scholarly journals Computable constraints on entanglement-sharing of multipartite quantum states

2010 ◽  
Vol 10 (3&4) ◽  
pp. 223-238
Author(s):  
Y.-C. Ou ◽  
M.S. Byrd
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Many Body ◽  
Pure States ◽  
Arbitrary Dimensions ◽  
Many Body Systems ◽  
Bipartite States ◽  
Entanglement Sharing

\Negativity is regarded as an important measure of entanglement in quantum information theory. In contrast to other measures of entanglement, it is easily computable for bipartite states in arbitrary dimensions. In this paper, based on the negativity and realignment, we provide a set of entanglement-sharing constraints for multipartite states, where the entanglement is not necessarily limited to bipartite and pure states, thus aiding in the quantification of constraints for entanglement-sharing. These may find applications in studying many-body systems.

scholarly journals Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 33 ◽  
Author(s):  
Liron Levy ◽  
Moshe Goldstein
Keyword(s):  
Phase Diagram ◽  
Information Theory ◽  
Quantum Information ◽  
Critical Point ◽  
Entanglement Entropy ◽  
Quantum Information Theory ◽  
Topological Phase ◽  
Many Body ◽  
Zero Modes ◽  
Many Body Systems

In recent years, tools from quantum information theory have become indispensable in characterizing many-body systems. In this work, we employ measures of entanglement to study the interplay between disorder and the topological phase in 1D systems of the Kitaev type, which can host Majorana end modes at their edges. We find that the entanglement entropy may actually increase as a result of disorder, and identify the origin of this behavior in the appearance of an infinite-disorder critical point. We also employ the entanglement spectrum to accurately determine the phase diagram of the system, and find that disorder may enhance the topological phase, and lead to the appearance of Majorana zero modes in systems whose clean version is trivial.

CAN ENTANGLEMENT BE EXTRACTED FROM MANY BODY SYSTEMS?

2007 ◽  
Vol 05 (01n02) ◽  
pp. 125-130
Author(s):  
GABRIELE DE CHIARA ◽  
ČASLAV BRUKNER ◽  
G. MASSIMO PALMA ◽  
ROSARIO FAZIO ◽  
VLATKO VEDRAL
Keyword(s):  
Information Theory ◽  
Heat Capacity ◽  
Magnetic Susceptibility ◽  
Quantum Information ◽  
Spin Chain ◽  
Optical Lattice ◽  
Quantum Information Theory ◽  
Many Body ◽  
Thermodynamical Properties ◽  
Many Body Systems

Some thermodynamical properties of solids, such as heat capacity and magnetic susceptibility, have recently been shown to be linked to the amount of entanglement in a solid. Until now, however, it was not clear whether this entanglement can be used as a resource in quantum information theory. Here we show that this entanglement is physical, demonstrating the principles of its extraction from a typical spin chain by scattering two particles off the system. Moreover, we show how to simulate this process using present-day optical lattice technology.

scholarly journals NATURAL METRIC FOR QUANTUM INFORMATION THEORY

2009 ◽  
Vol 07 (05) ◽  
pp. 1009-1019 ◽  
Author(s):  
P. W. LAMBERTI ◽  
M. PORTESI ◽  
J. SPARACINO
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Square Root ◽  
Mixed States ◽  
Basic Properties ◽  
Illustrative Application

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation to other distances is investigated. As an illustrative application, the proposed metric is evaluated for one-qubit mixed states.

