ENTANGLEMENT BOUNDS FOR A FAMILY OF TWO-MODE GAUSSIAN STATES

2004 ◽  
Vol 02 (02) ◽  
pp. 273-283 ◽  
Author(s):  
LI-ZHEN JIANG
Keyword(s):  
Relative Entropy ◽  
Upper Bound ◽  
Gaussian States ◽  
Entanglement Of Formation ◽  
Coherent Information ◽  
Relative Entropy Of Entanglement ◽  
Quantum Gaussian States

I study a family of bipartite quantum Gaussian states with three parameters, calculate Gaussian entanglement of formation analytically and the upper bound of relative entropy of entanglement, compare them with the coherent information of the states. Based on the numerical observation, I determine the relative entropy of entanglement and distillable entanglement of the states with infinitive squeezing.

Connections between relative entropy of entanglement and geometric measure of entanglement

2004 ◽  
Vol 4 (4) ◽  
pp. 252-272
Author(s):  
T.-C. Wei ◽  
M. Ericsson ◽  
P.M. Goldbart ◽  
W.J. Munro
Keyword(s):  
Lower Bound ◽  
Relative Entropy ◽  
Upper Bounds ◽  
Mixed States ◽  
Geometric Measure ◽  
Entanglement Of Formation ◽  
Entanglement Measures ◽  
Pure States ◽  
Relative Entropy Of Entanglement ◽  
Geometric Measure Of Entanglement

As two of the most important entanglement measures---the entanglement of formation and the entanglement of distillation---have so far been limited to bipartite settings, the study of other entanglement measures for multipartite systems appears necessary. Here, connections between two other entanglement measures---the relative entropy of entanglement and the geometric measure of entanglement---are investigated. It is found that for arbitrary pure states the latter gives rise to a lower bound on the former. For certain pure states, some bipartite and some multipartite, this lower bound is saturated, and thus their relative entropy of entanglement can be found analytically in terms of their known geometric measure of entanglement. For certain mixed states, upper bounds on the relative entropy of entanglement are also established. Numerical evidence strongly suggests that these upper bounds are tight, i.e., they are actually the relative entropy of entanglement.

scholarly journals MAX-RELATIVE ENTROPY OF ENTANGLEMENT, ALIAS LOG ROBUSTNESS

2009 ◽  
Vol 07 (02) ◽  
pp. 475-491 ◽  
Author(s):  
NILANJANA DATTA
Keyword(s):  
Relative Entropy ◽  
Upper Bound ◽  
Quantum Operations ◽  
Relative Entropy Of Entanglement ◽  
The One

Properties of the max-relative entropy of entanglement, defined in Ref. 10, are investigated, and its significance as an upper bound to the one-shot rate for perfect entanglement dilution, under a particular class of quantum operations, is discussed. It is shown that it is in fact equal to another known entanglement monotone, namely the log robustness, defined in Ref. 7. It is known that the latter is not asymptotically continuous and it is not known whether it is weakly additive. However, by suitably modifying the max-relative entropy of entanglement we obtain a quantity which is seen to satisfy both these properties. In fact, the modified quantity is shown to be equal to the regularized relative entropy of entanglement.

scholarly journals On the entanglement of formation of two-mode Gaussian states: a compact form

2015 ◽  
Vol 14 (11) ◽  
pp. 4179-4199 ◽  
Author(s):  
Y. Akbari-Kourbolagh ◽  
H. Alijanzadeh-Boura
Keyword(s):  
Compact Form ◽  
Gaussian States ◽  
Entanglement Of Formation

scholarly journals Continuity of relative entropy of entanglement

1999 ◽  
Vol 264 (4) ◽  
pp. 257-260 ◽  
Author(s):  
Matthew J. Donald ◽  
Michał Horodecki
Keyword(s):  
Relative Entropy ◽  
Relative Entropy Of Entanglement

scholarly journals ENTANGLEMENT AND FRUSTRATION IN ORDERED SYSTEMS

2003 ◽  
Vol 01 (04) ◽  
pp. 465-477 ◽  
Author(s):  
MICHAEL M. WOLF ◽  
FRANK VERSTRAETE ◽  
J. IGNACIO CIRAC
Keyword(s):  
Ground State ◽  
State Energy ◽  
Nearest Neighbor ◽  
Bell Inequalities ◽  
Harmonic Oscillators ◽  
Neighbor Interaction ◽  
Gaussian States ◽  
Classical Systems ◽  
Entanglement Of Formation ◽  
Starting Point

This article reviews and extends recent results concerning entanglement and frustration in multipartite systems which have some symmetry with respect to the ordering of the particles. Starting point of the discussion are Bell inequalities: their relation to frustration in classical systems and their satisfaction for quantum states which have a symmetric extension. We then discussed how more general global symmetries of multipartite systems constrain the entanglement between two neighboring particles. We prove that maximal entanglement (measured in terms of the entanglement of formation) is always attained for the ground state of a certain nearest neighbor interaction Hamiltonian having the considered symmetry with the achievable amount of entanglement being a function of the ground state energy. Systems of Gaussian states, i.e. quantum harmonic oscillators, are investigated in more detail and the results are compared to what is known about ordered qubit systems.

scholarly journals Entanglement Availability Differentiation Service for the Quantum Internet

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Laszlo Gyongyosi ◽  
Sandor Imre
Keyword(s):  
Quantum Entanglement ◽  
Relative Entropy ◽  
Time Domain ◽  
Fundamental Concept ◽  
Relative Entropy Of Entanglement ◽  
Quantum Networking ◽  
The Time Domain ◽  
Priority Levels ◽  
Quantum Internet ◽  
Made In

AbstractA fundamental concept of the quantum Internet is quantum entanglement. In a quantum Internet scenario where the legal users of the network have different priority levels or where a differentiation of entanglement availability between the users is a necessity, an entanglement availability service is essential. Here we define the entanglement availability differentiation (EAD) service for the quantum Internet. In the proposed EAD framework, the differentiation is either made in the amount of entanglement with respect to the relative entropy of entanglement associated with the legal users, or in the time domain with respect to the amount of time that is required to establish a maximally entangled system between the legal parties. The framework provides an efficient and easily-implementable solution for the differentiation of entanglement availability in experimental quantum networking scenarios.

scholarly journals Infinite mode quantum Gaussian states

2019 ◽  
Vol 31 (09) ◽  
pp. 1950030
Author(s):  
B. V. Rajarama Bhat ◽  
Tiju Cherian John ◽  
R. Srinivasan
Keyword(s):  
Fock Spaces ◽  
Gaussian Distributions ◽  
Gaussian States ◽  
Symmetry Properties ◽  
Quantum Gaussian States

Quantum Gaussian states on Boson Fock spaces are quantum versions of Gaussian distributions. In this paper, we explore infinite mode quantum Gaussian states. We extend many of the results of Parthasarathy in [ 14 , 16 ] to the infinite mode case, which includes various characterizations, convexity and symmetry properties.

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