The quantum measurement problem separates into operational questions: which observables are stable records, how outcome probabilities are represented, how conditional post-event states are updated, and how a detector event time is assigned. We give a compact architecture-conditional framework. In a finite-dimensional detector model, the detector-side relative-entropy flux is differentiated with the exact Fréchet derivative of the matrix logarithm. A noise-regularised timing distribution is defined and, under an explicitly assumed isolated non-degenerate maximum of the calibrated flux, Laplace asymptotics proves concentration at that maximum. Under stated fixed-point and detailed-balance hypotheses, the centre of the fixed-point algebra gives a canonical commutative record algebra. Outcome probabilities admit a POVM representation, and conditional updates use a completely positive (CP) instrument in its standard sense: CP maps whose traces give probabilities and whose normalised outputs give post-event states, summing to a trace-preserving map. Separately, an assumed modular-invariant inclusion of von Neumann algebras admits a state-preserving conditional expectation and CP retraction. A conditional quantum-error-correction lemma bounds accumulated record failure. These results do not derive unique outcomes from unitarity, construct a black-hole algebra inclusion, or resolve the black-hole information problem; they give a conditional framework, a worked illustration, and testable timing and record-stability criteria.
Physics describes evolution, causal structure, and measurement outcomes, but lacks an accepted physical account of why one outcome-conditioned quantum situation is actual as the present. This article develops a conditional account within the reconstruction program, which places a premetric relational layer prior to spacetime dynamics. Conventional evolution specifies how states are related once a state space, time parameter, and dynamical law are supplied; continued admissible reconstruction addresses the prior realization question of which identities, laws, and successor records can remain physically well defined. The Indefinite Reconstruction Stability Principle requires readable structures and laws to survive admissible continuation and to ignore unobservable distinctions. A present is proposed to be the outcome-conditioned quantum read-out of an IRSP-stable, history-bearing reconstruction boundary. Because the underlying relational record need not factorize, its read-out is generally entangled. Admissible successors are represented by a quantum instrument; one stable record sector and its conditioned state constitute the next present without an external observer. A worked qubit measurement and a Bell-pair example connect this architecture to standard laboratory quantum science. Given an operational event-identity bridge, positivity, normalization, exclusive additivity, and a Hilbert-space read-out, Gleason representation fixes the Born form conditionally. Linear history composition implies no genuine third-order successor interference. Proper ancestry inheritance supplies conditional acyclicity, stable small-step channels recover standard effective dynamics, and spacelike confluence replaces a preferred global simultaneity surface. The result is a reconstructional architecture of present actuality with explicit premises and failure conditions, but no fitted collapse rate or microscopic actualization threshold.
We develop a record-based account of internal time in quantum mechanics. Persistent records first define an ordinal chronology through inclusion of their accumulated Boolean algebras. On a specified record filtration, we prove that, under three minimal consistency requirements, namely dependence only on conditional Born weight, invariance under sequential refinement of the same recorded fact, and continuity, the actualization of each outcome contributes an internal time proportional to its \textit{surprisal}, defined as the negative logarithm of that probability. A certain outcome therefore contributes no duration, whereas less probable outcomes contribute larger increments. The mean and variance of the accumulated clock are governed by the Shannon entropy and varentropy of the record process, its moment-generating function is related to the R'enyi entropy spectrum, and its pathwise fluctuations admit a Doob decomposition into a predictable entropic compensator and a martingale. Two further results provide independent consistency checks. Within the stated class of finite-dimensional bipartite states, universal additivity of local clock readings across all admissible local record contexts is equivalent to the absence of entanglement. In the quantum Zeno regime, the number of monitoring rounds may diverge while the expected accumulated surprisal tends to zero. The construction therefore supplies a canonical internal-time functional for a specified quantum record process without presupposing an external clock. It does not by itself identify which physical record processes constitute material clocks; determining their production rates and dynamical realization remains a separate problem.
We construct an information theory framework in which the fundamental objects are binary sequences of length $n$, equipped with the bitwise XOR operation. The only physical observables are counts of XOR-generated symbol classes, while the exact locations of symbols are inaccessible. Averaging over those locations ultimately yields the Minkowski interval as an invariant object that maximizes (information) entropy. Correlations between two binary sequences are base-4 sequences that we label as ``events'', and events are connected with maps. The entire kinematic structure of Special Relativity is recovered under minimal assumptions, i.e. counts that represent space and time increments carry equal informational weight. The central claim is that Lorentz symmetry is the typical large-n behaviour of XOR counting. At finite $n$ the framework yields a discrete rapidity spectrum, a bound $\gamma_{\max} = O(\sqrt{n})$, and interval fluctuations of relative size $O(n^{-1/2})$, with standard special relativity recovered as $n \to \infty$. However, the light cone and one null coordinate are exact for every microscopic configuration, so the symmetry group is undeformed and dispersion relations are unmodified. Thus, the theory, though discrete, implies no Lorentz violation of the standard phenomenological kind. Ultra-high-energy cosmic rays already require $n \gtrsim 10^{23}$; interferometry excludes the variant in which $n$ scales linearly with system size, leaving a holographic area law. The most striking prediction of the framework concerns systems at the maximum of their information capacity, where $n$ is necessarily finite: black holes and de Sitter space. There the corrections are of order one within a Planck proper length of the horizon, regardless of the horizon's size, and the spacetime description fails altogether at the endpoint of black-hole evaporation, where $n$ itself is of order unity.
