Random Private Quantum States
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Random Private Quantum States. / Christandl, Matthias; Ferrara, Roberto; Lancien, Cecilia.
In: IEEE Transactions on Information Theory, Vol. 66, No. 7, 2020, p. 4621-4640.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Random Private Quantum States
AU - Christandl, Matthias
AU - Ferrara, Roberto
AU - Lancien, Cecilia
PY - 2020
Y1 - 2020
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 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.
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 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.
U2 - 10.1109/TIT.2020.2973155
DO - 10.1109/TIT.2020.2973155
M3 - Journal article
VL - 66
SP - 4621
EP - 4640
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
IS - 7
ER -
ID: 243381516