Private states, quantum data hiding and the swapping of perfect secrecy

Abstract

We derive a formal connection between quantum data hiding and quantum privacy, confirming the intuition behind the construction of bound entangled states from which secret bits can be extracted. We present three main results. First, we show how to simplify the class of private states and related states via reversible local operation and one-way communication. Second, we obtain a bound on the one-way distillable entanglement of private states in terms of restricted relative entropy measures, which is tight in many cases and shows that protocols for one-way distillation of key out of states with low distillable entanglement lead to the distillation of data hiding states. Third, we consider the problem of extending the distance of quantum key distribution with help of intermediate stations. In analogy to the quantum repeater, this paradigm has been called the quantum key repeater. We show that when extending private states with one-way communication, the resulting rate is bounded by the one-way distillable entanglement. In order to swap perfect secrecy it is thus essentially optimal to use entanglement swapping.

v3 published version, some details of the main proofs have been moved to the appendix, 21 pages. v2 claims changed from LOCC to one-way LOCC in the process of correcting a mistake found in v1 (in proof of Lemma 3). v1: 15 pages, 9 figures

References in corpus (4)

• Distillation of secret key and entanglement from quantum states
• Relative Entropy Bounds on Quantum, Private and Repeater Capacities
• Finding a maximally correlated state - Simultaneous Schmidt decomposition of bipartite pure states
• Experimental Extraction of Secure Correlations from a Noisy Private State

Cited by in corpus (14)

• Universal Limitations on Quantum Key Distribution over a Network
• Security of device-independent quantum key distribution protocols: a review
• When Do Composed Maps Become Entanglement Breaking?
• Multipartite entanglement measures: a review
• Upper bounds on device-independent quantum key distribution
• Asymptotics of quantum channels
• Eventually entanglement breaking Markovian dynamics: structure and characteristic times
• The PPT${}^2$ conjecture holds for all Choi-type maps
• Hybrid quantum network design against unauthorized secret-key generation, and its memory cost
• Random private quantum states
• The Role of Entanglement in Quantum Communication, and Analysis of the Detection Loophole
• Limitations for private randomness repeaters
• Upper bounds on the leakage of private data and operational approach to markovianity
• A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement