Random Private Quantum States

TY - GEN

T1 - Random Private Quantum States

AU - Christandl, Matthias

AU - Ferrara, Roberto

AU - Lancien, Cecilia

PY - 2018

Y1 - 2018

N2 - 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 characterized 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 centered around the concept of locally restricted measurements and include a new operator ordering, bounds on norms under tensoring with entangled states and continuity bounds for relative entropy measures. A full version of this paper is accessible at: http://arxiv.org/abs/1801.2861 [1].

AB - 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 characterized 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 centered around the concept of locally restricted measurements and include a new operator ordering, bounds on norms under tensoring with entangled states and continuity bounds for relative entropy measures. A full version of this paper is accessible at: http://arxiv.org/abs/1801.2861 [1].

UR - http://www.scopus.com/inward/record.url?scp=85052436356&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2018.8437895

DO - 10.1109/ISIT.2018.8437895

M3 - Article in proceedings

AN - SCOPUS:85052436356

SN - 9781538647806

SP - 1784

EP - 1788

BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018

PB - IEEE

T2 - 2018 IEEE International Symposium on Information Theory, ISIT 2018

Y2 - 17 June 2018 through 22 June 2018

ER -