Entanglement of a microcanonical ensemble

Verhulst, Tobias; Naudts, Jan

doi:10.1088/1751-8113/40/10/016

Cited by 13 publications

(14 citation statements)

References 19 publications

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“…Under such 'heavily thermodynamical' prescriptions -as are the ones we have adopted to construct the canonical and micro-canonical measures -equipartition prevents the entanglement from reaching the allowed maximum, evenly spreading the correlations between all the modes. Our measures, being compliant with the general canonical principle, should be suitable to the description of dynamical situations [36,18], also involving randomised interactions [7]. A systematic study of such processes -notably restricting to two-mode interactions, in the spirit of Ref.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Canonical and micro-canonical typical entanglement of continuous variable systems

Serafini¹,

Dahlsten²,

Gross³

et al. 2007

J. Phys. A: Math. Theor.

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Abstract. We present a framework, compliant with the general canonical principle of statistical mechanics, to define measures on the set of pure Gaussian states of continuous variable systems. Within such a framework, we define two specific measures, referred to as 'micro-canonical' and 'canonical', and apply them to study systematically the statistical properties of the bipartite entanglement of n-mode pure Gaussian states (as quantified by the entropy of a subsystem). We rigorously prove the "concentration of measure" around a finite average, occurring for the entanglement in the thermodynamical limit in both the canonical and the micro-canonical approach. For finite n, we determine analytically the average and standard deviation of the entanglement (as quantified by the reduced purity) between one mode and all the other modes. Furthermore, we numerically investigate more general situations, clearly showing that the onset of the concentration of measure already occurs at relatively small n.

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Section: Discussionmentioning

confidence: 99%

“…Let us finally mention that a definition of micro-canonical average entanglement has been very recently addressed for finite dimensional systems as well [18], with a major emphasis on the possibility of reducing time-averages to ensemble-averages. This paper is organised as follows.…”

Section: Typical Entanglement In Quantum Information Theorymentioning

confidence: 99%

Canonical and micro-canonical typical entanglement of continuous variable systems

Serafini¹,

Dahlsten²,

Gross³

et al. 2007

J. Phys. A: Math. Theor.

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“…In [16] it is shown how to replace the time average of non-linear quantities such as the entanglement by ensemble averages. This was applied by the present authors to study the entanglement of distinguishable particles [17].…”

Section: Average Entanglementmentioning

confidence: 99%

Ensemble-averaged entanglement of two-particle states in Fock space

Naudts

Verhulst

2007

Phys. Rev. A

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Recent results, extending the Schmidt decomposition theorem to wavefunctions of pairs of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band of the Hubbard model, and to a pair of bosons in the Bose-Hubbard model with infinite range hopping. The effect of degeneracy of the spectrum of the Hamiltonian on the average entanglement is emphasised.

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“…The logistic equation is a prototypical model for growth and spreading processes in nature [20]. It reads…”

Section: A Definitionmentioning

confidence: 99%

Extinction transitions in correlated external noise

2018

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We analyze the influence of long-range correlated (colored) external noise on extinction phase transitions in growth and spreading processes. Uncorrelated environmental noise (i.e., temporal disorder) was recently shown to give rise to an unusual infinite-noise critical point [Europhys. Lett. 112, 30002 (2015)EULEEJ0295-507510.1209/0295-5075/112/30002]. It is characterized by enormous density fluctuations that increase without limit at criticality. As a result, a typical population decays much faster than the ensemble average, which is dominated by rare events. Using the logistic evolution equation as an example, we show here that positively correlated (red) environmental noise further enhances these effects. This means, the correlations accelerate the decay of a typical population but slow down the decay of the ensemble average. Moreover, the mean time to extinction of a population in the active, surviving phase grows slower than a power law with population size. To determine the complete critical behavior of the extinction transition, we establish a relation to fractional random walks, and we perform extensive Monte Carlo simulations.

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Entanglement of a microcanonical ensemble

Cited by 13 publications

References 19 publications

Canonical and micro-canonical typical entanglement of continuous variable systems

Canonical and micro-canonical typical entanglement of continuous variable systems

Ensemble-averaged entanglement of two-particle states in Fock space

Extinction transitions in correlated external noise

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