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Time-reversal of an unknown quantum state

Physicists have long sought to understand the irreversibility of the surrounding world and have credited its emergence to the time-symmetric, fundamental laws of physics. According to quantum mechanics, the final irreversibility of conceptual time reversal requires extremely intricate and implausible scenarios that are unlikely to spontaneously occur in nature. Physicists had previously shown that while time-reversibility is exponentially improbable in a natural environmentâ€”it is possible to design an algorithm to artificially reverse a time arrow to a known or given state within an IBM quantum computer. However, this version of the reversed arrow-of-time only embraced a known quantum state and is therefore compared to the quantum version of pressing rewind on a video to "reverse the flow of time."

In a new report now published in Communications Physics, Physicists A.V. Lebedev and V.M. Vinokur and colleagues in materials, physics and advanced engineering in the U.S. and Russia, built on their previous work to develop a technical method to reverse the temporal evolution of an arbitrary unknown quantum state. The technical work will open new routes for general universal algorithms to send the temporal evolution of an arbitrary system backward in time. This work only outlined the mathematical process of time reversal without experimental implementations.

The arrow of time originates from expressing the direction of time in a singular route relative to the second law of thermodynamics, which implies that entropy growth stems from energy dissipation of the system to the environment. Scientists can therefore consider energy dissipation relative to the system's entanglement with the environment. Previous research solely focused on the quantum viewpoint of the arrow of time and on understanding the effects of the Landau-Neumann-Wigner hypothesis to quantify the complexity of reversing the arrow of time on an IBM quantum computer. In the present work, the scientists propose using a thermodynamic reservoir at finite temperatures to form a high-entropy stochastic bath to thermalize a given quantum system and experimentally increase thermal disorder or entropy in the system. However, experimentally, the IBM computers do not support thermalization, which forms the first step in the currently proposed cycle.

In theory, the presence of the thermal reservoir unexpectedly made it possible to prepare high-temperature thermal states of an auxiliary (alternative) quantum system elsewhere, governed by the same Hamiltonian (an operator corresponding to the sum of kinetic energy and potential energies for all particles in the system). This allowed Lebedev and Vinokur to mathematically devise an operator of backward-time evolution to reverse the chronological dynamics in a given quantum system.

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