Resource Theory of Coherence - Beyond States

Abstract

We generalize the recently proposed resource theory of coherence (or superposition) [Baumgratz, Cramer & Plenio, Phys. Rev. Lett. 113:140401; Winter & Yang, Phys. Rev. Lett. 116:120404] to the setting where not only the free ("incoherent") resources, but also the objects manipulated are quantum operations, rather than states. In particular, we discuss an information theoretic notion of coherence capacity of a quantum channel, and prove a single-letter formula for it in the case of unitaries. Then we move to the coherence cost of simulating a channel, and prove achievability results for unitaries and general channels acting on a $d$-dimensional system; we show that a maximally coherent state of rank $d$ is always sufficient as a resource if incoherent operations are allowed. We also show lower bounds on the simulation cost of channels that allow us to conclude that there exists bound coherence in operations, i.e. maps with non-zero cost of implementing them but zero coherence capacity; this is in contrast to states, which do not exhibit bound coherence.

V1 6 pages; v2 is improved in every respect - it has more pages (6>10), more figures (0>2), more authors (3>4), and of course many more results; v3 has several smaller improvements, it is the final version accepted by the journal; v4 includes an erratum as ancillary file, correcting Proposition 3 (journal reference of the erratum: Phys. Rev. A 96, 059903 (2017); DOI: 10.1103/PhysRevA.96.059903)

References in corpus (3)

• Measuring Quantum Coherence with Entanglement
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Measuring the quality of a quantum reference frame: the relative entropy of frameness

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• One-Shot Manipulation of Dynamical Quantum Resources
• Resource Preservability
• Amortization does not enhance the max-Rains information of a quantum channel
• Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps
• Completing the Grand Tour of asymptotic quantum coherence manipulation
• Coherence generating power of quantum dephasing processes
• Quantifying dynamical coherence with dynamical entanglement
• Resource theory of quantum uncomplexity
• Symmetries of quantum evolutions
• Communication, Dynamical Resource Theory, and Thermodynamics
• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements
• Maximum Relative Entropy of Coherence for Quantum Channels
• Coherence of operations and interferometry
• Resource theory of unextendibility and non-asymptotic quantum capacity
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems
• Accessible coherence in open quantum system dynamics
• Virtual quantum resource distillation: General framework and applications
• Creating and destroying coherence with quantum channels
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• Skew information-based coherence generating power of quantum channels
• Necessary and Sufficient Conditions on Measurements of Quantum Channels
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• Quantifying Superpositions Between Quantum Evolutions
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• An alternative framework for quantifying coherence of quantum channels
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• Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization
• Quantum thermodynamics aspects with a thermal reservoir based on $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Correlation between resource-generating capacities of quantum gates
• Fundamental limits on concentrating and preserving tensorized quantum resources
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• Coherence dynamics induced by attenuation and amplification Gaussian channels
• Analytically Computable Symmetric Quantum Correlations
• Strong superadditivity relations for multiqubit systems
• The best approximation of an objective state with a given set of quantum states
• Creation of quantum coherence with general measurement processes