Maximal coherence in generic basis

Abstract

Since quantum coherence is an undoubted characteristic trait of quantum physics, the quantification and application of quantum coherence has been one of the long-standing central topics in quantum information science. Within the framework of a resource theory of quantum coherence proposed recently, a \textit{fiducial basis} should be pre-selected for characterizing the quantum coherence in specific circumstances, namely, the quantum coherence is a \textit{basis-dependent} quantity. Therefore, a natural question is raised: what are the maximum and minimum coherences contained in a certain quantum state with respect to a generic basis? While the minimum case is trivial, it is not so intuitive to verify in which basis the quantum coherence is maximal. Based on the coherence measure of relative entropy, we indicate the particular basis in which the quantum coherence is maximal for a given state, where the Fourier matrix (or more generally, \textit{complex Hadamard matrices}) plays a critical role in determining the basis. Intriguingly, though we can prove that the basis associated with the Fourier matrix is a stationary point for optimizing the $l_1$ norm of coherence, numerical simulation shows that it is not a global optimal choice.

10 pages, 1 figures. Accepted for publication in Physical Review A

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• Maximal Coherence and the Resource Theory of Purity
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• Hierarchy of the nonlocal advantage of quantum coherence and Bell nonlocality
• Nonlocal advantage of quantum coherence in high-dimensional states
• Quantum coherence of multiqubit states in correlated noisy channels
• Maximum coherence in the optimal basis
• Maximal steered coherence and its conversion to entanglement in multiple bosonic reservoirs
• Finite-size scaling of coherence and steered coherence in the Lipkin-Meshkov-Glick model
• Monogamy inequality for any local quantum resource and entanglement
• Quantum coherence fraction
• Interpreting quantum coherence through a quantum measurement process
• Wave-particle duality employing quantum coherence in superposition with non-orthogonal pointers
• Coherence quantifiers from the viewpoint of their decreases in the measurement process
• Anomalies of weight-based coherence measure and mixed maximally coherent states
• Hierarchy of continuous-variable quantum resource theories
• Complementary properties of multiphoton quantum states in linear optics networks
• Experimental quantification of quantum coherence for a set of quantum states
• Experimentally realized local-global tradeoff in quantum resources