, and the reader are supplied; local reader synthesis, empirical calibration, absolute rate selection, and unique-event actualization are not established. Paper code: CFQR-P1 (Complementarity-First Quantum Records — Paper 1). The associated bundle contains the technical supplement, editable LaTeX, numerical checking programs and rational certificates, and selected Lean sources with returned build and axiom-audit evidence. The 39 supporting declarations are partially formalized; eleven recorded type excerpts contain printing elisions. This is not end-to-end formalization, external human peer review, an experimental detection of fundamental collapse, or a derivation of unique-event actualization. Author-owned manuscripts, documentation and mathematical data are CC BY 4.0; author-owned software is MIT, subject to the bundle’s licence map and third-party notices.
Standard one-way quantum computers (1WQC) combine time symmetric unitary evolution, with asymmetric treatment of boundaries: state preparation allows to enforce a chosen initial state, however, for the final state measurement chooses a random value instead. As e.g. pull/push, negative/positive pressure, stimulated emission/absorption causing deexcitation/excitation are CPT analogs, and one can be used for state preparation, the second should allow for its CPT analog, referred here as CPT(state preparation) - allowing for additional chosen enforcement of the final state, its more active treatment than measurement. It should act similarly to postselection, but through applied physical constraints (instead of running multiple times). Like pumped to ∣1⟩|1\rangle∣1⟩ prepared state vs its "unpumped" ⟨0∣\langle 0|⟨0∣ CPT analog, hopefully allowing to construct two-way quantum computers (2WQC) e.g. hydrodynamical, and hopefully photonic: seen as ⟨Φfinal∣Uquantum gates∣Φinitial⟩\langle Φ_{\textrm{final}}|U_{\textrm{quantum gates}}|Φ_{\textrm{initial}}\rangle⟨Φfinal​∣Uquantum gates​∣Φinitial​⟩ like for scattering matrix, with influenced both initial and final states. If possible, for example for an instance of 3-SAT problem on nnn variables, we could prepare ensemble of 2n2^n2n inputs with Hadamard gates, calculate 3-SAT alternatives for them, and use CPT(state preparation) to enforce outcomes of all these alternatives to '1'. This way hopefully restricting this ensemble to satisfying given 3-SAT problem: ∑a:SAT(a)∣a⟩\sum_{a:\textrm{SAT}(a)} |a\rangle∑a:SAT(a)​∣a⟩, in theory allowing to attack NP problems by simultaneously pushing and pulling information through the system for better control.
A quantum record can have locally accessible populations while its distinguishing phase remains correlated with a distant source. We study this access boundary in a specified finite recording apparatus with a returning, vacuum/one-excitation source. Source-position weights give finite-time cutoff bounds without removing any physical hopping or return coupling. For an initially far-tagged record and its incoherent mixture, every reader in a declared position-preserving local-control class obeys a phase-visibility envelope and a necessary access-time inequality. A separate finite local probe shows why that state-discrimination limit is not an unrestricted limit on distinguishing two dynamical laws: fresh local coherence can reveal a stipulated added dephaser without recovering the old record phase. We construct a bounded, degree-three reader accessing only source positions 1–32. With the initial tag fixed at position 65, exact finite-source arrival certificates and an analytical tail comparison yield recovery uniformly over every finite total source length at least 65. Accessible control faults are charged against the arrived signed-phase norm, while source-moving drift is charged against the full norm. At the fixed deadline 25.02/J, the matched phase-dependent difference between coherent and archive-gated dynamics exceeds 0.005, including the stated simultaneous control faults and four additional absolute response allowances of 0.008 each. Complementary results cover a vacuum-ready source and a stronger endpoint-prepared finite example. The conclusions are conditional on the supplied model, preparations, common realized controls and calibration bounds. They are not a switchable-fundamental-law experiment, a nuisance-independent classifier, an optimal-speed theorem or an end-to-end formal verification. The supporting Lean companion contains 59 declarations in eight modules with accepted returned Mac compilation, type and axiom evidence; physical analytical interfaces remain explicit hypotheses or outside that subset. The deposit files include the main manuscript, technical supplement and full research/reproduction package.
