Average subentropy, coherence and entanglement of random mixed quantum states

Journal Article · Wed Feb 15 04:00:00 EST 2017 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2016.12.024· OSTI ID:22617467

Zhang, Lin ^[1]; Singh, Uttam ^[2]

---

1. Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018 (China)
2. Harish-Chandra Research Institute, Allahabad, 211019 (India)

Compact expressions for the average subentropy and coherence are obtained for random mixed states that are generated via various probability measures. Surprisingly, our results show that the average subentropy of random mixed states approaches the maximum value of the subentropy which is attained for the maximally mixed state as we increase the dimension. In the special case of the random mixed states sampled from the induced measure via partial tracing of random bipartite pure states, we establish the typicality of the relative entropy of coherence for random mixed states invoking the concentration of measure phenomenon. Our results also indicate that mixed quantum states are less useful compared to pure quantum states in higher dimension when we extract quantum coherence as a resource. This is because of the fact that average coherence of random mixed states is bounded uniformly, however, the average coherence of random pure states increases with the increasing dimension. As an important application, we establish the typicality of relative entropy of entanglement and distillable entanglement for a specific class of random bipartite mixed states. In particular, most of the random states in this specific class have relative entropy of entanglement and distillable entanglement equal to some fixed number (to within an arbitrary small error), thereby hugely reducing the complexity of computation of these entanglement measures for this specific class of mixed states.

• OSTI ID: 22617467
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 377; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ENTROPY
MIXED STATES
PURE STATES
QUANTUM ENTANGLEMENT
RANDOMNESS