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arXiv:2205.00198 · Journal of Physics A Mathematical and Theoretical

Temporal witnesses of non-classicality and conservation laws

Giuseppe Di Pietra, Chiara Marletto

Published May 31, 2023• 5 citations
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Abstract

Abstract A general entanglement-based witness of non-classicality has recently been proposed, which can be applied to testing quantum effects in gravity. This witness is based on generating entanglement between two quantum probes via a mediator. In this paper we provide a ‘temporal’ variant of this witness, using a single quantum probe to assess the non-classicality of the mediator. Within the formalism of quantum theory, we show that if a system M is capable of inducing a coherent dynamical evolution of a quantum system Q, in the presence of a conservation law, then M must be non-classical. This argument supports witnesses of non-classicality relying on a single quantum probe, which can be applied to a number of open issues, notably in quantum gravity or quantum biology.

DOI
10.1088/1751-8121/acda6b

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Abstract A general entanglement-based witness of non-classicality has recently been proposed, which can be applied to testing quantum effects in gravity. This witness is based on generating entanglement between two quantum probes via a mediator. In this paper we provide a ‘temporal’ variant of this witness, using a single quantum probe to assess the non-classicality of the mediator. Within the formalism of quantum theory, we show that if a system M is capable of inducing a coherent dynamical evolution of a quantum system Q, in the presence of a conservation law, then M must be non-classical. This argument supports witnesses of non-classicality relying on a single quantum probe, which can be applied to a number of open issues, notably in quantum gravity or quantum biology.
The universality of quantum theory has been questioned ever since it was proposed. Key to this long-unsolved question is to test whether a given physical system has non-classical features. Here we connect recently proposed witnesses of non-classicality, based on information-theoretic ideas, with the theory of temporal entanglement. We provide a protocol to witness the non-classicality of a system by probing it with a qubit: we show that, assuming a general conservation law, violating temporal Bell inequalities on the qubit probe implies the non-classicality of the system under investigation. We also perform proof-of-principle experimental emulations of the proposed witness of non-classicality, using a three qubit Nuclear Magnetic Resonance quantum computer. Our result is robust, as it relies on minimal assumptions, and remarkably it can be applied in a broad range of contexts, from quantum biology to quantum gravity.
Quantum theory is one of the most successful theories in modern physics. It has been extensively tested in the microscopic domain, always with remarkable success. Yet, these tests do not currently extend in a conclusive way to all physical systems and across all scales. This leaves open the question of whether quantum theory provides a truly universal description of reality, especially in regimes where direct experimental access is limited, such as the gravitational field or complex macroscopic biological systems. This Thesis addresses this question through the study of hybrid systems, where a well-controlled quantum sector interacts with an unknown sector whose underlying description may or may not be quantum. It contributes to the emerging framework of information-theoretical witnesses of non-classicality, where the quantum sector is used as a probe to test the nature of the unknown system under minimal assumptions. We first examine spatial entanglement-based witnesses, in which the ability of an unknown system to mediate entanglement between two quantum probes by local means provides a sufficient condition for its non-classicality. We extend this framework by quantitatively showing that locally mediated quantum correlations lower bound the non-commutativity of the observables of the mediator, within quantum theory. We then introduce a novel class of single-probe temporal witnesses, where non-classicality is inferred from the temporal evolution of a probe under a global conservation law. We prove that quantum coherent evolution under such a constraint can only be mediated by a non-classical system, and propose an application to light-harvesting processes in photosynthetic complexes. Finally, we develop a temporal entanglement-based witness. Here, the sufficient condition for the non-classicality of the unknown system is the ability to mediate temporal entanglement relative to the probe's local conserved quantity and a non-commuting observable. This result provides a temporal extension of the spatial entanglement-based witness, representing a promising route for the development of the next generation of tests to probe the universality of quantum theory in previously inaccessible fields such as gravity and biology.
We propose a general argument to show that if a physical system can mediate locally the generation of entanglement between two quantum systems, then it itself must be nonclassical. Remarkably, we do not assume any classical or quantum formalism to describe the mediating physical system: our result follows from general information-theoretic principles, drawn from the recently proposed constructor theory of information. This argument provides a broader theoretical basis for recently proposed tests of nonclassicality in gravity, based on witnessing gravitationally induced entanglement in quantum probes, making them applicable in the context where quantum theory may not apply.
Abstract The task of testing whether quantum theory applies to all physical systems and all scales requires considering situations where a quantum probe interacts with another system that need not obey quantum theory in full. Important examples include the cases where a quantum mass probes the gravitational field, for which a unique quantum theory of gravity does not yet exist, or a quantum field, such as light, interacts with a macroscopic system, such as a biological molecule, which may or may not obey unitary quantum theory. In this context a class of experiments has recently been proposed, where the non-classicality of a physical system that need not obey quantum theory (the gravitational field) can be tested indirectly by detecting whether or not the system is capable of entangling two quantum probes. Here we illustrate some of the subtleties of the argument, to do with the role of locality of interactions and of non-classicality, and perform proof-of-principle experiments illustrating the logic of the proposals, using a Nuclear Magnetic Resonance quantum computational platform with four qubits.
Probing the quantum nature of gravity is one of the most profound open challenges in physics. A promising direction is the Gravitationally Induced Entanglement (GIE) protocol, where two initially unentangled probes become entangled solely through local interactions with a mediator of interaction, the gravitational field. Such entanglement would imply that gravity must carry quantum features, namely, it must possess at least a couple of incompatible observables. This thesis further expands the GIE protocol and its Theory-Independent argument by introducing a general, dynamics-independent inequality: the quantum correlation gain between the probes is upper-bounded by the non-commutativity of the mediator’s observables and its Hilbert space dimension. This bound holds for arbitrary interactions and any finite-dimensional systems. A decoherence analysis shows the bound vanishes when the mediator becomes classical. These results provide a quantitative, operational tool for observing the non-classicality of mediators, thereby expanding the conceptual and experimental reach of GIE-based tests of gravity.
Quantum information concepts and quantum technologies have opened the prospect of probing the quantum nature of gravity in table-top experiments. Most proposals rely on detecting gravitationally mediated entanglement, which requires measurements on both interacting systems. Here we propose an alternative test based on witnessing quantum memory effects in the dynamics of a single system. We show how the quantum memory concept allows the non-classicality of the interaction between two systems to be certified through local measurements on only one of them. We then develop a novel quantum memory witness, making the approach applicable to gravitationally coupled harmonic oscillators. This witness requires no assumptions about the dynamics, such as Gaussianity. Our results show that the quantumness of gravitational dynamics can be certified with access to only one subsystem, opening the door to asymmetric implementations that can offer conceptual and experimental advantages to probing the quantum nature of the gravitational interaction.