Coherence measures with respect to general quantum measurements

Abstract

Quantum coherence with respect to orthonormal bases has been studied extensively in the past few years. Recently, Bischof, et al. [Phys. Rev. Lett. 123, 110402 (2019)] generalized it to the case of general positive operator-valued measure (POVM) measurements. Such POVM-based coherence, including the block coherence as special cases, have significant operational interpretations in quantifying the advantage of quantum states in quantum information processing. In this work we first establish an alternative framework for quantifying the block coherence and provide several block coherence measures. We then present several coherence measures with respect to POVM measurements, and prove a conjecture on the l1-norm related POVM coherence measure.

Quantifying coherence with respect to general measurements via quantum Fisher information

“…It has been proved that (B2)+(B5) is equivalent to (B3)+(B4) [10] hence (B5) provide an alternative way for verifying a block coherence measure. For many cases verifying (B2)+(B5) is easier than verifying (B3)+(B4) [10].…”

“…So we expect that some of these standard coherence measures can be generalized to be the corresponding POVM coherence measures. In fact, several standard coherence measures have been properly generalized to be POVM coherence measures, such as the relative entropy of POVM coherence [1,5,7], robustness of POVM coherence [6,8,9], l 1 norm of POVM coherence [1,6,10], and the POVM coherence based on the Tsallis entropy [10][11][12][13][14]. Also, there is a physical interpretation for the relative entropy of POVM coherence * Electronic address: xxujianwei@nwafu.edu.cn [6].…”

The block-coherence measures and the coherence measures based on positive-operator-valued measures

“…[20]. In the resource theory of blockcoherence, the block-incoherent states can be considered to be generated by a von Neumann measurement P = {P i }, i = 1, 2, • • • , d, i.e., the block-incoherent state σ = d i=1 P i ρP i for state ρ ∈ S, where S denotes the set of quantum states on the Hilbert space H, the rank of the orthogonal projector P i is arbitrary and the orthogonal projectors form a complete set, i.e., [20][21][22].…”

Quantum Discord for multiqubit Systems

“…Understanding and quantifying various quantum correlations are the primary goals in quantum information theory. The quantum entanglement and nonlocal correlations can be considered the most fundamental resources in quantum information processing [1,2,[14][15][16][17][18][19][20], which are tightly related to quantum coherence [21][22][23][24][25][26].…”