It has been said about quantum interference, that ``in reality, it contains the only mystery''. Together with nonlocality, it is often considered the characteristic feature of quantum theory challenging our classical understanding of the world. In this work, we are concerned with the restricted setting of a single particle propagating in multipath interferometric circuits---that is, the physical realization of a qudit---which is host to many typically quantum mechanical effects including collapse of the wave function and contextuality. In this paper, we show that this framework can be simulated with classical resources without violating the locality principle. We present a local ontological model whose predictions are indistinguishable from the quantum case. In the model, `nonlocality' appears merely as an epistemic effect arising from a level of description by agents whose knowledge is incomplete. It is notably different from the multiparticle scenarios where entanglement leads to nonlocal correlations on an ontological level. This result exposes the conceptual difference between single- and multiparticle phenomena, pointing to the latter as a deeper quantum mystery.
It has been said about quantum interference, that ``in reality, it contains the only mystery''. Together with nonlocality, it is often considered the characteristic feature of quantum theory challenging our classical understanding of the world. In this work, we are concerned with the restricted setting of a single particle propagating in multipath interferometric circuits---that is, the physical realization of a qudit---which is host to many typically quantum mechanical effects including collapse of the wave function and contextuality. In this paper, we show that this framework can be simulated with classical resources without violating the locality principle. We present a local ontological model whose predictions are indistinguishable from the quantum case. In the model, `nonlocality' appears merely as an epistemic effect arising from a level of description by agents whose knowledge is incomplete. It is notably different from the multiparticle scenarios where entanglement leads to nonlocal correlations on an ontological level. This result exposes the conceptual difference between single- and multiparticle phenomena, pointing to the latter as a deeper quantum mystery.
It is said about quantum interference that "In reality, it contains the only mystery". Indeed, together with non-locality it is often considered as the characteristic feature of quantum theory which can not be explained in any classical way. In this work we are concerned with a restricted setting of a single particle propagating in multi-path interferometric circuits, that is physical realisation of a qudit. It is shown that this framework, including collapse of the wave function, can be simulated with classical resources without violating the locality principle. We present a local ontological model whose predictions are indistinguishable from the quantum case. 'Non-locality' in the model appears merely as an epistemic effect arising on the level of description by agents whose knowledge is incomplete. This result suggests that the real quantum mystery should be sought in the multi-particle behaviour, since single-particle interferometric phenomena are explicable in a classical manner.
We consider a typical realization of a qubit as a single particle in two-path interferometric circuits built from phase shifters, beam splitters and detectors. This framework is often taken as a standard example illustrating various paradoxes and quantum effects, including non-locality. In this paper we show that it is possible to simulate the behaviour of such circuits in a classical manner using stochastic gates and two kinds of particles, real ones and ghosts , which interact only locally. The model has built-in limited information gain and state disturbance in measurements which are blind to ghosts . We demonstrate that predictions of the model are operationally indistinguishable from the quantum case of a qubit, and allegedly ‘non-local’ effects arise only on the epistemic level of description by the agent whose knowledge is incomplete due to the restricted means of investigating the system.
Quantum nonlocality has been a long-standing and fascinating problem in the foundations of quantum theory since its proof by the Bell inequality. It seems to contradict our intuitive picture of space-time and thus urges us to reconsider its foundation. With the advent of quantum information science, it has attracted renewed interest from a fundamental point of view as well as from a quantum information-theoretic one. Another fundamental question on the nature of quantum theory is how we understand what quantum states represent. (Quantum states hereafter refer to pure states.) This is also a long-standing problem since the early days of quantum theory. Roughly speaking, there are two conflicting views on this matter: one is ontology and the other is epistemology. Ontological models of quantum theory are models in which we assume some underlying reality for physical systems and require that all the predictions of quantum theory should be reproduced. The ontological models are divided into two categories, depending on which views the models are based on, ontology or epistemology. In the models based on ontology, quantum states represent the underlying reality in some sense, and different quantum states correspond to different realities. In the models based on epistemology, quantum states do not necessarily correspond to the underlying realities, and even different quantum states can be consistent with a common underlying reality. The former type of ontological models of quantum theory is called 1⁄4-ontic. The latter is called 1⁄4-epistemic. Thus, it might be rather confusing that ontological models are classified further into 1⁄4-ontic models and 1⁄4-epistemic ones. We use these terms here in accordance with the recent literature on quantum foundations. (For details of these notions in the ontological models of quantum theory, see the paper by Harrigan and Spekkens.) Quite recently, the question just mentioned has been answered by Pusey et al., and one of the above models has been refuted. It was shown that 1⁄4-epistemic models are inconsistent with the predictions of quantum theory. In other words, epistemological views on quantum states turned out to be false as long as we assume some underlying reality for physical systems. Therefore, only 1⁄4-ontic models of quantum theory are valid for describing quantum systems. This significantly advances our understanding on the nature of quantum states. It is expected that various conclusions will be drawn from this fact. In this paper, we will discuss a connection with nonlocality. The above two fundamental questions, nonlocality and the nature of quantum states, are intimately connected, and the connection was first implicitly recognised by Einstein in the early days of quantum