Quantum privacy witness

TL;DR

This paper introduces the concept of a quantum privacy witness, a single observable capable of detecting secure keys even in bound entangled states, enabling efficient key estimation with minimal measurements.

Contribution

The paper develops the notion of a privacy witness and secret key estimation using few observables, reducing measurement complexity for detecting quantum privacy.

Findings

Privacy witness can detect secure keys in bound entanglement.

Few measurements suffice to estimate secret keys above distillable entanglement.

Experimental example shows significant reduction in measurement requirements.

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.