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. Experimentally probing such questions in quantum theory requires systems with near-perfect isolation from the environment and long coherence times. Ultracold atoms are uniquely suited to this task. 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. 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 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.
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. Experimentally probing such questions in quantum theory requires systems with near-perfect isolation from the environment and long coherence times. Ultracold atoms are uniquely suited to this task. 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. 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 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.
Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. Using a nuclear magnetic resonance setup, we measure the nonequilibrium entropy produced in an isolated spin-1/2 system following fast quenches of an external magnetic field. We experimentally demonstrate that it is equal to the entropic distance, expressed by the Kullback-Leibler divergence, between a microscopic process and its time reversal. Our result addresses the concept of irreversibility from a microscopic quantum standpoint.
Fluctuation theorems are relations constraining the out-of-equilibrium fluctuations of thermodynamic quantities like the entropy production that were initially introduced for classical or quantum systems in contact with a thermal bath. Here we show, in the absence of thermal bath, the dynamics of continuously measured quantum systems can also be described by a fluctuation theorem, expressed in terms of a recently introduced arrow of time measure. This theorem captures the emergence of irreversible behavior from microscopic reversibility in continuous quantum measurements. From this relation, we demonstrate that measurement-induced wave-function collapse exhibits absolute irreversibility, such that Jarzynski-like equalities are violated, and that this property is inherent to quantum information acquisition. We apply our results to different continuous measurement schemes on a qubit: dispersive measurement, homodyne, and heterodyne detection of qubit's fluorescence.
In both thermodynamics and quantum mechanics, the arrow of time is characterized by the statistical likelihood of physical processes. We characterize this arrow of time for the continuous quantum measurement dynamics of a superconducting qubit. By experimentally tracking individual weak measurement trajectories, we compare the path probabilities of forward and backward-in-time evolution to develop an arrow of time statistic associated with measurement dynamics. We compare the statistics of individual trajectories to ensemble properties showing that the measurement dynamics obeys both detailed and integral fluctuation theorems, thus establishing the consistency between microscopic and macroscopic measurement dynamics.
Uncovering the origin of the arrow of time remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the second law of thermodynamics, which declares that entropy growth proceeds from the system's entanglement with the environment. It remains to be seen, however, whether the irreversibility of time is a fundamental law of nature or whether, on the contrary, it might be circumvented. Here we show that, while in nature the complex conjugation needed for time reversal is exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state. Using this algorithm on an IBM quantum computer enables us to experimentally demonstrate a backward time dynamics for an electron scattered on a two-level impurity.
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.
Uncovering the origin of the "arrow of time" remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the Second Law of Thermodynamics, which declares that entropy growth proceeds from the system's entanglement with the environment. This poses a question of whether it is possible to develop protocols for circumventing the irreversibility of time and if so to practically implement these protocols. Here we show that, while in nature the complex conjugation needed for time reversal may appear exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state. Using this algorithm on an IBM quantum computer enables us to experimentally demonstrate a backward time dynamics for an electron scattered on a two-level impurity.