Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory

Pati, Arun Kumar; Wilde, Mark M.; Devi, A. R. Usha; Rajagopal, A. K.; Sudha,

doi:10.1103/physreva.86.042105

Cited by 155 publications

(122 citation statements)

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“…While the left hand side of the theorem in [7] is 1 9 (2 − p − 3 − 3p 2 )(4 + p + 3 − 3p 2 ) and the right hand side is 0. From the result in [4], the left hand side is − 2(2−p) 3 log 2 2−p 6 − 2(1+p) 3 log 2 1+p 6 − 2, the bound is the same as the left hand side, see Fig. 1 for comparision.…”

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confidence: 70%

“…The result of [3] was further improved to depend on the quantum discord between particles A and B in [4]. Recently the authors in [5] obtained entropic uncertainty relations for multiple measurements with quantum memory.…”

Section: Pacs Number(s)mentioning

confidence: 99%

“…Figure 1 Axe y is the uncertainty and its lower bound. The result in [4] is represented by blue thick line, the corresponding lower bound is represented by blue dotted line; the result in [7] is represented by green dotdashed line, the lower bound is 0; the left hand side of our theorem is represented by blue dashed line and the lower bound of our theorem is represented by red line.…”

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confidence: 99%

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Uncertainty relations based on skew information with quantum memory

Ma¹,

Chen²,

Fei³

2016

Sci. China Phys. Mech. Astron.

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PACS number(s): 03.67. 75.10.Pq, 03.67.Mn Dear Editors, Uncertainty principle is one of the most fascinating features of the quantum world. It asserts a fundamental limit on the precision with which certain pairs of physical properties of a particle, such as position and momentum, can not be simultaneously known. The uncertainty principle has attracted considerable attention since the innovation of quantum mechanics and has been investigated in terms of various types of uncertainty inequalities: as informational recourses in entropic terms, by means of majorization technique and based on sum of variances and standard deviations.For a pair of observables R and S , the well-known Heisenberg-Robertson uncertainty relation [1] says that,, where [R, S ] = RS − S R is the commutator and V ρ (R) is the standard deviation of R. The entropies serve as appropriate measures of the information content. It is also used to quantify the quantum uncertainty: the sum of the Shannon entropy of the probability distribution of the outcomes is no less than log 2 1 c [2] when R and S are measured. The term 1/c quantifies the complementarity of the two observables R and S . It has been proved that the entropy uncertainty relations do imply the Heisenberg's uncertainty relation.Concerning bipartite systems, the authors in [3] provided a bound on the uncertainties which depends on the amount of entanglement between the measured particle A and the quantum memory B. The result of [3] was further improved to depend on the quantum discord between particles A and B in [4]. Recently the authors in [5] obtained entropic uncertainty relations for multiple measurements with quantum memory.The quantum uncertainty relation can be also described in terms of skew information. I (ρ, H) = − 1 2 Tr √ ρ, H 2 is introduced to quantify the degree of non-commutativity of a state ρ and an observable H, which is reduced to the variance V ρ (H) when ρ is a pure state [6]. It can be interpreted as quantum uncertainty of H in ρ. Luo introduced another quantity, where {X, Y} is the anticommutator, H 0 = H − Tr(ρH)I with I the identity operator. The following inequality holds [7],I (ρ, R) J ρ (R) can be regarded as a kind of measure for quantum uncertainty.Hence we define UN(ρ, R) := I (ρ, R) J ρ (R). Then we define the uncertainty of ρ associated to the projective measurement {φ k } as:, where φ k = |φ k φ k | and ψ k = |ψ k ψ k | are the rank one spectral projectors of two non-degenerate observables R and S with eigenvectors |φ k and |ψ k , respectively. Now we consider the case of bipartite state ρ AB in tensor space H A ⊗ H B [8]. Recall that quantum discord is a kind of quantum correlation that is different from the entanglement and has found many novel applications [9]. A bipartite state ρ AB is of zero discord if and only if it is a classical-quantum correlated state (CQ state). Besides the definition of the original discord, there are some other discord-like measures sharing the same properties such that their values are zero iff the state is a CQ sta...

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confidence: 70%

Section: Pacs Number(s)mentioning

confidence: 99%

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confidence: 99%

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Uncertainty relations based on skew information with quantum memory

Ma¹,

Chen²,

Fei³

2016

Sci. China Phys. Mech. Astron.

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“…S(A|B) is negative if S(ρ A ) = 0, i.e., ρ A = |µ µ|, with |µ being the orthonormal basis of H A . Recently, a necessary and sufficient equality condition for the inequality (16) was derived in [39]. It states that S(ρ B ) − S(ρ A ) = S(ρ AB ) if and only if the complex Hilbert space H B can be factorized…”

Section: Negative Conditional Entropymentioning

confidence: 99%

“…Meanwhile, the related relations expressed by other entropic quantities, such as the Rényi entropy which is important in physical models [8], are also exploited [9,10]. Since it has a fundamental role, this quantum-memory-assisted entropic uncertainty relation can be studied from various viewpoints [11][12][13], and can be applied to other quantum information processes [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Competition between quantum correlations in the quantum-memory-assisted entropic uncertainty relation

Fan

2013

Phys. Rev. A

117

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With the aid of a quantum memory, the uncertainty about the measurement outcomes of two incompatible observables of a quantum system can be reduced. We investigate this measurement uncertainty bound by considering an additional quantum system connected with both the quantum memory and the measured quantum system. We find that the reduction of the uncertainty bound induced by a quantum memory, on the other hand, implies its increasing for a third participant. We also show that the properties of the uncertainty bound can be viewed from perspectives of both quantum and classical correlations, in particular, the behavior of the uncertainty bound is a result of competitions of various correlations between different parties.

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Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

et al. 2018

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The Heisenberg uncertainty principle describes a basic restriction on an observer's ability of precisely predicting the measurement of a pair of noncommuting observables, and virtually is at the core of quantum mechanics. Herein, the aim is to study the entropic uncertainty relation (EUR) under the background of a Schwarzschild black hole and its control. Explicitly, dynamical features of the measuring uncertainty via entropy are developed in a practical model where a stationary particle interacts with its surrounding environment while another particle-serving as a quantum memory reservoir-undergoes free fall in the vicinity of the event horizon of the Schwarzschild space-time. It shows higher Hawking temperatures would give rise to an inflation of the entropic uncertainty on the measured particle. This is suggestive of the fact the measurement uncertainty is strongly correlated with degree of mixing present in the evolving particles. Additionally, based on information flow theory, a physical interpretation for the observed dynamical behaviors related with the entropic uncertainty in such a genuine scenario is provided. Finally, an efficient strategy is proposed to reduce the uncertainty by non-tracing-preserved operations. Therefore, our explorations may improve the understanding of the dynamic entropic uncertainty in a curved space-time, and illustrate predictions of quantum measurements in relativistic quantum information sciences.

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Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory

Cited by 155 publications

References 31 publications

Uncertainty relations based on skew information with quantum memory

Uncertainty relations based on skew information with quantum memory

Competition between quantum correlations in the quantum-memory-assisted entropic uncertainty relation

Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

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