The dependence structure and the amplitude distribution of stationary random sequences are linked, with specification of one placing constraints on the other. Time-reversible processes can be Gaussian or non-Gaussian, but all Gaussian processes must be time reversible. We examine the thermodynamics of measurement, showing that while ‘‘information” can be extracted from a system without altering system entropy, mat measurement techniques irreversibly alter thermodynamic state with a consequent entropy increase. Because of the second law of thermodynamics, such entropy changes cannot be undone and measurements reflecting thermodynamic state cannot be time reversible. We conclude that physical measurements are not time reversible, implying that onZy non-time-reversible processes model physically relevant signals. Consequently, Gaussian processes would seem to be imprecise representations of physical measurements.The dependence structure and the amplitude distribution of stationary random sequences are linked, with specification of one placing constraints on the other. Time-reversible processes can be Gaussian or non-Gaussian, but all Gaussian processes must be time reversible. We examine the thermodynamics of measurement, showing that while ‘‘information” can be extracted from a system without altering system entropy, mat measurement techniques irreversibly alter thermodynamic state with a consequent entropy increase. Because of the second law of thermodynamics, such entropy changes cannot be undone and measurements reflecting thermodynamic state cannot be time reversible. We conclude that physical measurements are not time reversible, implying that onZy non-time-reversible processes model physically relevant signals. Consequently, Gaussian processes would seem to be imprecise representations of physical measurements.

Jan 1, 19918 citations

Time-reversibility in quantum measurement

P. M. Harrington, Andrew N. Jordan, Kater W. Murch

Bulletin of the American Physical SocietyMar 15, 20170 citations

Boson sampling with Gaussian measurements

Levon Chakhmakhchyan, Nicolas J. Cerf

We develop an alternative boson sampling model operating on single-photon states followed by linear interferometry and Gaussian measurements. The hardness proof for simulating such continuous-variable measurements is established in two main steps, making use of the symmetry of quantum evolution under time reversal. Namely, we first construct a twofold version of scattershot boson sampling in which, as opposed to the original proposal, both legs of a collection of two-mode squeezed vacuum states undergo parallel linear-optical transformations. This twofold scattershot model yields, as a corollary, an instance of boson sampling from Gaussian states where photon counting is hard to simulate. Then, a time-reversed setup is used to exhibit a boson sampling model in which the simulation of Gaussian measurements---namely the outcome of eight-port homodyne detection---is proven to be computationally hard. These results illustrate how the symmetry of quantum evolution under time reversal may serve as a tool for analyzing the computational complexity of novel physically motivated computational problems.We develop an alternative boson sampling model operating on single-photon states followed by linear interferometry and Gaussian measurements. The hardness proof for simulating such continuous-variable measurements is established in two main steps, making use of the symmetry of quantum evolution under time reversal. Namely, we first construct a twofold version of scattershot boson sampling in which, as opposed to the original proposal, both legs of a collection of two-mode squeezed vacuum states undergo parallel linear-optical transformations. This twofold scattershot model yields, as a corollary, an instance of boson sampling from Gaussian states where photon counting is hard to simulate. Then, a time-reversed setup is used to exhibit a boson sampling model in which the simulation of Gaussian measurements---namely the outcome of eight-port homodyne detection---is proven to be computationally hard. These results illustrate how the symmetry of quantum evolution under time reversal may serve as a tool for analyzing the computational complexity of novel physically motivated computational problems.

arXiv:1705.05299Physical Review ASep 14, 201753 citations

Time reversal of quantum experiments

Wolfgang J. Mantke

International Journal of Theoretical PhysicsJul 1, 19960 citations

Efficient certification of time-reversal symmetry requires entanglement

Zhenhuan Liu, Zhenyu Du, Yifan Tang +3 more

Time-reversal symmetry is a fundamental principle of physics describing the invariance of physical laws under reversal of the direction of time. We formulate a Bell-inequality-like test of this antiunitary symmetry using only forward access and trusted quantum operations: entanglement converts temporal input--output relations into measurable spatial exchange symmetry. For $n$ -qubit unitary dynamics, we prove that reliably distinguishing the time-reversal-symmetric circular ensembles from Haar-random dynamics requires $Ω(\min\{2^{n/2},2^{n-e}\})$ queries for any classically adaptive protocol. Here, $e=\min\{e_{\mathrm s},e_{\mathrm m}\}$ with $e_{\mathrm s}$ and $e_{\mathrm m}$ representing the probe and measurement logarithmic entanglement negativities, respectively. Maximally entangled probes and SWAP measurements reduce this cost to a constant number of queries. Furthermore, we develop a time-reversal symmetry test for arbitrary fixed, compatible probes and measurements, relate its query complexity to their logarithmic negativities, and match the lower-bound scaling in the high-entanglement regime by optimizing the probe and measurement. Our results establish a quantitative connection between entanglement and time-reversal symmetry, bridging two central concepts in quantum information science and fundamental physics.Time-reversal symmetry is a fundamental principle of physics describing the invariance of physical laws under reversal of the direction of time. We formulate a Bell-inequality-like test of this antiunitary symmetry using only forward access and trusted quantum operations: entanglement converts temporal input--output relations into measurable spatial exchange symmetry. For $n$-qubit unitary dynamics, we prove that reliably distinguishing the time-reversal-symmetric circular ensembles from Haar-random dynamics requires $Ω(\min\{2^{n/2},2^{n-e}\})$ queries for any classically adaptive protocol. Here, $e=\min\{e_{\mathrm s},e_{\mathrm m}\}$ with $e_{\mathrm s}$ and $e_{\mathrm m}$ representing the probe and measurement logarithmic entanglement negativities, respectively. Maximally entangled probes and SWAP measurements reduce this cost to a constant number of queries. Furthermore, we develop a time-reversal symmetry test for arbitrary fixed, compatible probes and measurements, relate its query complexity to their logarithmic negativities, and match the lower-bound scaling in the high-entanglement regime by optimizing the probe and measurement. Our results establish a quantitative connection between entanglement and time-reversal symmetry, bridging two central concepts in quantum information science and fundamental physics.

quant-pharXiv:2610.01555Oct 2, 20260 citations

n

-qubit unitary dynamics, we prove that reliably distinguishing the time-reversal-symmetric circular ensembles from Haar-random dynamics requires

Ω(\min\{2^{n/2},2^{n-e}\})

queries for any classically adaptive protocol. Here,

e=\min\{e_{\mathrm s},e_{\mathrm m}\}

with

e_{\mathrm s}

and

e_{\mathrm m}

representing the probe and measurement logarithmic entanglement negativities, respectively. Maximally entangled probes and SWAP measurements reduce this cost to a constant number of queries. Furthermore, we develop a time-reversal symmetry test for arbitrary fixed, compatible probes and measurements, relate its query complexity to their logarithmic negativities, and match the lower-bound scaling in the high-entanglement regime by optimizing the probe and measurement. Our results establish a quantitative connection between entanglement and time-reversal symmetry, bridging two central concepts in quantum information science and fundamental physics.