Random private quantum states

TL;DR

This paper investigates the entanglement properties of random private quantum states, revealing they are nearly indistinguishable from separable states and have low repeatable key despite containing one bit of secret key.

Contribution

The work introduces new analytical tools for studying private quantum states, including a novel operator ordering and bounds on norms under tensoring with entangled states.

Findings

Random private quantum states are nearly indistinguishable from separable states.

They possess low repeatable key despite containing one bit of secret key.

New techniques include bounds on norms and a continuity bound for relative entropy.

Abstract

The study of properties of randomly chosen quantum states has in recent years led to many insights into quantum entanglement. In this work, we study private quantum states from this point of view. Private quantum states are bipartite quantum states characterised by the property that carrying out simple local measurements yields a secret bit. This feature is shared by the maximally entangled pair of quantum bits, yet private quantum states are more general and can in their most extreme form be almost bound entangled. In this work, we study the entanglement properties of random private quantum states and show that they are hardly distinguishable from separable states and thus have low repeatable key, despite containing one bit of key. The technical tools we develop are centred around the concept of locally restricted measurements and include a new operator ordering, bounds on norms under tensoring with entangled states and a continuity bound for a relative entropy measure.