On the geometric distance between quantum states with positive partial transposition and private states

Abstract

We prove an analytic positive lower bound for the geometric distance between entangled positive partial transpose (PPT) states of a broad class and any private state that delivers one secure key bit. Our proof holds for any Hilbert space of finite dimension. Although our result is proven for a specific class of PPT states, we show that our bound nonetheless holds for all known entangled PPT states with non-zero distillable key rates whether or not they are in our special class.

16 pages

References in corpus (2)

• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• Bound entangled states with nonzero distillable key rate

Cited by in corpus (3)

• Bound entangled states with extremal properties
• Increasing distillable key rate from bound entangled states by using local filtration
• Hybrid quantum network design against unauthorized secret-key generation, and its memory cost