Detecting when the dependence between two components of a multivariate time series changes, while the marginals drift freely, requires a dependence-specific statistic. We take the inferential object to be a density operator -- the trace-normalised second moment of unit-norm random Fourier features of ranks -- rather than a probability distribution. Partial traces recover the marginal operators exactly, so von Neumann entropies yield a quantum mutual information (QMI) statistic computed from prefix sums of small matrices, without density estimation, matrix inversion, or a tuned parameter. We develop the inference it needs: a segment-separable cost that drives penalised optimal partitioning, its split gain a Holevo information; finite-sample exact calibration by joint pair permutation, a block-permutation form for serially dependent series, and an exact, provably consistent exchangeability diagnostic that selects between them. We also prove a weighted chi-square boundary law, at the segment length and not its square root, for the rank-based statistic exactly as computed. In 500 replicates QMI detects nonlinear, correlation-free dependence changes with more power than the Hilbert-Schmidt independence criterion, distance correlation, Spearman, and empirical-copula statistics on the same ranks, by at least 15 percentage points wherever any statistic detects the change. Its false-alarm rate stays near nominal under marginal drift, where the empirical-copula statistic reaches 0.87. On eight years of hourly Korean weather observations, a two-stage segment-and-certify procedure finds dependence-change candidates above chance (five of 27 at p $\le$ 0.05 against 1.4 expected); stage two certifies one as a pure coupling change and reclassifies eight as marginal-driven.
We study quantum processes in which information extracted from a forward simulation is returned as input to an earlier internal time of the simulated dynamics: externally the protocol is an ordinary causally ordered circuit, but internally it is future-referential. Contracting a process tensor with a leakage instrument and a controller induces a completely positive trace-preserving map on a message register, and we classify its fixed points by five operational properties: stability, informativeness, feedability, coherence, and preservation of quantum correlations. Four results separate notions that informal discussions of"information from the future"often conflate. A two-parameter unitary-dilation family yields a closed-form, globally attractive, coherent fixed point (Proposition 1), yet is entanglement breaking whenever future records are perfectly distinguishable (Lemma 1). Releasing that orthogonality, a four-parameter partial-swap family admits a nonempty open non-entanglement-breaking region (Proposition 2), with an explicit Choi partial-transpose neighborhood of half-width $0.0163\pi$ (Proposition 3). Combining outward-rounded interval enclosures with perturbation bounds tracking the channel and its stationary-state drift, we certify an explicit parameter square of half-width $0.0013\pi$ on which the feedback channel is simultaneously strictly contractive (margin $\ge 0.237$), coherent ($\ge 0.416$), informative about the designated future variable ($\ge 0.172$ bits), and non-entanglement-breaking (NPT margin $\ge 0.188$) (Proposition 4). Direct evaluation shows all four properties persisting over a region an order of magnitude larger, so the certified square is a proof of principle rather than a phase boundary. All enclosures and margins are confirmed by a machine-verified ball-arithmetic certificate, and the complete code and certificate accompany the paper.
Metastability in open quantum systems is usually inferred from spectral separation in the Liouvillian, which governs unconditional, ensemble-averaged dynamics. We show that this diagnosis is incomplete at the level of individual quantum trajectories: conditioned realizations of the same unconditional dynamics can bypass, transiently access, or operationally preserve a metastable memory, depending on the monitored channel and the observed record. We demonstrate these mechanisms in a driven-dissipative nonlinear oscillator realizing a quantum associative memory, by comparing spectra, target fidelities, and phase-space distributions. The non-Hermitian dynamics obtained by post-selecting on the absence of detected events supports metastable retrieval, but with a distinct long-time fate: normalization selects the least-decaying mode of the non-Hermitian spectrum rather than the addressed memory branch. In contrast, stochastic jump trajectories can preserve retrieval over extended times when the post-measurement update remains compatible with the coherent memory structure. Thus trajectory-level metastability is not determined by the averaged generator alone; it requires compatibility between the monitored channel, the measurement record, and the metastable manifold.
Manali Malakar, Roberta Zambrini, G. Giorgi· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
