### Abstract

Language | English |
---|---|

Article number | 113001 |

Number of pages | 33 |

Journal | New Journal of Physics |

Volume | 16 |

Issue number | 11 |

DOIs | |

Publication status | Published - 31 Oct 2014 |

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### Keywords

- von Neumann measurement
- correlations
- quantum data hiding

### Cite this

*New Journal of Physics*,

*16*(11), [113001]. https://doi.org/10.1088/1367-2630/16/11/113001

}

*New Journal of Physics*, vol. 16, no. 11, 113001. https://doi.org/10.1088/1367-2630/16/11/113001

**Quantumness of correlations, quantumness of ensembles and quantum data hiding.** / Piani, Marco; Narasimhachar, Varun; Calsamiglia, John.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantumness of correlations, quantumness of ensembles and quantum data hiding

AU - Piani, Marco

AU - Narasimhachar, Varun

AU - Calsamiglia, John

PY - 2014/10/31

Y1 - 2014/10/31

N2 - We study the quantumness of correlations for ensembles of bi- and multi-partite systems and relate it to the task of quantum data hiding. Quantumness is here intended in the sense of minimum average disturbance under local measurements. We consider a very general framework, but focus on local complete von Neumann measurements as cause of the disturbance, and, later on, on the trace-distance as quantifier of the disturbance. We discuss connections with entanglement and previously defined notions of quantumness of correlations. We prove that a large class of quantifiers of the quantumness of correlations are entanglement monotones for pure bipartite states. In particular, we define an entanglement of disturbance for pure states, for which we give an analytical expression. Such a measure coincides with negativity and concurrence for the case of two qubits. We compute general bounds on disturbance for both single states and ensembles, and consider several examples, including the uniform Haar ensemble of pure states, and pairs of qubit states. Finally, we show that the notion of ensemble quantumness of correlations is most relevant in quantum data hiding. Indeed, while it is known that entanglement is not necessary for a good quantum data hiding scheme, we prove that ensemble quantumness of correlations is.

AB - We study the quantumness of correlations for ensembles of bi- and multi-partite systems and relate it to the task of quantum data hiding. Quantumness is here intended in the sense of minimum average disturbance under local measurements. We consider a very general framework, but focus on local complete von Neumann measurements as cause of the disturbance, and, later on, on the trace-distance as quantifier of the disturbance. We discuss connections with entanglement and previously defined notions of quantumness of correlations. We prove that a large class of quantifiers of the quantumness of correlations are entanglement monotones for pure bipartite states. In particular, we define an entanglement of disturbance for pure states, for which we give an analytical expression. Such a measure coincides with negativity and concurrence for the case of two qubits. We compute general bounds on disturbance for both single states and ensembles, and consider several examples, including the uniform Haar ensemble of pure states, and pairs of qubit states. Finally, we show that the notion of ensemble quantumness of correlations is most relevant in quantum data hiding. Indeed, while it is known that entanglement is not necessary for a good quantum data hiding scheme, we prove that ensemble quantumness of correlations is.

KW - von Neumann measurement

KW - correlations

KW - quantum data hiding

UR - http://iopscience.iop.org/1367-2630

U2 - 10.1088/1367-2630/16/11/113001

DO - 10.1088/1367-2630/16/11/113001

M3 - Article

VL - 16

JO - New Journal of Physics

T2 - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 11

M1 - 113001

ER -