Estimation on Geometric Measure of Quantum Coherence

Zhang, Haijun; Chen, Bin; Li, Ming; Fei, Shao-Ming; Long, Gui Lu

doi:10.1088/0253-6102/67/2/166

Cited by 46 publications

(38 citation statements)

References 34 publications

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“…where |a| 2 + |b| 2 ≤ 1. Then we have C l 1 (ρ) = 2|b| and C g (ρ) = [20]. It can be seen that C l 1 (ρ) and C g (ρ) are both increasing functions with respect to |b|.…”

Section: Ordering States With Coherence Measuresmentioning

confidence: 90%

Ordering states with various coherence measures

Yang

Chen

Fei

et al. 2018

Quantum Inf Process

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Quantum coherence is one of the most significant theories in quantum physics.Ordering states with various coherence measures is an intriguing task in quantification theory of coherence. In this paper, we study this problem by use of four important coherence measures -the l 1 norm of coherence, the relative entropy of coherence, the geometric measure of coherence and the modified trace distance measure of coherence. We show that each pair of these measures give a different ordering of qudit states when d ≥ 3. However, for single-qubit states, the l 1 norm of coherence and the geometric coherence provide the same ordering. We also show that the relative entropy of coherence and the geometric coherence give a different ordering for single-qubit states. Then we partially answer the open question proposed in [Quantum Inf. Process. 15, 4189 (2016)] whether all the coherence measures give a different ordering of states.Keywords l 1 -norm of coherence, relative entropy of coherence, geometric measure of coherence, modified trace distance of coherence, ordering states.

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“…where |a| 2 + |b| 2 ≤ 1. Then we have C l 1 (ρ) = 2|b| and C g (ρ) = [20]. It can be seen that C l 1 (ρ) and C g (ρ) are both increasing functions with respect to |b|.…”

Section: Ordering States With Coherence Measuresmentioning

confidence: 90%

Ordering states with various coherence measures

Yang

Chen

Fei

et al. 2018

Quantum Inf Process

Self Cite

View full text Add to dashboard Cite

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“…Calculating the matrix L t = XD t X −1 , we finally have η t/2 B B cosh φt − A − sinh φt sinh φt sin 2θ − η sinh φt sin 2θ B cosh φt + A − sinh φt , since A 2 − − B 2 = η sin 2 2θ. Due to r x (0) = sin θ and r z (0) = cos θ, we finally get (33) and (34). The original Grover search is beyond the case (ii).…”

Section: Appendix A: Solutions Of the Recursion Equationmentioning

confidence: 99%

“…The geometric coherence is an interesting quantifier of different character [23]. Twosided estimates on the geometric coherence were obtained in [34]. Complementarity relations for quantum coherence can be formulated in several ways [35][36][37][38][39].…”

Section: Preliminariesmentioning

confidence: 99%

Degradation of Grover’s search under collective phase flips in queries to the oracle

Rastegin

2018

Front. Phys.

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We address the case, when querying to the oracle in Grover's algorithm is exposed to noise including phase distortions. The oracle-box wires can be altered by an opposite party that tries to prevent correct receiving data from the oracle. This situation reflects an experienced truth that any access to prophetic knowledge cannot be common and direct. To study the problem, we introduce a simple model of collective phase distortions on the base of phase damping channel. In the model used, the success probability is not altered via the oracle-box wires per se. Phase distortions of the considered type can hardly be detected via any one-time query to the oracle. However, the success probability is significantly changed, when such errors are introduced as an intermediate step into the Grover iteration. We investigate the success probability with respect to variations the parameter that characterizes the amount of phase errors. It turns out that the success probability is decreased significantly even if the error amount is not very high. Moreover, this probability quickly reduces to the value of one half, which corresponds to the completely mixed state. We also study trade-off relations between quantum coherence and the success probability in the presence of noise of the considered type.

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“…In literature, an upper and lower bound of the geometric coherence measure is proposed in Ref. [42]. In this work, we focus on numerical calculations of C g , C max , C min based on the unified definition in the last section.…”

Section: Computing the Coherence Measure Via Sdpmentioning

confidence: 99%

Quantum coherence via conditional entropy

Liu

Zhao

Yuan

2018

J. Phys. A: Math. Theor.

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Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated and quantified. Operationally, considering the projective measurement of the state in the computational basis, coherence quantifies the intrinsic randomness of the measurement outcome conditioned on all the other quantum systems. However, such a relation is only proven when randomness is characterized by the Von-Neumann entropy. In this work, we consider several recently proposed coherence measures and relate them to the general uncertainties of the projective measurement outcome conditioned on all the other systems. Our work thus provides a unified framework for redefining several coherence measures via general conditional entropies. Based on the relation, we numerically calculate the coherence measures via semi-definite programming. Furthermore, we discuss the operational meaning of the unified definition. Our result highlights the close relation between single partite coherence and bipartite quantum correlation.

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Estimation on Geometric Measure of Quantum Coherence

Cited by 46 publications

References 34 publications

Ordering states with various coherence measures

Ordering states with various coherence measures

Degradation of Grover’s search under collective phase flips in queries to the oracle

Quantum coherence via conditional entropy

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