Thresholds for reduction-related entanglement criteria in quantum information theory

2015 ◽  
Vol 15 (13&14) ◽  
pp. 1165-1184
Author(s):  
Maria A. Jivulescu ◽  
Nicolae Lupa ◽  
Ion Nechita
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum State ◽  
Random Matrix ◽  
Matrix Theory ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Absolute Reduction ◽  
Open Questions ◽  
Pure Quantum State

We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the resulting bipartite quantum state satisfies the reduction criterion in different asymptotic regimes. We consider as well the basis-independent version of the reduction criterion (the absolute reduction criterion), computing thresholds for the corresponding eigenvalue sets. We do the same for other sets relevant in the study of absolute separability, using techniques from random matrix theory. Finally, we gather and compare the known values for the thresholds corresponding to different entanglement criteria, and conclude with a list of open questions.

scholarly journals ENTANGLEMENT SHARING: FROM QUBITS TO GAUSSIAN STATES

2006 ◽  
Vol 04 (03) ◽  
pp. 383-393 ◽  
Author(s):  
GERARDO ADESSO ◽  
FABRIZIO ILLUMINATI
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Continuous Variable ◽  
Quantum Systems ◽  
Tripartite Entanglement ◽  
Gaussian States ◽  
Trade Off ◽  
Entanglement Sharing

It is a central trait of quantum information theory that there exist limitations to the free sharing of quantum correlations among multiple parties. Such monogamy constraints have been introduced in a landmark paper by Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a trade-off between the couplewise and the genuine tripartite entanglement for states of three qubits. Since then, a lot of efforts have been devoted to the investigation of distributed entanglement in multipartite quantum systems. In this paper we report, in a unifying framework, a bird's eye view of the most relevant results that have been established so far on entanglement sharing in quantum systems. We will take off from the domain of N qubits, graze qudits, and finally land in the almost unexplored territory of multimode Gaussian states of continuous variable systems.

scholarly journals SINGULAR VALUE DECOMPOSITION AND MATRIX REORDERINGS IN QUANTUM INFORMATION THEORY

2011 ◽  
Vol 22 (09) ◽  
pp. 897-918 ◽  
Author(s):  
JAROSŁAW ADAM MISZCZAK
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Singular Value Decomposition ◽  
Computing System ◽  
Quantum Information Theory ◽  
Singular Value ◽  
Quantum States ◽  
Quantum Channels ◽  
Basic Functions ◽  
Value Decomposition

We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyze the correspondence between quantum states and operations with the help of Jamiołkowski isomorphism. The presented matrix reorderings allow us to obtain simple formulae for the composition of quantum channels and partial operations used in quantum information theory. To provide examples of the discussed operations, we utilize a package for the Mathematica computing system implementing basic functions used in the calculations related to quantum information theory.

scholarly journals IMPOSSIBILITY OF PARTIAL SWAPPING OF QUANTUM INFORMATION

2007 ◽  
Vol 05 (04) ◽  
pp. 605-609 ◽  
Author(s):  
I. CHAKRABARTY
Keyword(s):  
Information Theory ◽  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Higher Dimensions ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Two Dimensional ◽  
Bloch Sphere ◽  
Two Parameters

It is a well–known fact that a quantum state |ψ(θ, ϕ)〉 is represented by a point on the Bloch sphere, characterized by two parameters θ and ϕ. Here in this work, we find out another impossible operation in quantum information theory. We name this impossibility as 'Impossibility of partial swapping of quantum information'. By this we mean that if two unknown quantum states are given at the input port, there exists no physical process, consistent with the principles of quantum mechanics, by which we can partially swap either of the two parameters θ and ϕ between these two quantum states. In this work, we provided the impossibility proofs for the qubits (i.e. the quantum states taken from two-dimensional Hilbert space) and this impossible operation can be shown to hold in higher dimensions also.

scholarly journals JENSEN–SHANNON DIVERGENCE AS A MEASURE OF THE DEGREE OF ENTANGLEMENT

2008 ◽  
Vol 06 (supp01) ◽  
pp. 715-720 ◽  
Author(s):  
A. P. MAJTEY ◽  
A. BORRAS ◽  
M. CASAS ◽  
P. W. LAMBERTI ◽  
A. PLASTINO
Keyword(s):  
Information Theory ◽  
Hilbert Space ◽  
Quantum Information ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Jensen Shannon Divergence ◽  
Degree Of Entanglement

The notion of distance in Hilbert space is relevant in many scenarios. In particular, "distances" between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon divergence (QJSD) between quantum states. Here we study this distance as a geometrical measure of entanglement and apply it to different families of states.

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