Entropic Energy-Time Uncertainty Relation

Coles, Patrick J.; Katariya, Vishal; Lloyd, Seth; Marvian, Iman; Wilde, Mark M.

doi:10.1103/physrevlett.122.100401

Cited by 40 publications

(59 citation statements)

References 55 publications

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“…We note that this coincides with the particular version of the recent result presented in Ref. [23], where the authors studied entropic formulations of energy-time uncertainty relation. Thus, any improvements over the permutohedron bound could also tighten inequalities derived there.…”

Section: A Permutohedron Bound and M -Distinguishabilitysupporting

confidence: 90%

Distinguishing classically indistinguishable states and channels

Korzekwa

Czachórski

Puchała

et al. 2019

J. Phys. A: Math. Theor.

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We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between M quantum states that become identical under a completely decohering map. Similarly, we study distinguishability of M quantum channels that cannot be distinguished when one is restricted to decohered input and output states. The studied problems arise naturally in the presence of a superselection rule, allow one to quantify the amount of information that can be encoded in phase degrees of freedom (coherences), and are related to time-energy uncertainty relation. We present a collection of results on both necessary and sufficient conditions for the existence of M perfectly distinguishable states (channels) that are classically indistinguishable.

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Section: A Permutohedron Bound and M -Distinguishabilitysupporting

confidence: 90%

Distinguishing classically indistinguishable states and channels

Korzekwa

Czachórski

Puchała

et al. 2019

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…(62) still holds if we jointly measure n quadratures on a larger N -dimensional system i.e. when the sum over k in equation (61) goes to N (with N > n) [56].…”

Section: Entropic Uncertainty Relation For Arbitrary Quadraturesmentioning

confidence: 99%

“…Similarly, Hall considered an entropic time-energy uncertainty relation for bound quantum systems (thus having discrete energy eigenvalues), which expresses the balance between a discrete entropy for the energy distribution and a continuous entropy for the time shift applied to the system [60]. Recently, an entropic time-energy uncertainty relation has also been formulated for general time-independent Hamiltonians, where the time uncertainty is associated with measuring the (continuous) time state of a quantum clock [61].…”

Section: Other Entropic Uncertainty Relationsmentioning

confidence: 99%

Continuous-variable entropic uncertainty relations

Hertz

Cerf

2019

J. Phys. A: Math. Theor.

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Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we review recent results on entropic uncertainty relations involving continuous variables, such as position x and momentum p. This includes the generalization to arbitrary (not necessarily canonically-conjugate) variables as well as entropic uncertainty relations that take x-p correlations into account and admit all Gaussian pure states as minimum uncertainty states. We emphasize that these continuous-variable uncertainty relations can be conveniently reformulated in terms of entropy power, a central quantity in the information-theoretic description of random signals, which makes a bridge with variance-based uncertainty relations. In this review, we take the quantum optics viewpoint and consider uncertainties on the amplitude and phase quadratures of the electromagnetic field, which are isomorphic to x and p, but the formalism applies to all such variables (and linear combinations thereof) regardless of their physical meaning. Then, in the second part of this paper, we move on to new results and introduce a tighter entropic uncertainty relation for two arbitrary vectors of intercommuting continuous variables that takes correlations into account. It is proven conditionally on reasonable assumptions. Finally, we present some conjectures for new entropic uncertainty relations involving more than two continuous variables.

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“…The aim of this work is to formulate entropic uncertainty relations for energy and its complement taken within the Pegg approach [37]. Our consideration is rather complementary to entropic uncertainty relations obtained recently in [36]. We present entropic uncertainty relations that are immediately related to measurement statistics.…”

Section: Introductionmentioning

confidence: 93%

“…The latter is rather inadequate clock for aperiodic systems. The quantum-clock view on time uncertainty was recently developed in [36].…”

Section: Introductionmentioning

confidence: 99%

On Entropic Uncertainty Relations for Measurements of Energy and Its “Complement”

Rastegin

2019

Annalen der Physik

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Reformulation of Heisenberg's uncertainty principle in application to energy and time is a powerful heuristic principle. In a qualitative form, this statement plays the important role in foundations of quantum theory and statistical physics. A typical meaning of energy-time uncertainties is as follows. If some state exists for a finite interval of time, then it cannot have a completely definite value of energy. It is also well known that the case of energy and time principally differs from more familiar examples of two non-commuting observables. Since quantum theory was originating, many approaches to energy-time uncertainties have been proposed. Entropic approach to formulating the uncertainty principle is currently the subject of active researches. Using the Pegg concept of complementarity of the Hamiltonian, we obtain uncertainty relations of the "energy-time" type in terms of the Rényi and Tsallis entropies. Although this concept is somehow restricted in scope, derived relations can be applied to systems typically used in quantum information processing. Both the state-dependent and state-independent formulations are of interest. Some of the derived stateindependent bounds are similar to the results obtained within a more general approach on the base of sandwiched relative entropies. In this regard, our relations provide an alternative viewpoint on such bounds. The developed approach also allows us to address the case of detection inefficiencies. It is worth for several reasons including possible information-processing applications.

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Entropic Energy-Time Uncertainty Relation

Cited by 40 publications

References 55 publications

Distinguishing classically indistinguishable states and channels

Distinguishing classically indistinguishable states and channels

Continuous-variable entropic uncertainty relations

On Entropic Uncertainty Relations for Measurements of Energy and Its “Complement”

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