Quantum privacy witness

Abstract

While it is usually known that the mean value of a single observable is enough to detect entanglement or its distillability, the counterpart of such an approach in the case of quatum privacy has been missing. Here we develop the concept of a privacy witness, i.e. a single observable that may detect presence of the secure key even in the case of bound entanglement. Then we develop the notion of secret key estimation based on few observables and discuss the witness decomposition into local measurements. The surprising property of the witness is that with the help of a low number of product mesurements involved it may still report the key values that are {\it strictly above} distillable entanglement of the state. For an exemplary four-qubit state studied in a recent experiment [K. Dobek {\em et al.}, Phys. Rev. Lett. {\bf 106}, 030501 (2011)] this means 6 Pauli operator product measurements versus 81 needed to carry out the complete quantum state tomography. The present approach may be viewed as a paradigm for the general program of experimentally friendly detection and estimation of task-dedicated quantum entanglement.

8 pages, 5 figures

References in corpus (4)

• Distillation of secret key and entanglement from quantum states
• Quantifying Entanglement with Witness Operators
• Relating quantum privacy and quantum coherence: an operational approach
• Experimental Extraction of Secure Correlations from a Noisy Private State

Cited by in corpus (7)

• Quantum mechanical which-way experiment with an internal degree of freedom
• Construction of optimal teleportation witness operators from entanglement witnesses
• Experimental generation of complex noisy photonic entanglement
• Increasing distillable key rate from bound entangled states by using local filtration
• Bipartite Bound Entanglement
• Upper bounds on the leakage of private data and operational approach to markovianity
• Construction and properties of a class of private states in arbitrary dimensions