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Probing the Limits of Time-Symmetry and the Projection Postulate in Sequential Quantum Measurements

Piechocinska, Barbara

Published Nov 14, 2025• 0 citations
Publisher

Abstract

This paper proposes two precise, platform-independent experiments that aim to test the foundational assumptions of quantum mechanics: namely, whether time-reversal symmetry holds exactly at the quantum level, and whether quantum measurements truly erase all information about unrealized possibilities. While inspired by larger theoretical ideas of generative wholeness, the experiments are intentionally designed in a model-agnostic way and can be implemented with current technologies such as trapped ions, superconducting qubits, or advanced photonic systems. The first experiment compares the statistical outcomes of a quantum system measured in one order with those when the same measurements are applied in reverse order. Under standard theory, no irreducible asymmetry should remain after all known disturbances are controlled. Detecting a residual asymmetry would signal a fundamental microscopic arrow of time. The second experiment examines whether a quantum system retains an intrinsic “memory” of measurements that were performed but whose results were ignored or not recorded. By comparing two sequences, one where an intermediate measurement is omitted entirely and another where it is performed but discarded, the design tests for subtle deviations from the standard projection rule. A confirmed deviation would indicate non-Markovian, intrinsic memory effects in quantum measurement itself. Both proposals are framed as “null tests”: if the orthodox theory is complete, the results should vanish within error bars. Any non-zero finding would open a doorway to new physics, probing the nature of time, measurement, and possibility in the quantum domain. Keywords: time asymmetry, projection postulate, quantum measurement, sequential measurements, intrinsic memory, non-Markovianity, trapped ions, superconducting qubits, photonics, foundational tests of quantum mechanics.

