Entanglement conditions for tripartite systems via indeterminacy relations

AbstractFrom the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation.

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ENTANGLEMENT CRITERION FOR COHERENT SUBTRACTION AND COHERENT ADDITION OF BIPARTITE CONTINUOUS VARIABLE STATES

International Journal of Quantum Information ◽

10.1142/s0219749913500603 ◽

2013 ◽

Vol 11 (06) ◽

pp. 1350060

Author(s):

LI-ZHEN JIANG ◽

XIAO-YU CHEN ◽

TIAN-YU YE ◽

FANG-YU HONG ◽

LIANG-NENG WU

Keyword(s):

Thermal Noise ◽

Photon Number ◽

Sufficient Conditions ◽

Continuous Variable ◽

Entangled State ◽

Gaussian States ◽

Non Gaussian ◽

Entanglement Criterion ◽

Entanglement Conditions ◽

Thermal States

We study the entanglement conditions of two quite general classes of two-mode non-Gaussian states. Using computable cross norm and realignment criterion, we obtain the sufficient conditions of entanglement for coherently added or subtracted two-mode squeezed thermal states, and the sufficient condition of entanglement for any photon number entangled state (PNES) evolving in a thermal noise and amplitude damping channel.

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Application of entanglement conditions to spin systems

Physical Review A ◽

10.1103/physreva.81.062311 ◽

2010 ◽

Vol 81 (6) ◽

Cited By ~ 3

Author(s):

Hongjun Zheng ◽

Ho Trung Dung ◽

Mark Hillery

Keyword(s):

Spin Systems ◽

Entanglement Conditions

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Entanglement Conditions for Two-Mode States

Physical Review Letters ◽

10.1103/physrevlett.96.050503 ◽

2006 ◽

Vol 96 (5) ◽

Cited By ~ 269

Author(s):

Mark Hillery ◽

M. Suhail Zubairy

Keyword(s):

Entanglement Conditions

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General mapping of multiqudit entanglement conditions to nonseparability indicators for quantum-optical fields

Physical Review Research ◽

10.1103/physrevresearch.1.032041 ◽

2019 ◽

Vol 1 (3) ◽

Author(s):

Junghee Ryu ◽

Bianka Woloncewicz ◽

Marcin Marciniak ◽

Marcin Wieśniak ◽

Marek Żukowski

Keyword(s):

Optical Fields ◽

General Mapping ◽

Quantum Optical ◽

Entanglement Conditions

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ENTANGLED MARKOV CHAINS ARE INDEED ENTANGLED

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025706002445 ◽

2006 ◽

Vol 09 (03) ◽

pp. 379-390 ◽

Cited By ~ 9

Author(s):

LUIGI ACCARDI ◽

TAKASHI MATSUOKA ◽

MASANORI OHYA

Keyword(s):

Markov Chains ◽

Tensor Products ◽

Many Body ◽

Matrix Algebras ◽

Entanglement Conditions

Entangled Markov chains (EMC) were so baptized on the basis of the conjecture that they provide examples of states, on infinite tensor products of matrix algebras, which are in some sense "entangled".2 In this paper we introduce the notion of multiple (or "many-body") entanglement and extend the two-body criterion of entanglement obtained in Ref. 17 to this case. We then apply this extension to EMC and prove that "generically" they satisfy the entanglement conditions.

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