Probability density of quantum expectation values

Venuti, Lorenzo Campos; Zanardi, Paolo

doi:10.1016/j.physleta.2013.05.041

Cited by 6 publications

(4 citation statements)

References 28 publications

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“…For completeness, we will give a different proof of it although the following result is already obtained in [28]:…”

Section: Then the Pdf Of Amentioning

confidence: 99%

“…The Duistermaat-Heckman measure on moment polytope has been used to derive the probability distribution density of one-body quantum marginal states of multipartite random quantum states [24,25] and that of classical probability mixture of random quantum states [26,27]. As a function of random quantum pure states, the probability density function (PDF) of the quantum expectation value of an observable is also analytical calculated [28]. Motivated by these works, we investigate the joint PDFs of uncertainties of observables.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Probability density functions of quantum mechanical observable uncertainties

Zhang¹,

Huang²,

Wang³

et al. 2022

Commun. Theor. Phys.

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We study the uncertainties of quantum mechanical observables, quantified by the standard deviation (square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions (PDFs) of the uncertainties of arbitrary qubit observables. Based on these PDFs, the uncertainty regions of the observables are characterized by the supports of the PDFs. The state-independent uncertainty relations are then transformed into the optimization problems over uncertainty regions, which opens a new vista for studying state independent uncertainty relations. Our results may be generalized to multiple observable case in higher dimensional spaces.

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“…For completeness, we will give a different proof of it although the following result is already obtained in [28]:…”

Section: Then the Pdf Of Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probability density functions of quantum mechanical observable uncertainties

Zhang¹,

Huang²,

Wang³

et al. 2022

Commun. Theor. Phys.

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show abstract

“…In this framework, the ensemble defines the equilibrium and the wave functions are possible realizations of the equilibrium state. A key point of this approach is that we are considering a statistical distribution of quantum states; therefore, we can also define the corresponding ensemble distribution of observables . As an example, by drawing random pure states from the subspace Π E centered at energy E , we will obtain a distribution on the energy expectation value with statistical variance on the ensemble vanishing for N → ∞ (strong typicality).…”

Section: Introductionmentioning

confidence: 99%

Thermal Pure States for Finite and Isolated Quantum Systems

et al. 2017

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We study an ensemble of quantum pure states, the thermalization resilient ensemble (TRE), providing the statistical characterization of the thermal equilibrium of isolated quantum systems. Following a previous work where the ensemble was defined based on the invariance of the average populations upon thermal contact of identical systems, here we introduce a general methodology to generate quantum states according to the TRE statistic. The sampling is employed to characterize the ensemble distribution of thermodynamic functions like the entropy, internal energy, and temperature. The possibility of defining the temperature also for isolated quantum systems with a limited number of degrees of freedom is a distinctive feature of the TRE statistic which has no counterpart in other quantum statistical ensembles. The results are illustrated by explicit calculations for spin model systems.

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“…These ideas have been adopted with different degrees of intensity by several authors in the last years using even different distributions (see Refs. [10][11][12][13][14][15][16][17][18][19][20][21][22] for some examples). In this work we focus on the particular state-space distribution introduced in Refs.…”

Section: Introductionmentioning

confidence: 99%

Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble

et al. 2015

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Schrodinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schrodinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system.In this work we focus on one of the best known of these distributions, and we prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schrödinger's idea can not be used to construct an appropriate quantum equilibrium thermodynamics.

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Probability density of quantum expectation values

Cited by 6 publications

References 28 publications

Probability density functions of quantum mechanical observable uncertainties

Probability density functions of quantum mechanical observable uncertainties

Thermal Pure States for Finite and Isolated Quantum Systems

Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble

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