No<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow></mml:math>-Epistemic Model Can Fully Explain the Indistinguishability of Quantum States

Barrett, Jonathan; Cavalcanti, Eric G.; Lal, Raymond; Maroney, O. J. E.

doi:10.1103/physrevlett.112.250403

Cited by 126 publications

(138 citation statements)

References 33 publications

(58 reference statements)

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“…In this letter, I have exhibited a family of states for which the ratio of classical to quantum overlaps must be ≤ 2e −cd in Hilbert space dimensions d that are divisible by 4, and where c is a positive constant. This represents an exponential improvement in asymptotic scaling over the previous result of 4/(d − 1) [16]. This presents a severe problem for the ψ-epistemic explanation of quantum indistinguishability, as the portion of the indistinguishability that can be accounted for by the overlap of probability measures decreases rapidly in large Hilbert space dimension.…”

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confidence: 76%

“…Following this, Barrett et al showed that the ratio of an overlap measure derived from the variational distance to a comparable measure of the indistinguishability of quantum states must scale like 4/(d − 1) in Hilbert space dimension for a particular family of states [16]. In this letter, I exhibit a family of states in Hilbert space dimensions d that are divisible by 4 for which the same ratio must be ≤ de −cd , where c is a positive constant.…”

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confidence: 98%

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ψ-Epistemic Models are Exponentially Bad at Explaining the Distinguishability of Quantum States

Leifer

2014

Phys. Rev. Lett.

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The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (state of knowledge) or an ontic state (state of reality)? In realist models of quantum theory, the epistemic view asserts that nonorthogonal quantum states correspond to overlapping probability measures over the true ontic states. This naturally accounts for a large number of otherwise puzzling quantum phenomena. For example, the indistinguishability of nonorthogonal states is explained by the fact that the ontic state sometimes lies in the overlap region, in which case there is nothing in reality that could distinguish the two states. For this to work, the amount of overlap of the probability measures should be comparable to the indistinguishability of the quantum states. In this letter, I exhibit a family of states for which the ratio of these two quantities must be ≤ 2de −cd in Hilbert spaces of dimension d that are divisible by 4. This implies that, for large Hilbert space dimension, the epistemic explanation of indistinguishability becomes implausible at an exponential rate as the Hilbert space dimension increases. The status of the quantum state is one of the most controversial issues in the foundations of quantum theory. Is it a state of knowledge (an epistemic state), or a state of physical reality (an ontic state)? Many realist interpretations of quantum theory employ ontic quantum states, but the rise of quantum information science has revived interest in the epistemic alternative because many of the puzzling phenomena employed in quantum information are explained quite naturally in terms of the epistemic quantum states [1]. For example, consider the fact that two nonorthogonal quantum states cannot be perfectly distinguished. On the ontic view, the two states represent distinct arrangements of physical reality, so it is puzzling that this distinctness cannot be detected. However, on the epistemic view, a quantum state is represented by a probability measure over the physical properties of a system and nonorthogonal states correspond to overlapping probability measures. Indistinguishability is thus explained by the fact that preparations of the two quantum states sometimes result in the same physical properties of the system, in which case there is nothing existing in reality that could distinguish them.Recently, several theorems have been proved aiming to show that the quantum state must be ontic [2-6]. These have been proved within the ontological models framework [7], which is a refinement of the hidden variable approach used to prove earlier no-go results, such as Bell's theorem [8] and the Kochen-Specker theorem [9]. Each of these theorems employs questionable auxiliary assumptions 1 . Without such assumptions, explicit counterexamples show that the epistemic view of quantum states can be maintained [11,12]. Within the ontological models framework, a model is ψ-ontic if the probability measures corresponding to every pair of pure quantum states have zero overlap, ...

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confidence: 76%

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confidence: 98%

ψ-Epistemic Models are Exponentially Bad at Explaining the Distinguishability of Quantum States

Leifer

2014

Phys. Rev. Lett.

