Time-reversal of an unknown quantum state

Abstract

For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time-symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is set by the measurement procedure and that the time-reversal requires complex conjugation of the wave function, which is overly complex to spontaneously appear in nature. Building on this Landau-Wigner conjecture, it became possible to demonstrate that time-reversal is exponentially improbable in a virgin nature and to design an algorithm artificially reversing a time arrow for a given quantum state on the IBM quantum computer. However, the implemented arrow-of-time reversal embraced only the known states initially disentangled from the thermodynamic reservoir. Here we develop a procedure for reversing the temporal evolution of an arbitrary unknown quantum state. This opens the route for general universal algorithms sending temporal evolution of an arbitrary system backward in time. The concept of arrow of time expressing time asymmetric nature is intrinsically related to the second law of thermodynamics and increase of entropy. The authors show how a thermodynamic bath expected to add to entropy increase can be the key to time reversal for an unknown quantum state, paving the way to universal algorithms sending temporal evolution of an arbitrary system backward in time.