Phenomenological--Velocity Relational Event Completion (\(\PV\text{-}\REC\)) is formulated here as a time-symmetric source--absorber boundary-event proposal. The preparation-side source record λ0=(v,ϵ,J,Ξ) \lambda_0=(v,\epsilon,\mathcal J,\Xi) λ0​=(v,ϵ,J,Ξ) is assumed to be statistically independent of the later detector settings. It is not, however, identified with the complete Bell screening variable. The completed four-dimensional event includes the later local absorber boundary conditions, Λabcomp=(λ0,BA(a),BB(b)). \Lambda_{ab}^{\mathrm{comp}} = (\lambda_0,\mathcal B_A(a),\mathcal B_B(b)). Λabcomp​=(λ0​,BA​(a),BB​(b)). Thus the proposal retains preparation independence but rejects emission-time scalar screening-off. In the balanced singlet sector, the source--absorber compatibility of the candidate joint event (x,y)(x,y)(x,y) is the usual singlet projector weight mxy(a,b)=14(1−xycos⁡(a−b)). m_{xy}(a,b)=\frac14\left(1-xy\cos(a-b)\right). mxy​(a,b)=41​(1−xycos(a−b)). PV-REC treats this as a linear boundary compatibility rather than directly as the final event probability. With Ixy=−log⁡mxy,κ(v)=1−v2c2, I_{xy}=-\log m_{xy}, \qquad \kappa(v)=\sqrt{1-\frac{v^2}{c^2}}, Ixy​=−logmxy​,κ(v)=1−c2v2​​, the PV rule rescales the event-action barrier by Ixy↦κ(v)Ixy, I_{xy}\mapsto\kappa(v)I_{xy}, Ixy​↦κ(v)Ixy​, giving raw susceptibility mxyκ(v)m_{xy}^{\kappa(v)}mxyκ(v)​. To prevent setting-dependent total count-rate or latency signals, the physical hazards are normalized to constant total flux, \[ \widehat\Gamma_{xy}^{\PV} = \Gamma_{\mathrm{trial}} \frac{m_{xy}^{\kappa(v)}}{\sum_{x',y'}m_{x'y'}^{\kappa(v)}}. \] With independent exponential race seeds this gives \[ P_{\PV}(x,y\mid a,b,v) = \frac{m_{xy}(a,b)^{\kappa(v)}} {\sum_{x',y'}m_{x'y'}(a,b)^{\kappa(v)}}. \] Consequently, \[ E_{\PV}(a,b\mid v) = -\tanh\!\left[ \kappa(v)\artanh(\cos(a-b)) \right]. \] At v=0v=0v=0, the ordinary singlet law E=−cos⁡(a−b)E=-\cos(a-b)E=−cos(a−b) is recovered; fixed sectors with v≠0v\neq0v=0 predict a distinct non-Born angular deformation. The construction is not Bell-local in the factorization/local-causality sense. Same-source replay generally fails: (X,Y)=Kab(λ0) (X,Y)=K_{ab}(\lambda_0) (X,Y)=Kab​(λ0​) does not factor into separated scalar response functions X=XA(a,λ0),Y=YB(b,λ0). X=X_A(a,\lambda_0), \qquad Y=Y_B(b,\lambda_0). X=XA​(a,λ0​),Y=YB​(b,λ0​). Thus the model is \emph{Bell-nonseparable}. In the standard Bell vocabulary this is Bell-nonlocality in the technical factorization sense. In the present ontology it is more accurately described as global boundary-contextuality: the completed event depends on the full source--absorber boundary context, not on a directed controllable signal from one wing to the other. Operational no-signalling is retained. Beyond the balanced singlet sector, no-signalling is imposed by marginal-preserving boundary flux balancing, implemented for finite bipartite outcome spaces by Sinkhorn scaling and, more generally, by entropic projection onto the no-signalling constraint set. The proposal is phenomenological. It is not claimed here that standard quantum field theory, the Born rule, or the singlet compatibility kernel has been derived from the direct-action embedding. The value of the construction is instead that it supplies a precise time-symmetric, Bell-nonseparable, operationally no-signalling event law with explicit empirical consequences. A visibility-independent diagnostic is provided by the shape function \[ f_\kappa(z)=\tanh(\kappa\artanh z), \] for which, in a fixed-vvv sector, fκ′′′(0)fκ′(0)=2(1−κ2)=2v2/c2. \frac{f_\kappa'''(0)}{f_\kappa'(0)} = 2(1-\kappa^2) = 2v^2/c^2. fκ′​(0)fκ′′′​(0)​=2(1−κ2)=2v2/c2. Dense angular correlation data can therefore either bound vvv close to zero or reveal a deviation from the ordinary singlet shape.