<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ψ</mml:mi></mml:math>-epistemic theories: The role of symmetry

Aaronson, Scott; Bouland, Adam; Chua, Lynn; Lowther, George

doi:10.1103/physreva.88.032111

Cited by 78 publications

(151 citation statements)

References 14 publications

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“…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, and it is ψ-epistemic otherwise.…”

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confidence: 99%

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: 99%

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

Leifer

2014

Phys. Rev. Lett.

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“…Ref. [15] goes further, demonstrating that for a quantum system of arbitrary dimension, a ψ-epistemic model exists with the additional property that ω C (µ ψ , µ φ ) > 0 for every pair of non-orthogonal states |ψ and |φ . Refs.…”

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“…It is interesting to investigate what can be established without this assumption. Various works have investigated what can be concluded by considering measurements on a single system only, i.e, without any assumption about independent systems [11][12][13][14][15]. Here, we consider a single quantum system, and derive bounds on the extent to which the probability distributions corresponding to distinct quantum states can overlap.…”

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

et al. 2014

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According to a recent no-go theorem (M. Pusey, J. Barrett and T. Rudolph, Nature Physics 8 475 (2012)), models in which quantum states correspond to probability distributions over the values of some underlying physical variables must have the following feature: the distributions corresponding to distinct quantum states do not overlap. This is significant because if the distributions do not overlap, then the quantum state itself is encoded by the physical variables. In such a model, it cannot coherently be maintained that the quantum state merely encodes information about underlying physical variables. The theorem, however, considers only models in which the physical variables corresponding to independently prepared systems are independent. This work considers models that are defined for a single quantum system of dimension d, such that the independence condition does not arise. We prove a result in a similar spirit to the original no-go theorem, in the form of an upper bound on the extent to which the probability distributions can overlap, consistently with reproducing quantum predictions. In particular, models in which the quantum overlap between pure states is equal to the classical overlap between the corresponding probability distributions cannot reproduce the quantum predictions in any dimension d ≥ 3. The result is noise tolerant, and an experiment is motivated to distinguish the class of models ruled out from quantum theory.No-go theorems such as Bell's [1] are of central importance to our understanding of quantum mechanics. Bell's theorem shows that locally causal models must make different predictions from quantum theory. In addition to the fundamental significance of this result, Bell's theorem has applications in quantum information processing, most notably in deviceindependent cryptography and randomness generation [2][3][4][5].Recently, a number of new no-go results have been derived, addressing a different question than whether nature can be described by a locally causal theory. The question concerns whether the quantum state should be viewed as a description of the physical state of a system, or as an observer's information about the system. Many authors (see, e.g., Refs. [6][7][8], and references therein) have argued for the latter, pointing out, for example, that quantum collapse is analogous to Bayesian updating of a classical probability distribution when new data is obtained, or that the indistinguishability of nonorthogonal quantum states is analogous to the indistinguishability of overlapping probability distributions. Ref. [9], following Ref. [10], considers models of a specific form, in which the quantum state corresponds to a probability distribution over some set of underlying physical states, hence can be thought of as representing an observer's partial information about the physical state. It is shown that such models cannot recover the quantum predictions unless the distributions are disjoint for distinct quantum states. Roughly speaking, if the assumptions of Ref. [9] are accepted,...

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“…From Born and Heisenberg arguing for a probabilistic interpretation to date it is in discussion about whether ψ-ontology of the wave-function is ontic or epistemic (Pusey et al, 2012, Aaronson et al, 2013, Leifer 2014. It is a delicate matter.…”

Section: Ontology Of I-observermentioning

confidence: 99%

Can ‘Theory of Everything’ Be Global Theory of Consciousness? Ontology and Psychodynamics of I-observer.

Yurchenko¹

2017

Neuroquantology

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The 'theory of everything' (TOE) is conceived to embrace all natural sciences Today the TOE is discussed mostly in physics. From Copenhagen interpretation to date, another discussion is widely unfolded on the role of consciousness in quantum experience and physical descriptions in general. The paper combines both the discussions and argues for a global theory of consciousness (GTC). It will be proven that the naturalistic postulate on the world's independent existence is not quite correct but requires independence of any privileged anthropic I-observer with regard to relational observer-dependent scenario. The stream ( ) of consciousness is introduced by analogy with causal set modeling in quantum cosmology as a Markov chain (or a Turing machine) taken to be a set of the instant I-World states. In dynamics, the cogito emerges to be an unclosed loop on ( ) related directly to ψ-ontology. Further, it can be naturally extended to the perpetum cogito mechanism that entangles the triple 'past-present-future'. In fact, it is a noncommutative algebra for physics on a boundary. I-observer moves in superposition through every current present and in 'back-position' towards the arrow of time.

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ψ-epistemic theories: The role of symmetry

Cited by 78 publications

References 14 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

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

Can ‘Theory of Everything’ Be Global Theory of Consciousness? Ontology and Psychodynamics of I-observer.

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