We investigate $k$ -nonseparability of $n$ -partite quantum states which is an important kind of correlations characterizing multipartite entanglement. We derive some $k$ -nonseparability criteria in the form of variance and quantum Fisher information, and illustrate their complementary features in the detection of $k$ -nonseparability through several examples.We investigate $k$-nonseparability of $n$-partite quantum states which is an important kind of correlations characterizing multipartite entanglement. We derive some $k$-nonseparability criteria in the form of variance and quantum Fisher information, and illustrate their complementary features in the detection of $k$-nonseparability through several examples.

Physical Review AApr 8, 201620 citations

Phase-Entanglement Complementarity with Time-Energy Uncertainty

Fulin Zhang, Mai-Lin Liang

We present a unified view of the Berry phase of a quantum system and its entanglement with surroundings. The former reflects the nonseparability between a system and a classical environment as the latter for a quantum environment, and the concept of geometric time-energy uncertainty can be adopted as a signature of the nonseparability. Based on this viewpoint, we study their relationship in the quantum-classical transition of the environment, with the aid of a spin-half particle (qubit) model exposed to a quantum-classical hybrid field. In the quantum-classical transition, the Berry phase has a similar connection with the time-energy uncertainty as the case with only a classical field, whereas the geometric phase for the mixed state of the qubit exhibits a complementary relationship with the entanglement. Namely, for a fixed time-energy uncertainty, the entanglement is gradually replaced by the mixed geometric phase as the quantum field vanishes. And the mixed geometric phase becomes the Berry phase in the classical limit. The same results can be draw out from a displaced harmonic oscillator model.We present a unified view of the Berry phase of a quantum system and its entanglement with surroundings. The former reflects the nonseparability between a system and a classical environment as the latter for a quantum environment, and the concept of geometric time-energy uncertainty can be adopted as a signature of the nonseparability. Based on this viewpoint, we study their relationship in the quantum-classical transition of the environment, with the aid of a spin-half particle (qubit) model exposed to a quantum-classical hybrid field. In the quantum-classical transition, the Berry phase has a similar connection with the time-energy uncertainty as the case with only a classical field, whereas the geometric phase for the mixed state of the qubit exhibits a complementary relationship with the entanglement. Namely, for a fixed time-energy uncertainty, the entanglement is gradually replaced by the mixed geometric phase as the quantum field vanishes. And the mixed geometric phase becomes the Berry phase in the classical limit. The same results can be draw out from a displaced harmonic oscillator model.

arXiv:1312.1218Dec 4, 20130 citations

We investigate

k

-nonseparability of

n

-partite quantum states which is an important kind of correlations characterizing multipartite entanglement. We derive some

k

-nonseparability criteria in the form of variance and quantum Fisher information, and illustrate their complementary features in the detection of

k

-nonseparability through several examples.