From quantum coherence to quantum correlations

Abstract

In quantum mechanics, quantum coherence of a state relative to a quantum measurement can be identified with the quantumness that has to be destroyed by the measurement. In particular, quantum coherence of a bipartite state relative to a local quantum measurement encodes quantum correlations in the state. If one takes minimization with respect to the local measurements, then one is led to quantifiers which capture quantum correlations from the perspective of coherence. In this vein, quantum discord, which quantifies the minimal correlations that have to be destroyed by quantum measurements, can be identified as the minimal coherence, with the coherence measured by the relative entropy of coherence. To advocate and formulate this idea in a general context, we first review coherence relative to Lüders measurements which extends the notion of coherence relative to von Neumann measurements (or equivalently, orthonomal bases), and highlight the observation that quantum discord arises as minimal coherence through two prototypical examples. Then, we introduce some novel measures of quantum correlations in terms of coherence, illustrate them through examples, investigate their fundamental properties and implications, and indicate their applications to quantum metrology.

Quantum correlations for anonymous metrology

“…The anonymity resources should arguably be viewed as a hybrid of coherence and correlation. One could describe it as correlated coherence, though this appears distinct from the correlated coherence of [34][35][36][37].…”

“…We can view WA states as having correlated coherence in the eigenbasis of the unitaries. There is a formal similarity with the correlated coherence defined in [34][35][36][37].…”

Geometric measures of discordlike quantum correlations based on Tsallis relative entropy

“…Recently, the coherence measures are generalized to Lüders measurement picture as a partial coherence quantification [21] [22] [23] [24]. In this section we show that the coherence measure in terms of quantum Tsallis relative entropy can be also generalized into this setting.…”

Analytically Computable Symmetric Quantum Correlations

“…[26][27][28][29][30][31][32][33][34][35][36][37][38][39] The same is true for its counterpart quantity, [40][41][42] that is, the measurementinduced nonlocality (MIN) which characterizes the global disturbance in a composite state caused by a local nondisturbing measurement on one subsystem. In particular, with the development of the resource theory of quantum coherence, [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70] it was shown that the coherence of a system could be converted through incoherent operations into the SQD, instead of the asymmetric QD, of a composite system. [42][43][44][45][46][47][48][49] However, neither the QD nor the MIN of a bipartite system is symmetric in the sense that different results will be obtained (especially for some zero-discord states) if the two subsystems are swapped, which implies that the QD and MIN cannot completely quantify all of the quantum correlations present in a state.…”

“…[40] Recently, some progress has been made in regard to analytical expressions for certain classes of states or effective numerical methods. [54,65,66] By considering different bases, the coherence can also be related to the SMIN. To overcome this shortcoming, symmetric versions of the QD and the MIN are defined, that is, the symmetric quantum discord (SQD) [50][51][52] and the symmetric measurement-induced nonlocality (SMIN).…”