theory. In a private correspondence with Schrodinger, Einstein constructed a fascinating argument that relates the above two. (That argument is distinctly different from the well-known EPR argument.) Recently, it was revisited and reconstructed in accordance with more rigorous notions in quantum foundations. Nonlocality is usually shown by violations of Bell inequalities. (Bell inequalities hereafter include all the subsequent developments such as the CHSH inequality.) Even if it is not clear whether the models of quantum theory are 1⁄4-ontic or 1⁄4-epistemic, we can prove nonlocality just by showing the violation of Bell inequalities. However, the above argument originated by Einstein implies that if we know the models are 1⁄4-ontic in advance (as we do now), we can prove nonlocality in a simpler way without Bell inequalities. (This argument had been known in quantum foundations before the refutation of 1⁄4-epistemic models.) Nonlocality is rigorously defined as a violation of the notion of local causality defined by Bell. Showing the violation of Bell inequalities is one way of demonstrating the violation of local causality. Since the simpler proof initiated by Einstein directly demonstrates the violation of local causality, it is a more straightforward proof of nonlocality from a conceptual point of view. In the following, we will see that this simple argument of nonlocality without Bell inequalities can be used to show multipartite nonlocality as well. Before moving onto multipartite cases, first let us define the necessary notions for presenting our result. First of all, we assume that there exists a complete specification of the properties of a physical system, which we refer to as the ontic state of that system. The ontic states represent the underlying realities and are not necessarily equal to ordinary quantum states. (In other words, the ontic states correspond to hidden variables.) Ontological models of quantum theory are models that assume ontic states and reproduce all the predictions of quantum theory. An important question is how ontic states correspond to quantum states in quantum theory. In order to frame the question accurately, we need the notion of an epistemic state, which represents the relation between them. Suppose we prepare a physical system in a quantum state 1⁄4. Although the system is uniquely specified as 1⁄4 in quantum theory, there still remains a possibility that it allows a more detailed specification in the ontic state space, in which case many different ontic states turn out to be consistent with 1⁄4. The relation between ontic states and the preparation procedure, P1⁄4, is described by a conditional probability distribution over the ontic state space, pð jP1⁄4Þ, which we refer to as an epistemic state. In general, the preparation P can be a preparation of a physical system in a mixed sate. Unless there exists a one-to-one correspondence between ontic states and quantum states, the probability distribution spreads over . (See Fig. 1.) The question of whether an ontological model is 1⁄4-ontic or 1⁄4-epistemic is concerned with the behaviour of the epistemic states for two distinct preparations of quantum states. Consider two distinct preparations of quantum states, Journal of the Physical Society of Japan 82 (2013) 055003
Quantum nonlocality can be revealed ``via local contextuality'' in qudit-qudit entangled systems with d>2, that is, through the violation of inequalities containing Alice-Bob correlations that admit a local description, and Alice-Alice correlations (between the results of sequences of measurements on Alice's subsystem) that admit a local (but contextual) description. A fundamental question to understand the respective roles of entanglement and local contextuality is whether nonlocality via local contextuality exists when the parties have only qubit-qubit entanglement. Here we respond affirmatively to this question. This result further clarifies the connection between contextuality and nonlocality and opens the door for observing nonlocality via local contextuality in actual experiments.
Gennaro Auletta University of Cassino gennaro.auletta@gmail.com Classically, the main ontological attempts at understanding quantum mechanics focus on the corpuscular behavior of these systems and especially on detection events, since these are the most classical phenomena that we have in such a context (indeed, they also require the presence of a classical apparatus). The main trend has been to consider wave-like aspects as deprived of ontological substrate and as reflecting rather the mathematical abstract formalism of the theory. The few attempts that have been done in order to assign some form of ontological reference to wave-like aspects have tried to interpreted this in terms of classical waves and have been disproved across the last 30 years (see Auletta & Tarozzi, 2004b; Auletta & Torcal, 2011). It is perhaps time to try a different approach, by renouncing any attempt at a classical ontology and by taking seriously into account the non-local aspects of the theory (which are mostly associated with wave-like phenomena). When we consider things in this perspective, we shall discover that all non-local phenomena in quantum mechanics, although different, have something in common: they all rely on non-local interdependencies among possible events or measurement outcomes (see Auletta, 2011). This is true for all interference phenomena for isolated systems, this is true for entangled systems, this is true for the Aharonov-Bohm effect, and so on. What is sad is that we do not have until now a name for denoting this mysterious reality. It is indeed mysterious, since we cannot directly measure it. There is in fact no way to have a direct experimental evidence of it. In most cases we can only reconstruct the interference profile after many experimental runs, a circumstance that has led many scientists to discard any ontological attribution to wave-like phenomena. However, a proposed
The status of the quantum wave function is one of the most debated issues in quantum foundations---whether it corresponds directly to the reality or just represents knowledge or information about some aspect of reality. We propose a $\ensuremath{\psi}$-ontology theorem that excludes a class of ontological explanations where the quantum wave function is treated as mere information. Our result, unlike the acclaimed Pusey-Barrett-Rudolph's theorem, does not presume the absence of holistic ontological properties for product quantum preparations. At the core of our derivation, we utilize the seminal no-go result by Bell that rules out any local realistic world view for quantum theory. We show that the observed phenomenon of quantum nonlocality cannot be incorporated in a class of $\ensuremath{\psi}$-epistemic models. Using the well-known Clauser-Horne-Shimony-Holt inequality, we obtain a threshold bound on the degree of epistemicity above which the ontological models are not compatible with quantum statistics.