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arXiv:1406.7023

A Macroscopic Classical System with Entanglement

David W. Snoke

Published Jun 26, 2014• 0 citations
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Abstract

It is possible to construct a classical, macroscopic system which has a mathematical structure that is exactly the same as that of a quantum mechanical system and which can be put into a state which is identical to quantum mechanical entanglement. This paper presents a simple example, including a way in which the system can be measured to violate Bell's inequalities. This classical simulation of a quantum system allows us to visualize entanglement and also helps us to see what aspects of quantum mechanical systems are truly nonclassical.

DOI
10.48550/arxiv.1406.7023

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It is possible to construct a classical, macroscopic system which has a mathematical structure that is exactly the same as that of a quantum mechanical system and which can be put into a state which is identical to quantum mechanical entanglement. This paper presents a simple example, including a way in which the system can be measured to violate Bell's inequalities. This classical simulation of a quantum system allows us to visualize entanglement and also helps us to see what aspects of quantum mechanical systems are truly nonclassical.
Characterization of nonclassicality or quantumness of a state is fundamental to foundations of quantum mechanics and quantum information. At the heart of the problem is the question whether there exist classical systems---howsoever complicated---that can mimic a given quantum state. Whilst this has been traditionally addressed through the violation of Bell inequality or nonseparability, we show that it is possible to go beyond them, by introducing the concept of classical simulation. Focusing on the two-qubit case, we show that, while for pure states, classical simulability is equivalent to existence of a local hidden variable (LHV) model, the conditions for simulability can be weaker for mixed states, demanding what we call only a generalized LHV description. Consequently, quantum states which defy a classical simulation---which we call exceptional---may require conditions which are more stringent than violation of Bell inequalities. We illustrate these features with a number of representative examples and discuss the underlying reasons, by employing fairly simple arguments.
The quantum description of the microscopic world is incompatible with the classical description of the macroscopic world, both mathematically and conceptually. Nevertheless, it is generally accepted that classical mechanics emerges from quantum mechanics in the macroscopic limit. In this paper, we challenge this perspective and demonstrate that the behaviour of a macroscopic system can retain all aspects of the quantum formalism, in a way that is robust against decoherence, particle losses and coarse-grained (imprecise) measurements. This departure from the expected classical description of macroscopic systems is not merely mathematical but also conceptual, as we show by the explicit violation of a Bell inequality and a Leggett–Garg inequality.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation.
An example of a classical system violating Bell’s inequalities is discussed. Existence of a classical system violating Bell’s inequalities takes away the “mysterious ” property usually called “non-locality ” which according to some characterizes quantum-mechanical systems. In recent years there has been an explosion of research on consequences from what initially had been an attempt by Einstein, Podolsky and Rosen (EPR)[1] to put quantum mechanics (QM) in question. Turning the tide is mainly due to the theoretical paper of Bell [2] discussing a two -spin particle system proposed by Bohm [3] as a special case of the system discussed in the initial critique by EPR [1]. Despite the initial questions posed by EPR the problems regarding QM are usually considered nowadays as settled and questioning it is considered highly unusual. Furthermore, claimed
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from some of the most fundamental concepts of classical physics-in particular that properties of an object are well-defined independent of measurements (realism) and only affected by local interactions (locality). The violation of these bounds unambiguously shows that the measured system does not behave classically, void of any assumption on the validity of quantum theory. It has also found applications in quantum technologies for certifying the suitability of devices for generating quantum randomness, distributing secret keys and for quantum computing. Here we report on the violation of a Bell inequality involving a massive, macroscopic mechanical system. We create light-matter entanglement between the vibrational motion of two silicon optomechanical oscillators, each comprising approx. 10^{10} atoms, and two optical modes. This state allows us to violate a Bell inequality by more than 4 standard deviations, directly confirming the nonclassical behavior of our optomechanical system under the fair sampling assumption.
We have recently presented a general scheme enabling quantum modeling of different types of situations that violate Bell's inequalities [1]. In this paper, we specify this scheme for a combination of two concepts. We work out a quantum Hilbert space model where 'entangled measurements' occur in addition to the expected 'entanglement between the component concepts', or 'state entanglement'. We extend this result to a macroscopic physical entity, the 'connected vessels of water', which maximally violates Bell's inequalities. We enlighten the structural and conceptual analogies between the cognitive and physical situations which are both examples of a nonlocal non-marginal box modeling in our classification.