Generic bound coherence under strictly incoherent operations

Abstract

We compute analytically the maximal rates of distillation of quantum coherence under strictly incoherent operations (SIO) and physically incoherent operations (PIO), showing that they coincide for all states, and providing a complete description of the phenomenon of bound coherence. In particular, we establish a simple, analytically computable necessary and sufficient criterion for the asymptotic distillability under SIO and PIO. We use this result to show that almost every quantum state is undistillable --- only pure states as well as states whose density matrix contains a rank-one submatrix allow for coherence distillation under SIO or PIO, while every other quantum state exhibits bound coherence. This demonstrates fundamental operational limitations of SIO and PIO in the resource theory of quantum coherence. We show that the fidelity of distillation of a single bit of coherence under SIO can be efficiently computed as a semidefinite program, and investigate the generalization of this result to provide an understanding of asymptotically achievable distillation fidelity.

arXiv comment5+7 pages; accepted version

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• Tight constraints on probabilistic convertibility of quantum states
• One-shot entanglement distillation beyond local operations and classical communication
• Catalyst-Assisted Probabilistic Coherence Distillation for Mixed States
• Completing the Grand Tour of asymptotic quantum coherence manipulation
• Maximum Relative Entropy of Coherence for Quantum Channels
• Coherence of operations and interferometry
• Information-based approach towards a unified resource theory
• One-shot Coherence Distillation with Catalysts
• Coherence manipulation with dephasing-covariant operations
• Optimal probabilistic distillation of quantum coherence
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• Average skew information-based coherence and its typicality for random quantum states
• Experimental demonstration of one-shot coherence distillation: High-dimensional state conversions
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• Generic aspects of the resource theory of quantum coherence
• Characterizing coherence with quantum observables
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• Conversion of Gaussian states under incoherent Gaussian operations
• Approximate distillation of quantum coherence
• Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound
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• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
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• Fundamental limits on concentrating and preserving tensorized quantum resources
• Coherence, superposition, and Löwdin symmetric orthogonalization
• State convertibility under genuinely incoherent operations
• Incoherent Operations Enable State Transformations Impossible under Dephasing-covariant Incoherent Operations
• Coherent preorder of quantum states
• The coherent measurement cost of coherence distillation
• Strictly incoherent operations for one-qubit systems