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Nova Scientia

Population rate of quantum states and the reverse of the arrow of time

Manuél Ávila, José Eladio Hernández Vázquez

Published Nov 10, 2022• 0 citations
Publisher

Abstract

Recently it has been pointed out that an outstanding application of an IBM quantum computer is to reverse the arrow of time (Lesovik et al., 2019). It is explored such a possibility in a two qubits system coupled to a common structured reservoir at zero temperature. It is shown that population rates of the quantum states become the same both towards the remote past and towards the remote future. A two qubits system in presence of noise can reverse the arrow of time.

DOI
10.21640/ns.v14i29.3099

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Recently it has been pointed out that an outstanding application of an IBM quantum computer is to reverse the arrow of time (Lesovik et al., 2019). It is explored such a possibility in a two qubits system coupled to a common structured reservoir at zero temperature. It is shown that population rates of the quantum states become the same both towards the remote past and towards the remote future. A two qubits system in presence of noise can reverse the arrow of time.
Recently it has been pointed out that an outstanding application of an IBM quantum computer is to reverse the arrow of time [Lesovik et al. Sci. Rep. 9, 1 (2019)]. The issue of the consequences of the reversal of the arrow of time on the execution of a CNOT gate by a quantum device is addressed. It is predicted that if the CNOT gate is executed towards the future then this was previously executed in the past. The above might confirm the paradigm that an event in the present time influences another event in the past time [2]. Such a physical phenomena is called retrocausality.
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.
Uncovering the origin of the arrow of time remains a fundamental scientifc 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.
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.
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 problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing an irreversible process. However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory showirreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility?