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Irreversibility in unitary quantum homogenisation: Theory and Experiment

Chiara Marletto, Vlatko Vedral, Laura T. Knoll, Fabrizio Piacentini, Enrico Rebufello, Ettore Bernardi, Alessio Avella, Marco Gramegna, Ivo Pietro Degiovanni, Marco Genovese

Published Sep 30, 2020• 0 citations
OpenAlex

Abstract

Is it possible to fit irreversibility exactly in a universe whose laws are time-reversal symmetric? This vexed open problem, dating back to the origin of statistical mechanics, is crucial for the realisability of logically irreversible computations such as erasure. A well-known type of irreversibility is epitomised by Joule's experiment, involving a volume of fluid and a stirrer powered by mechanical means, e.g. a suspended weight: while it is possible to construct a cycle heating up the water by mechanical means only, it is impossible to cool the water down via a cycle that likewise utilises mechanical means only. This irreversibility is of particular interest because, unlike others, it is based on a system that performs some transformation, or task, operating in a cycle. First introduced via a thermodynamic cycle (e.g. Carnot's), this idea was generalised by von Neumann to a constructor - a system that can perform a given task on another system and crucially retains the ability to perform the task again. On this ground, a task is possible if there is no limitation to how well it can be performed by some constructor; it is impossible otherwise. Here we shall define a irreversibility, generalising Joule's, requiring that a task $T$ is possible, while the transpose task (where $T$'s input and output are switched) is not. We shall demonstrate the compatibility of this constructor-based irreversibility with quantum theory's time-reversal symmetric laws, confining attention to an example using the universal quantum homogeniser. This result is an essential further step for understanding irreversibility within quantum theory, one of the most fundamental theories of physics we posses at present. We will also simulate the irreversibility experimentally with high-quality photon qubits.

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Quantum mechanics is widely recognised as being incomplete. It is not consistent with the second law of thermodynamics and does not provide a scientifically credible physical account of the measurement process, the means by which coherence is broken and classically observable states are recorded. This has led to many ad hoc assumptions being used to account for various properties of quantum systems, among which is the coherence time of quantum devices that determines their ability to perform computations. Here, we show that all these properties can be accommodated naturally and consistently in the context of mixing quantum systems which exhibit continuous spectra, as arises in the thermodynamic limit in quantum statistical mechanics and quantum gravity. In particular, for isolated systems we show that the time-reversal symmetry associated with unitary time evolution of the quantum state gives rise to time-symmetry breaking and a semi-group evolution which attains thermodynamic equilibrium at long times. Moreover, the emergence of this non-unitary time-asymmetry leads to microcanonical equilibrium states in which all quantum coherence is lost and is accompanied by the transformation of pure states into mixtures, leading in turn to an increase in entropy. Inclusion of a macroscopic measurement apparatus shows how the outcome of a measurement corresponds to the von Neumann projection postulate, arising with probabilities in conformance with the Born rule. The mathematical structure of the theory which applies to quantum systems with continuous spectra is closely analogous to the classical ergodic theory of dynamical systems and the conditions under which they attain equilibrium states.

