Maximally coherent mixed states: Complementarity between maximal coherence and mixedness

Abstract

Quantum coherence is a key element in topical research on quantum resource theories and a primary facilitator for design and implementation of quantum technologies. However, the resourcefulness of quantum coherence is severely restricted by environmental noise, which is indicated by the loss of information in a quantum system, measured in terms of its purity. In this work, we derive the limits imposed by the mixedness of a quantum system on the amount of quantum coherence that it can possess. We obtain an analytical trade-off between the two quantities that upperbound the maximum quantum coherence for fixed mixedness in a system. This gives rise to a class of quantum states, "maximally coherent mixed states," whose coherence cannot be increased further under any purity-preserving operation. For the above class of states, quantum coherence and mixedness satisfy a complementarity relation, which is crucial to understand the interplay between a resource and noise in open quantum systems.

8 pages, 1 figure, REVTex 4.1, close to published version

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Cited by in corpus (9)

• Maximum coherence in the optimal basis
• Maximal coherence in generic basis
• A new coherence measure based on fidelity
• Uncertainty Relations for Quantum Coherence
• Coherence breaking channels and coherence sudden death
• Thermal effects on coherence and excitation transfer
• Coherence convertibility for mixed states
• The role of quantum coherence in dimer and trimer excitation energy transfer
• Wave-Particle-Mixedness Complementarity