Basis-independent quantum coherence and its distribution

Abstract

We analyze a basis-independent definition of quantum coherence. The maximally mixed state is used as the reference state, which allows for a way of defining coherence that is invariant under arbitrary unitary transformations. The basis-independent approach is applied to finding the distri- bution of the coherence within a multipartite system, where the contributions due to correlations between the subsystems and within each subsystem are isolated. The use of the square root of the Jensen-Shannon divergence allows for inequality relations to be derived between these quantities, giving a geometrical picture within the Hilbert space of the system. We describe the relationship between the basis-independent and the basis-dependent approaches, and argue that many advan- tages exist for the former method. The formalism is illustrated with several numerical examples which show that the states can be characterized in a simple and effective manner.

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• Certifying nonstabilizerness in quantum processors
• Absolute dimensionality of quantum ensembles
• Polynomially restricted operator growth in dynamically integrable models
• Basis-independent Coherence in Noninertial Frames
• Distance-based approach to quantum coherence and nonclassicality
• Probabilistic Coherence Transformation Under Strictly Incoherent Operation
• Frame-dependent coherence of a quantum state