Local model of a qubit in the interferometric setup

Błasiak, Paweł

doi:10.1088/1367-2630/17/11/113043

Cited by 6 publications

(10 citation statements)

References 35 publications

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“…A recent article by Blasiak [21] has also described a classical statistical model that can account for some of the phenomenology of interference without violating locality, thereby challenging Feynman's claim. In Appendix B, we discuss the ways in which the toy field theory described here differs from this model.…”

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confidence: 99%

Why interference phenomena do not capture the essence of quantum theory

Catani¹,

Leifer²,

Schmid³

et al. 2021

Preprint

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Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued that such phenomena force us to accept a number of radical interpretational conclusions, including: that a photon is neither a particle nor a wave but rather a schizophrenic sort of entity that toggles between the two possibilities, that reality is observer-dependent, and that systems either do not have properties prior to measurements or else have properties that are subject to nonlocal or backwards-in-time causal influences. In this work, we show that such conclusions are not, in fact, forced on us by the phenomena. We do so by describing an alternative to quantum theory, a statistical theory of a classical discrete field (the 'toy field theory') that reproduces the relevant phenomenology of quantum interference while rejecting these radical interpretational claims. It also reproduces a number of related interference experiments that are thought to support these interpretational claims, such as the Elitzur-Vaidman bomb tester, Wheeler's delayed-choice experiment, and the quantum eraser experiment. The systems in the toy field theory are field modes, each of which possesses, at all times, both a particle-like property (a discrete occupation number) and a wave-like property (a discrete phase). Although these two properties are jointly possessed, the theory stipulates that they cannot be jointly known. The phenomenology that is generally cited in favour of nonlocal or backwards-in-time causal influences ends up being explained in terms of inferences about distant or past systems, and all that is observer-dependent is the observer's knowledge of reality, not reality itself.

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confidence: 99%

Why interference phenomena do not capture the essence of quantum theory

Catani¹,

Leifer²,

Schmid³

et al. 2021

Preprint

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“…As such, it provides exhaustive reconstruction of singleparticle phenomena in a unified framework as opposed to separate models devised for simulation of particular effects, cf. [28][29][30][31][32][33][34][35][36][37][38].…”

Section: Discussionmentioning

confidence: 99%

“…On the one hand, there are various models indicating analogies on the grounds of classical probabilistic theories, see e.g. [28][29][30][31][32][33][34][35][36][37][38]. On the other hand, none of these results fully reconstruct quantum predictions for general single-particle scenarios.…”

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confidence: 99%

Is single-particle interference spooky?

Błasiak¹

2017

Preprint

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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.

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“…Following this reasoning, we have shown in [1] that such an agent in all her actions remains confined within a certain non-trivial subset of distributions in P(Λ). This set has an interesting geometry which can be analysed by coarse-graining distributions into classes indistinguishable to the agent.…”

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confidence: 83%

“…1 (on the left). Quantum description of such a dual-rail system boils down to a qubit.In this note we report construction of a classical local stochastic model which faithfully reconstructs quantum predictions for the dual-rail qubit [1]. It shows that this kind of framework is not enough to establish genuine quantum non-locality, since for a dual-rail qubit alleged 'nonlocality' can be explained as an epistemic effect due to restricted means of investigating the system.…”

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confidence: 95%

Local ontology for a dual-rail qubit

Błasiak

2016

J. Phys.: Conf. Ser.

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Abstract. We show that quantum predictions for the dual-rail realisation of a qubit can be faithfully simulated with classical stochastic gates and particles which interact entirely in a local manner. In the presented model 'non-locality' appears only on the epistemic level of description.We consider single quantum particle in a circuit which consists of two spatially separated paths (i = 0, 1) and a sequence of gates which include phase shifters P (ω) and detectors D i attached to each path separately, and beam splitters B(ξ) on which the paths cross; cf. Fig. 1 (on the left). Quantum description of such a dual-rail system boils down to a qubit.In this note we report construction of a classical local stochastic model which faithfully reconstructs quantum predictions for the dual-rail qubit [1]. It shows that this kind of framework is not enough to establish genuine quantum non-locality, since for a dual-rail qubit alleged 'nonlocality' can be explained as an epistemic effect due to restricted means of investigating the system. In the following, we sketch out the main concepts of the model. Ontology of the model. We postulate existence of two kinds of local particles carrying inner degrees of freedom which propagate along the paths: real ones described by a unit vector ⃗ n ∈ S 2 in 3D and ghosts carrying a phase φ ∈ S 1 . The crucial difference between the particles is that detectors register only real particles and remain blind to ghosts. For the purpose at hand, we restrict our attention to situations in which there is a single real particle present in the system with a ghost in the other path or the other path being empty ; see Fig. 1 (on the left). Hence, at each time the system is fully characterised by a triple (i, ⃗ n, φ) in the ontic state space:where S 1 * ≡ S 1 ∪{∅}. The first component i = 0, 1 specifies position of the real particle carrying vector ⃗ n and the other path featuring a ghost with phase φ or being empty φ = ∅. In general, the system is described by a probability distribution over the ontic states, i.e. a point in P(Λ).Building blocks of the model. To complete description of the model we need to specify the stochastic counterparts of the interferometric gates by defining action on the ontic states Λ → P(Λ) which does not violate the locality principle. Here are the definitions:-Detector D j placed in the j-th path is a deterministic gate: (i, ⃗ n, φ)

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Local model of a qubit in the interferometric setup

Cited by 6 publications

References 35 publications

Why interference phenomena do not capture the essence of quantum theory

Why interference phenomena do not capture the essence of quantum theory

Is single-particle interference spooky?

Local ontology for a dual-rail qubit

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