![]() The probability of wavefunction collapse compared to the probability of wavefunction uncollapse can be used to determine an arrow of time for the wavefunction collapse process 7. One of the interesting possibilities that a weak quantum measurement allows is that of undoing a given quantum measurement with some probability, uncollapsing the wavefunction 11, 28. Recent technological advances that allow new classes of measurements on quantum systems, such as quantum weak measurements, enable us to explore this and related questions 25, 26, 27. Irreversibility in this context seems then to be a question of paramount importance to fundamental quantum theory: is it possible to discuss the emergence of irreversibility in quantum measurements from a time-symmetric measurement dynamics (and how can we quantify this)? Measurements made on quantum systems, however, are usually described in terms of irreversible wavefunction collapse. ![]() Quantum systems have inherently time-reversal symmetric dynamics. Questions of irreversibility find new relevance today in the context of quantum measurement 11, 17, 18, 19, 20, 21, 22, 23, 24. Such an association arises quite naturally in the context of thermodynamics of small systems 12, 13, where a system is considered small in the thermodynamic sense if the energy exchanges are on the order of a few k BT such that energy fluctuations can be measured 14 here, the statistical weight for each realization of the experiment corresponds to the entropy produced, and relates to the emergence of laws of thermodynamics for the small system in the form of fluctuation theorems 15, 16. For each realization of the experiment, represented by a time-series data, the physicist associates a statistical weight (using Bayesian inference) that quantifies the estimate for how likely it is that the given realization is obtained forward as opposed to backward 7, 11. Motivated by this, the inference of a statistical arrow of time can be posed as a game where a physicist is given access to an ensemble of realizations of a particular experiment. The resolution to the paradoxical situation emerges from the statistics of these experimental realizations: realizations with a backward arrow of time in which the system returns to its initial conditions are exponentially less likely to occur compared to their forward counterparts. Nevertheless, the time symmetry of dynamical equations also implies that if we repeat an experiment sufficiently many times, we might be able to record statistically rare events where the state of the system reverts to its initial conditions. The arrow of time, as a mathematical construct, deals with the emergence of irreversibility from time-reversal symmetric dynamical laws 1, 2, 3, 4, 5, 6, 7, 8, 9, 10: the dynamical equations of physics are time-reversal symmetric, while ensembles of physical systems pick out configurations that prefer an increase in entropy, or a preferred arrow of time. We further demonstrate absolute irreversibility for measurements performed on a quantum many-body entangled wavefunction-a unique opportunity afforded by our platform-with implications for studying quantum many-body dynamics and quantum thermodynamics. Our experiments include statistically rare events where the arrow of time is inferred backward nevertheless we provide evidence for absolute irreversibility and a strictly positive average arrow of time for the measurement process, captured by a fluctuation theorem. We experimentally demonstrate a striking parallel between the statistical irreversibility of wavefunction collapse and the arrow of time problem in the weak measurement of the quantum spin of an atomic cloud. Ultracold atoms are uniquely suited to this task. Experimentally probing such questions in quantum theory requires systems with near-perfect isolation from the environment and long coherence times. The origin of macroscopic irreversibility from microscopically time-reversible dynamical laws-often called the arrow-of-time problem-is of fundamental interest in both science and philosophy.
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