DOI
10.5281/zenodo.17607993

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This paper proposes two precise, platform-independent experiments that aim to test the foundational assumptions of quantum mechanics: namely, whether time-reversal symmetry holds exactly at the quantum level, and whether quantum measurements truly erase all information about unrealized possibilities. While inspired by larger theoretical ideas of generative wholeness, the experiments are intentionally designed in a model-agnostic way and can be implemented with current technologies such as trapped ions, superconducting qubits, or advanced photonic systems. The first experiment compares the statistical outcomes of a quantum system measured in one order with those when the same measurements are applied in reverse order. Under standard theory, no irreducible asymmetry should remain after all known disturbances are controlled. Detecting a residual asymmetry would signal a fundamental microscopic arrow of time. The second experiment examines whether a quantum system retains an intrinsic “memory” of measurements that were performed but whose results were ignored or not recorded. By comparing two sequences, one where an intermediate measurement is omitted entirely and another where it is performed but discarded, the design tests for subtle deviations from the standard projection rule. A confirmed deviation would indicate non-Markovian, intrinsic memory effects in quantum measurement itself. Both proposals are framed as “null tests”: if the orthodox theory is complete, the results should vanish within error bars. Any non-zero finding would open a doorway to new physics, probing the nature of time, measurement, and possibility in the quantum domain. Keywords: time asymmetry, projection postulate, quantum measurement, sequential measurements, intrinsic memory, non-Markovianity, trapped ions, superconducting qubits, photonics, foundational tests of quantum mechanics.
The duration, strength, and structure of memory effects are crucial properties of physical evolution. Because of the invasive nature of quantum measurement, such properties must be defined with respect to the probing instruments employed. Here, using a photonic platform, we experimentally demonstrate this necessity via two paradigmatic processes: future-history correlations in the first process can be erased by an intermediate quantum measurement; for the second process, a noisy classical measurement blocks the effect of history. We then apply memory truncation techniques to recover an efficient description that approximates expectation values for multitime observables. Our proof-of-principle analysis paves the way for experiments concerning more general non-Markovian quantum processes and highlights where standard open systems techniques break down.
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The standard measurement postulate of quantum mechanics stipulates an instantaneous, non-local update of the global wavefunction upon measurement of an entangled subsystem. This postulate has been a persistent source of foundational tension, both with the locality structure of relativistic physics and with the dynamical character of the decoherence program. We separate the measurement postulate into three logically independent claims: definite outcome realization, Born-rule probability assignment, and instantaneous projection for the global wavefunction. We argue that the third claim can be eliminated at the axiomatic level and propose a modified measurement postulate, Postulate M, that replaces it. Under Postulate M, a single pointer outcome is realized locally when environmental decoherence has einselected a pointer basis at the measurement site; the corresponding selection acts on the global wavefunction as a conditional restriction to a branch rather than as a physical operation on spacelike-separated regions. We show that Postulate M recovers the standard measurement postulate as a limiting idealization for vanishing decoherence time, derives Lüders’ rule for sequential measurements, and yields no-signaling as an automatic structural consequence — not only at the level of measurement statistics but at the level of physical states themselves. Two explicit illustrations in the EPR scenario — with one and with both particles coupled to local spin environments — demonstrate the framework concretely and exhibit its frame-independent, manifestly local character. The framework is built on standard decoherence theory, compatible with multiple candidate mechanisms for single-outcome realization including gravitationally-induced collapse proposals, and naturally situated within a ψ-ontic reading of the quantum state. It represents, we argue, a reformulation of quantum mechanics as a local, state-realist theory — preserving Einstein’s aspiration for an objective physical world in the only form consistent with the empirical content of quantum mechanics, namely realism about the wavefunction rather than about pre-measurement observable values.
This study proposes a time-symmetric framework for quantum measurement that restores microscopic reversibility at the level of the dynamical description while remaining compatible with causality and thermodynamic consistency. Instead of invoking a stochastic wavefunction collapse, the measurement process is modeled as a bidirectional informational update between a forward-evolving state and a backward-propagating effect, governed by a completely positive generator and its adjoint. Within this operator-based formalism, pre- and post-selected statistics are treated on an equal footing, yielding a unified description of both. The proposed scheme rigorously preserves complete positivity, normalization, and the no-signalling principle, and it is shown to satisfy Spohn's inequality for the associated quantum Markov semigroup, thereby ensuring non-negative entropy production within this setting. The framework admits a direct experimental interpretation across a range of scenarios, including weak measurements, EPR-Bell tests, homodyne detection, and photon counting. Furthermore, in the classical limit, the bidirectional update is demonstrated to reduce to the well-established Kalman filter and Rauch-Tung-Striebel (RTS) smoother used in classical estimation theory. These results support the view that the apparent temporal asymmetry of quantum measurement arises not from fundamental dynamical irreversibility, but from informational conditioning, specifically, the one-sided way in which measurement outcomes are incorporated into our description. In this sense, the arrow of time in measurement theory may be understood as an arrow of information.
Unlike regular time evolution governed by the Schr\"odinger equation, standard quantum measurement appears to violate time-reversal symmetry. Measurement creates random disturbances (e.g., collapse) that prevent back-tracing the quantum state of the system. The effect of these disturbances is explicit in the results of subsequent measurements. In this way, the joint result of sequences of measurements depends on the order in time in which those measurements are performed. One might expect that if the disturbance could be eliminated this time-ordering dependence would vanish. Following a recent theoretical proposal [Bednorz, Franke, and Belzig, New J. Phys. 15, 023043 (2013)], we experimentally investigate this dependence for a kind of measurement that creates an arbitrarily small disturbance: weak measurement. We perform various sequences of a set of polarization weak measurements on photons. We experimentally demonstrate that, although the weak measurements are minimally disturbing, their time ordering affects the outcome of the measurement sequence for quantum systems.
Quantum mechanics is widely recognised as being incomplete. It is not consistent with the second law of thermodynamics and does not provide a scientifically credible physical account of the measurement process, the means by which coherence is broken and classically observable states are recorded. This has led to many ad hoc assumptions being used to account for various properties of quantum systems, among which is the coherence time of quantum devices that determines their ability to perform computations. Here, we show that all these properties can be accommodated naturally and consistently in the context of mixing quantum systems which exhibit continuous spectra, as arises in the thermodynamic limit in quantum statistical mechanics and quantum gravity. In particular, for isolated systems we show that the time-reversal symmetry associated with unitary time evolution of the quantum state gives rise to time-symmetry breaking and a semi-group evolution which attains thermodynamic equilibrium at long times. Moreover, the emergence of this non-unitary time-asymmetry leads to microcanonical equilibrium states in which all quantum coherence is lost and is accompanied by the transformation of pure states into mixtures, leading in turn to an increase in entropy. Inclusion of a macroscopic measurement apparatus shows how the outcome of a measurement corresponds to the von Neumann projection postulate, arising with probabilities in conformance with the Born rule. The mathematical structure of the theory which applies to quantum systems with continuous spectra is closely analogous to the classical ergodic theory of dynamical systems and the conditions under which they attain equilibrium states.