Entropy distance: New quantum phenomena

Weis, Stephan; Knauf, Andreas

doi:10.1063/1.4757652

Cited by 25 publications

(49 citation statements)

References 36 publications

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“…It may seem counter-intuitive that both the maximum entropy inference * ρ and its entropy can be discontinuous [9] as functions of the local measurement data α. When we say * ρ is discontinuous, we mean the state itself, not its entropy, is discontinuous.…”

Section: The General Casementioning

confidence: 99%

“…By the principle of maximum entropy, the best such inference compatible with the given local measurement results is the unique quantum state * ρ with the maximum von Neumann entropy [7]. It is known that in the classical case, the maximum entropy inference is continuous [7,9,24]. This means that, for any two sets of local measurement results α and α′ close to each other, the corresponding inference * ( ) α ρ and * ( ) α ρ ′ are also close to each other.…”

Section: Introductionmentioning

confidence: 99%

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Discontinuity of maximum entropy inference and quantum phase transitions

Chen

et al. 2015

New J. Phys.

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In this paper, we discuss the connection between two genuinely quantum phenomena-the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit.

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Section: The General Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discontinuity of maximum entropy inference and quantum phase transitions

Chen

et al. 2015

New J. Phys.

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“…However it is known that the MaxEnt procedure possesses a discontinuity in the quantum-mechanical case: arbitrarily small changes in values of the Q i constraints can produce large changes in the associated generalized Gibbs state. This feature is due to non-commutativity [45,46], and has connections with quantum phase transitions in many-body quantum systems [47]. In contrast to the analysis conducted here, the way in which this non-commutativity is detected is through the varying of the external constraints (for example the switching of classical field strengths).…”

Section: Discussionmentioning

confidence: 96%

Quantum Thermodynamics with Multiple Conserved Quantities

Mingo

Guryanova

Faist

et al. 2018

Fundamental Theories of Physics

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In this chapter we address the topic of quantum thermodynamics in the presence of additional observables beyond the energy of the system. In particular we discuss the special role that the generalized Gibbs ensemble plays in this theory, and derive this state from the perspectives of a micro-canonical ensemble, dynamical typicality and a resource-theory formulation. A notable obstacle occurs when some of the observables do not commute, and so it is impossible for the observables to simultaneously take on sharp microscopic values. We show how this can be circumvented, discuss information-theoretic aspects of the setting, and explain how thermodynamic costs can be traded between the different observables. Finally, we discuss open problems and future directions for the topic.

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“…The maximum-entropy states are known as thermal states because they describe systems in thermal equilibrium [5,81]. Discontinuities of ρ * A exist [78] if H 0 H 1 = H 1 H 0 and d ≥ 3. All discontinuity points lie in the relative boundary of W and they are non-removable, in the sense that there is no continuous extension of ρ * A from the relative interior 3 of W to them, see Thm.…”

Section: Introductionmentioning

confidence: 99%

Signatures of quantum phase transitions from the boundary of the numerical range

Spitkovsky

Weis

2018

Journal of Mathematical Physics

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The ground state energy of a finite-dimensional one-parameter Hamiltonian and the continuity of a maximum-entropy inference map are discussed in the context of quantum critical phenomena. The domain of the inference map is a convex compact set in the plane, called the numerical range. We study the differential geometry of its boundary in relation to the ground state energy. We prove that discontinuities of the inference map correspond to C 1 -smooth crossings of the ground state energy with a higher energy level. Discontinuities may appear only at C 1 -smooth points of the boundary of the numerical range considered as a manifold. Discontinuities exist at all C 2 -smooth non-analytic boundary points and are essentially stronger than at analytic points or at points which are merely C 1 -smooth (non-exposed points).2010 Mathematics Subject Classification. 82B26, 52A10, 47A12, 15A18, 32C25, 62F30, 94A17, 54C08, 46T20.

show abstract

Entropy distance: New quantum phenomena

Cited by 25 publications

References 36 publications

Discontinuity of maximum entropy inference and quantum phase transitions

Discontinuity of maximum entropy inference and quantum phase transitions

Quantum Thermodynamics with Multiple Conserved Quantities

Signatures of quantum phase transitions from the boundary of the numerical range

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