### Abstract

We analyze the general nonclassicality of correlations of a composite quantum system as measured by the negativity of quantumness. The latter corresponds to the minimum entanglement, as quantified by the negativity that is created between the system and an apparatus that is performing local measurements on a selection of subsystems. The negativity of quantumness thus quantifies the degree of nonclassicality on the measured subsystems. We demonstrate a number of possible different interpretations for this measure and for the concept of quantumness of correlations in general. In particular, for general bipartite states in which the measured subsystem is a qubit, the negativity of quantumness acquires a geometric interpretation as the minimum trace distance from the set of classically correlated states. This can be further reinterpreted as minimum disturbance, with respect to trace norm, due to a local measurement or a nontrivial local unitary operation. We calculate the negativity of quantumness in closed form for Werner and isotropic states and for all two-qubit states for which the reduced state of the system that is locally measured is maximally mixed; this includes all Bell diagonal states. We discuss the operational significance and potential role of the negativity of quantumness in quantum information processing.

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

Article number | 012117 |

Number of pages | 18 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 88 |

Issue number | 1 |

DOIs | |

Publication status | Published - 18 Jul 2013 |

### Fingerprint

### Keywords

- quantumness
- physics
- astronomy

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*88*(1), [012117]. https://doi.org/10.1103/PhysRevA.88.012117

}

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 88, no. 1, 012117. https://doi.org/10.1103/PhysRevA.88.012117

**Negativity of quantumness and its interpretations.** / Nakano, Takafumi; Piani, Marco; Adesso, Gerardo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Negativity of quantumness and its interpretations

AU - Nakano, Takafumi

AU - Piani, Marco

AU - Adesso, Gerardo

PY - 2013/7/18

Y1 - 2013/7/18

N2 - We analyze the general nonclassicality of correlations of a composite quantum system as measured by the negativity of quantumness. The latter corresponds to the minimum entanglement, as quantified by the negativity that is created between the system and an apparatus that is performing local measurements on a selection of subsystems. The negativity of quantumness thus quantifies the degree of nonclassicality on the measured subsystems. We demonstrate a number of possible different interpretations for this measure and for the concept of quantumness of correlations in general. In particular, for general bipartite states in which the measured subsystem is a qubit, the negativity of quantumness acquires a geometric interpretation as the minimum trace distance from the set of classically correlated states. This can be further reinterpreted as minimum disturbance, with respect to trace norm, due to a local measurement or a nontrivial local unitary operation. We calculate the negativity of quantumness in closed form for Werner and isotropic states and for all two-qubit states for which the reduced state of the system that is locally measured is maximally mixed; this includes all Bell diagonal states. We discuss the operational significance and potential role of the negativity of quantumness in quantum information processing.

AB - We analyze the general nonclassicality of correlations of a composite quantum system as measured by the negativity of quantumness. The latter corresponds to the minimum entanglement, as quantified by the negativity that is created between the system and an apparatus that is performing local measurements on a selection of subsystems. The negativity of quantumness thus quantifies the degree of nonclassicality on the measured subsystems. We demonstrate a number of possible different interpretations for this measure and for the concept of quantumness of correlations in general. In particular, for general bipartite states in which the measured subsystem is a qubit, the negativity of quantumness acquires a geometric interpretation as the minimum trace distance from the set of classically correlated states. This can be further reinterpreted as minimum disturbance, with respect to trace norm, due to a local measurement or a nontrivial local unitary operation. We calculate the negativity of quantumness in closed form for Werner and isotropic states and for all two-qubit states for which the reduced state of the system that is locally measured is maximally mixed; this includes all Bell diagonal states. We discuss the operational significance and potential role of the negativity of quantumness in quantum information processing.

KW - quantumness

KW - physics

KW - astronomy

UR - http://www.scopus.com/inward/record.url?scp=84880580321&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.88.012117

DO - 10.1103/PhysRevA.88.012117

M3 - Article

VL - 88

JO - Physical Review A - Atomic, Molecular, and Optical Physics

T2 - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 1

M1 - 012117

ER -