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Is it possible to fit irreversibility exactly in a universe whose laws are time-reversal symmetric? This vexed open problem, dating back to the origin of statistical mechanics, is crucial for the realisability of logically irreversible computations such as erasure. A well-known type of irreversibility is epitomised by Joule's experiment, involving a volume of fluid and a stirrer powered by mechanical means, e.g. a suspended weight: while it is possible to construct a cycle heating up the water by mechanical means only, it is impossible to cool the water down via a cycle that likewise utilises mechanical means only. This irreversibility is of particular interest because, unlike others, it is based on a system that performs some transformation, or task, operating in a cycle. First introduced via a thermodynamic cycle (e.g. Carnot's), this idea was generalised by von Neumann to a constructor - a system that can perform a given task on another system and crucially retains the ability to perform the task again. On this ground, a task is possible if there is no limitation to how well it can be performed by some constructor; it is impossible otherwise. Here we shall define a irreversibility, generalising Joule's, requiring that a task TTT is possible, while the transpose task (where TTT's input and output are switched) is not. We shall demonstrate the compatibility of this constructor-based irreversibility with quantum theory's time-reversal symmetric laws, confining attention to an example using the universal quantum homogeniser. This result is an essential further step for understanding irreversibility within quantum theory, one of the most fundamental theories of physics we posses at present. We will also simulate the irreversibility experimentally with high-quality photon qubits.
How irreversibility arises in a universe with time-reversal symmetric laws is a central problem in physics. In this Letter, we discuss a radically different take on the emergence of irreversibility, adopting the recently proposed constructor theory framework. Irreversibility is expressed as the requirement that a task is possible, while its inverse is not. We prove the compatibility of such irreversibility with quantum theory's time-reversal symmetric laws, using a dynamical model based on the universal quantum homogenizer. We also test the physical realizability of this model by means of an experimental demonstration with high-quality single-photon qubits.
Abstract Erasure is fundamental for information processing. It is also key in connecting information theory and thermodynamics, as it is a logically irreversible task. We provide a new angle on this connection, noting that there may be an additional cost to erasure, that is not captured by standard results such as Landauer’s principle. To make this point we use a model of irreversibility based on constructor theory—a recently proposed generalization of the quantum theory of computation. The model uses a machine called the ‘quantum homogenizer’, which has the ability to approximately realise the transformation of a qubit from any state to any other state and remain approximately unchanged, through overall entirely unitary interactions. We argue that when performing erasure via quantum homogenization there is an additional cost to performing the erasure step of the Szilard’s engine, because it is more difficult to reliably produce pure states in a cycle than to produce maximally mixed states. We also discuss the implications of this result for the cost of erasure in more general terms.
The fundamental laws of classical mechanics, quantum mechanics, and general relativity are time-symmetric, yet macroscopic experience is irreversible without exception. Standard physics bridges this gap with statistical argument: reversal is treated as merely improbable, not physically inadmissible. This paper argues that the gap is an artifact of treating space as a continuum, and that it closes once space is treated as discrete, as in Quantum-Geometry Dynamics (QGD). Two independent grounds are identified for the categorical, non-statistical irreversibility of every elementary interaction in discrete space: a local ground, the loss of individual addressability when one particle's constituent preon(+)s merge into another upon absorption; and a global ground, the irreducible universal gravitational trace left by any positional change, given that gravity in QGD is instantaneous and universal in scope. Applied across four domains, this single result dissolves the arrow-of-time problem, grounds the second law of thermodynamics in dynamics rather than probability, dissolves the apparent asymmetry between unitary evolution and measurement collapse, and shows the reversible/irreversible distinction in quantum gate theory to be a feature of the abstract computational model rather than of physical mechanism. The result is shown to be compatible with, and silent on, whether a finite deterministic system's forward dynamics eventually revisit an earlier configuration by a non-retracing causal path. No new axiom or free parameter is introduced: the result follows from elements of QGD already established for independent reasons.
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?
Quantum mechanics is widely recognised as being incomplete. It is not consistent with the second law of thermodynamics and does not provide a scientifically credible physical account of the measurement process, the means by which coherence is broken and classically observable states are recorded. This has led to many ad hoc assumptions being used to account for various properties of quantum systems, among which is the coherence time of quantum devices that determines their ability to perform computations. Here, we show that all these properties can be accommodated naturally and consistently in the context of mixing quantum systems which exhibit continuous spectra, as arises in the thermodynamic limit in quantum statistical mechanics and quantum gravity. In particular, for isolated systems we show that the time-reversal symmetry associated with unitary time evolution of the quantum state gives rise to time-symmetry breaking and a semi-group evolution which attains thermodynamic equilibrium at long times. Moreover, the emergence of this non-unitary time-asymmetry leads to microcanonical equilibrium states in which all quantum coherence is lost and is accompanied by the transformation of pure states into mixtures, leading in turn to an increase in entropy. Inclusion of a macroscopic measurement apparatus shows how the outcome of a measurement corresponds to the von Neumann projection postulate, arising with probabilities in conformance with the Born rule. The mathematical structure of the theory which applies to quantum systems with continuous spectra is closely analogous to the classical ergodic theory of dynamical systems and the conditions under which they attain equilibrium states.