Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction

Budiyono, Agung; Rohrlich, Daniel

doi:10.1038/s41467-017-01375-w

Cited by 42 publications

(106 citation statements)

References 60 publications

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“…t /2to hold simultaneously, and validate the uncertainty relation(31). These inequalities impose an upper bound for time as a function of σ 0 , in such a way that the greater σ 0 the greater the time domain within which the irrealities are valid nonnegative quantities and the discretized model applies.…”

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confidence: 59%

Quantifying continuous-variable realism

Freire

Angelo

2019

Phys. Rev. A

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The debate instigated by the seminal works of Einstein, Podolsky, Rosen, and Bell put the notions of realism and nonlocality at the core of almost all philosophical and physical discussions underlying the foundations of quantum mechanics. However, while experimental criteria and quantifiers are by now well established for nonlocality, there is no clear quantitative measure for the degree of reality associated with continuous variables such as position and momentum. This work aims at filling this gap. Considering position and momentum as effectively discrete observables, we implement an operational notion of projective measurement and, from that, a criterion of reality for theses quantities. Then we introduce a quantifier for the degree of irreality of a discretized continuous variable which, when applied to the conjugated pair position-momentum, is shown to obey an uncertainty relation, meaning that quantum mechanics prevents classical realism for conjugated quantities. As an application of our formalism, we study the emergence of elements of reality in an instance where a Gaussian state is submitted to the dissipative dynamics implied by the Caldirola-Kanai Hamiltonian. In particular, at equilibrium, we make some links with the measurement problem and identify aspects that can be taken as the quantum counterpart for the notion of rest.

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confidence: 59%

Quantifying continuous-variable realism

Freire

Angelo

2019

Phys. Rev. A

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“…We have also argued in Ref [18] that the epistemic restriction of Eqs. (2) or (6) 6) and (3) to further respect the conservation of average energy and trajectories (probability current) [18]. This includes those that describe quantum dynamical interactions between subsystems, generating quantum entanglement.…”

Section: =ô (See Sectionmentioning

confidence: 78%

“…, N. It describes a momentum field fluctuating randomly due to the fluctuation of ξ. As argued in Ref [18],. Eq.…”

mentioning

confidence: 88%

“…(6). Note however that Wiseman's starting point is standard quantum mechanics, while we started from a statistical phase space model to reconstruct quantum mechanics from scratch using the notion of epistemic restriction parameterized by a global variable ξ fluctuating randomly on the order of Planck constant [18].…”

Section: Namely We Have Tr{̺ô}mentioning

confidence: 99%

“…Partly motivated by this conceptual problem, a novel phase space representation for quantum mechanics was proposed in Ref. [18]. In the phase space representation, a quantum wave function is associated with a phase space distribution which explicitly incorporates a specific epistemic restriction parameterized by a global random variable on the order of Planck constant, transparently manifesting quantum uncertainty relation in a classical phase space.…”

Section: Introductionmentioning

confidence: 99%

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Epistemically restricted phase-space representation, weak momentum value, and reconstruction of the quantum wave function

Budiyono

2019

Phys. Rev. A

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A phase space distribution associated with a quantum state was previously proposed, which incorporates a specific epistemic restriction parameterized by a global random variable on the order of Planck constant, transparently manifesting quantum uncertainty in phase space. Here we show that the epistemically restricted phase space (ERPS) distribution can be determined via weak measurement of momentum followed by post-selection on position. In the ERPS representation, the phase and amplitude of the wave function are neatly captured respectively by the positiondependent (conditional) average and variance of the epistemically restricted momentum fluctuation.They are in turn respectively determined by the real and imaginary parts of the weak momentum value, permitting a reconstruction of wave function using weak momentum value measurement, and an interpretation of momentum weak value in term of epistemically restricted momentum fluctuations. The ERPS representation thus provides a transparent and rich framework to study the deep conceptual links between quantum uncertainty embodied in epistemic restriction, quantum wave function, and weak momentum measurement with position post-selection, which may offer useful insight to better understand their meaning.

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Detecting Quantum Phase Transitions in Spin Chains

Lin

2022

Quantum Science and Technology

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We study three aspects of work statistics in the context of the fluctuation theorem for the quantum spin chains by numerical methods based on matrix-product states. First, we elaborate that the work done on the spin-chain by a sudden quench can be used to characterize the quantum phase transitions (QPT). We further obtain the numerical results to demonstrate its capability of characterizing the QPT of both Landau-Ginzbrug types, such as the Ising chain, or topological types, such as the Haldane chain. Second, we propose to use the fluctuation theorem, such as Jarzynski's equality, which relates the real-time correlator to the ratio of the thermal partition functions, as a benchmark indicator for the numerical real-time evolving methods. Third, we study the passivity of ground and thermal states of quantum spin chains under some cyclic impulse processes. We verify the passivity of thermal states. Furthermore, we find that some ground states in the Ising-like chain, with less overall spin order from spontaneous or explicit symmetry breaking, can be active so that they can be exploited for quantum engines.

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Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction

Cited by 42 publications

References 60 publications

Quantifying continuous-variable realism

Quantifying continuous-variable realism

Epistemically restricted phase-space representation, weak momentum value, and reconstruction of the quantum wave function

Detecting Quantum Phase Transitions in Spin Chains

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