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“…Barrett et al [16] showed that the ratio between two directly comparable measures for the classical and quantum overlaps had to scale at most like 1/d for certain pairs of quantum states when the dimension d increases, while Leifer [18] exhibited states for which the same ratio has to decrease exponentially with d. Following these works, and in particular the approach of Barrett et al…”

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confidence: 99%

“…[12,16,18], the probability of successfully distinguishing the two quantum states |ψ , |φ using optimal quantum measurements, and that of distinguishing the two epistemic states µ ψ , µ φ given that one knows the ontic state λ (assuming in each case that |ψ and |φ , respectively µ ψ and µ φ , have been prepared with equal probabilities). These probabilities of success are given, respectively, by 1 − ω Q (|ψ , |φ )/2 and 1 − ω C (µ ψ , µ φ )/2, where the quantum and classical overlaps ω Q and ω C are defined as [16] Clearly, one has 0 ≤ ω C (µ ψ , µ φ ) ≤ ω Q (|ψ , |φ ) ≤ 1 in any model that reproduces quantum measurement statistics [12]. Indeed, given λ one can reproduce the optimal quantum measurement that gives a probability 1 − ω Q (|ψ , |φ )/2 of distinguishing the two preparations; the optimal classical strategy for distinguishing µ ψ and µ φ cannot give a lower probability of success.…”

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confidence: 99%

“…In this respect, Maroney and Leifer [9][10][11] showed that a certain (asymmetric) measure of overlap of classical probability distributions had to be smaller than | φ|ψ | 2 for some quantum states |ψ , |φ in any Hilbert space of dimension d ≥ 3. Barrett et al [16] showed that the ratio between two directly comparable measures for the classical and quantum overlaps had to scale at most like 1/d for certain pairs of quantum states when the dimension d increases, while Leifer [18] exhibited states for which the same ratio has to decrease exponentially with d. Following these works, and in particular the approach of Barrett et al…”

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Howψ-Epistemic Models Fail at Explaining the Indistinguishability of Quantum States

Branciard

2014

Phys. Rev. Lett.

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We study the extent to which ψ-epistemic models for quantum measurement statistics-models where the quantum state does not have a real, ontic status-can explain the indistinguishability of nonorthogonal quantum states. This is done by comparing the overlap of any two quantum states with the overlap of the corresponding classical probability distributions over ontic states in a ψ-epistemic model. It is shown that in Hilbert spaces of dimension d ≥ 4, the ratio between the classical and quantum overlaps in any ψ-epistemic model must be arbitrarily small for certain nonorthogonal states, suggesting that such models are arbitrarily bad at explaining the indistinguishability of quantum states. For dimensions d = 3 and 4, we construct explicit states and measurements that can be used experimentally to put stringent bounds on the ratio of classical-to-quantum overlaps in ψ-epistemic models, allowing one in particular to rule out maximally ψ-epistemic models more efficiently than previously proposed.Despite its central role, the quantum state remains one of the most mysterious objects of quantum theory. Does it correspond to any physical reality, or does it merely represent one's information on a quantum system? These questions have triggered intense debates among physicists and philosophers since the advent of quantum theory, and are still the subject of active research in the study of quantum foundations.The general framework of ontological models [1] proposes a rigorous approach to address such questions. This framework presupposes the existence of underlying states of physical reality-ontic states-and describes the quantum state as a state of knowledge-an epistemic stateabout the actual ontic state of a given quantum system, represented by a probability distribution over the set of ontic states. A fundamental distinction is made between so-called ψ-ontic models, in which any underlying ontic state determines the quantum state uniquely, and socalled ψ-epistemic models, where the same ontic state can be compatible with different quantum states; i.e., the probability distributions corresponding to two different quantum states can overlap. In the former case, the ontic state "encodes" the quantum state, which can hence be understood as a physical property of the system, while in the latter case the quantum state cannot be given the status of a real physical property.The epistemic view of the quantum state is quite attractive, as it gives a natural explanation to many puzzling quantum phenomena [2]-including, for instance, the collapse of the wave function, or the impossibility to perfectly distinguish nonorthogonal quantum states. However, it has been shown that ψ-epistemic models must be severely constrained if they are to reproduce the statistics of quantum measurements. Notably, Pusey, Barrett, and Rudolph showed that no ψ-epistemic models satisfying some natural independence condition for composite systems can reproduce quantum predictions [3]. A number of other no-go theorems have since been proven, under various a...

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Eight Oxford Questions: Quantum Mechanics Under a New Light

Ares

Pearson

Briggs

2020

Fundamental Theories of Physics

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Noψ-Epistemic Model Can Fully Explain the Indistinguishability of Quantum States

Cited by 126 publications

References 33 publications

ψ-Epistemic Models are Exponentially Bad at Explaining the Distinguishability of Quantum States

ψ-Epistemic Models are Exponentially Bad at Explaining the Distinguishability of Quantum States

Howψ-Epistemic Models Fail at Explaining the Indistinguishability of Quantum States

Eight Oxford Questions: Quantum Mechanics Under a New Light

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