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arXiv:2102.10615 · Journal of Physics A Mathematical and Theoretical

Vindication of entanglement-based witnesses of non-classicality in hybrid systems

Emanuele Marconato, Chiara Marletto

Published Aug 6, 2021• 9 citations
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Abstract

Recently, Vedral and one of us proposed an entanglement-based witness of non-classicality in systems that need not obey quantum theory, based on information-theoretic ideas [ 1 , 3 ], which offers a robust foundation for newly proposed table-top tests of non-classicality in gravity, [ 2 , 3 ]. The witness asserts that if a mediator can entangle locally two quantum systems, then it has to be non-classical. Hall and Reginatto [ 4 , 7 ] claimed that there are classical systems that can entangle two quantum systems, thus violating our proposed witness. Here we refute that claim, explaining that the counterexample proposed by Hall and Reginatto in fact validates the witness, vindicating the witness of non-classicality in its full generality.

DOI
10.1088/1751-8121/ac1b78

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Recently, Vedral and one of us proposed an entanglement-based witness of non-classicality in systems that need not obey quantum theory, based on information-theoretic ideas [ 1 , 3 ], which offers a robust foundation for newly proposed table-top tests of non-classicality in gravity, [ 2 , 3 ]. The witness asserts that if a mediator can entangle locally two quantum systems, then it has to be non-classical. Hall and Reginatto [ 4 , 7 ] claimed that there are classical systems that can entangle two quantum systems, thus violating our proposed witness. Here we refute that claim, explaining that the counterexample proposed by Hall and Reginatto in fact validates the witness, vindicating the witness of non-classicality in its full generality.
In a recent paper, we vindicated a general entanglement-based witness of non-classicality in hybrid quantum systems. Our vindication refutes a counterexample to the witness, proposed by Hall and Reginatto. These authors recently commented further, claiming to expose "a huge number of errors and misconceptions" in it. However, their comment contains no refutation of our arguments, nor does it expose any error or misconception in them. But it does include a number of misconceptions about the witness of non-classicality. Here we respond to those.
Models of quantum-classical interactions fall into two classes: those which allow the generation of quantum entanglement via a classical mediator (such as gravity), and those which do not. Marconato and Marletto have recently sought to distinguish between these classes by claiming that known members of the first class (based on the configuration-ensemble formalism introduced by us) fail to model the mediator as a 'classical' system, and are nonlocal. We explicitly show that this claim is incorrect, and expose a large number of errors and misconceptions in their reasoning. We also point to a very simple and transparent example of the generation of entanglement between two qubits via a classical bit. It follows that there are models permitting the generation of entanglement via quantum-classical interactions that lie outside the remit of the theorem cited by Marconato and Marletto. We clarify the reasons for the limited applicability of various no-go theorems for entanglement generation.
Abstract Two very similar proposals have been made recently for witnessing nonclassical features of gravity, by Bose et al and by Marletto and Vedral. However, while these proposals are asserted to be very general, they are in fact based on a very strong claim: that quantum systems cannot become entangled via a classical intermediary. We point out that the support provided for this claim is only applicable to a very limited class of quantum-classical interaction models, corresponding to Koopman-type dynamics. We show that the claim is also valid for mean-field models, but that it is contradicted by explicit counterexamples based on the configuration-ensemble model. Thus, neither proposal provides a definitive test of nonclassical gravity.
Two of us recently proposed an entanglement-based witness of non-classicality, which can be applied to testing quantum effects in gravity in what is known as the Bose-Marletto-Vedral (BMV) effect. The witness is based on this idea: if a system can create entanglement between two quantum probes by local means only, then it must be non-classical. In this note we discuss the role of locality as an assumption for the theorem supporting the witness; we also discuss other related notions of locality and comment on their mutual relations.
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.
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.