scholarly journals Entangled symmetric states and copositive matrices

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 561
Author(s):  
Carlo Marconi ◽  
Albert Aloy ◽  
Jordi Tura ◽  
Anna Sanpera
Keyword(s):  
Quantum States ◽  
Copositive Matrices ◽  
Entanglement Witnesses ◽  
Symmetric Quantum ◽  
Symmetric States ◽  
Odd Dimensions

Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For the simplest symmetric states, i.e., the diagonal symmetric (DS) states, it has been shown that there exists a correspondence between exceptional (non-exceptional) copositive matrices and non-decomposable (decomposable) Entanglement Witnesses (EWs). Here we show that EWs of symmetric, but not DS, states can also be constructed from extended copositive matrices, providing new examples of bound entangled symmetric states, together with their corresponding EWs, in arbitrary odd dimensions.

scholarly journals An elementary introduction to the geometry of quantum states with pictures

2019 ◽  
Vol 32 (02) ◽  
pp. 2030001 ◽  
Author(s):  
J. Avron ◽  
O. Kenneth
Keyword(s):  
Convex Body ◽  
Cross Sections ◽  
Convex Bodies ◽  
Quantum States ◽  
Entangled States ◽  
High Dimensions ◽  
Geometric Properties ◽  
Precise Sense ◽  
Entanglement Witnesses ◽  
Elementary Methods

This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of [Formula: see text] qubits, the dimension is exponentially large in [Formula: see text]. The space of states can be visualized, to some extent, by its simple cross sections: Regular simplexes, balls and hyper-octahedra. a When the dimension gets large, there is a precise sense in which the space of states resembles, almost in every direction, a ball. The ball turns out to be a ball of rather low purity states. We also address some of the corresponding, but harder, geometric properties of separable and entangled states and entanglement witnesses. “All convex bodies behave a bit like Euclidean balls.” Keith Ball

scholarly journals Efficient optimal minimum error discrimination of symmetric quantum states

2010 ◽  
Vol 81 (1) ◽  
Author(s):  
Antonio Assalini ◽  
Gianfranco Cariolaro ◽  
Gianfranco Pierobon
Keyword(s):  
Quantum States ◽  
Minimum Error ◽  
Symmetric Quantum

Optimum measurements for discrimination among symmetric quantum states and parameter estimation

1997 ◽  
Vol 36 (6) ◽  
pp. 1269-1288 ◽  
Author(s):  
Masashi Ban ◽  
Keiko Kurokawa ◽  
Rei Momose ◽  
Osamu Hirota
Keyword(s):  
Parameter Estimation ◽  
Quantum States ◽  
Symmetric Quantum

NONLOCAL MEASUREMENTS IN THE TIME-SYMMETRIC QUANTUM MECHANICS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1528-1535 ◽  
Author(s):  
LEV VAIDMAN ◽  
IZHAR NEVO
Keyword(s):  
Quantum Mechanics ◽  
Quantum Systems ◽  
Quantum Measurements ◽  
Quantum States ◽  
Standard Quantum ◽  
Time Direction ◽  
Quantum Formalism ◽  
Symmetric Quantum ◽  
Time Symmetric Quantum Mechanics

Although for some nonlocal variables the standard quantum measurements which are reliable, instantaneous, and nondemolition, are impossible, demolition reliable instantaneous measurements of all variables are possible. It is shown that this is correct also in the framework of the time-symmetric quantum formalism, i.e. nonlocal variables of composite quantum systems with quantum states evolving both forward and backward in time are measurable in a demolition way. The result follows from the possibility to reverse with certainty the time direction of backward evolving quantum states.

scholarly journals Pairwise concurrence in cyclically symmetric quantum states

2019 ◽  
Vol 100 (4) ◽  
Author(s):  
Alexander Meill ◽  
David A. Meyer
Keyword(s):  
Quantum States ◽  
Symmetric Quantum

scholarly journals Separability of diagonal symmetric states: a quadratic conic optimization problem

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 45 ◽  
Author(s):  
Jordi Tura ◽  
Albert Aloy ◽  
Ruben Quesada ◽  
Maciej Lewenstein ◽  
Anna Sanpera
Keyword(s):  
Quantum Information ◽  
Optimization Problem ◽  
Entangled States ◽  
Conic Optimization ◽  
Entanglement Witnesses ◽  
Partial Transposition ◽  
Separability Problem ◽  
Necessary And Sufficient ◽  
Ppt Criterion ◽  
Symmetric States

We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS) states. First, we show that separability in the case of DS inCd⊗Cd(symmetric qudits) can be reformulated as a quadratic conic optimization problem. This connection allows us to exchange concepts and ideas between quantum information and this field of mathematics. For instance, copositive matrices can be understood as indecomposable entanglement witnesses for DS states. As a consequence, we show that positivity of the partial transposition (PPT) is sufficient and necessary for separability of DS states ford≤4. Furthermore, ford≥5, we provide analytic examples of PPT-entangled states. Second, we develop new sufficient separability conditions beyond the PPT criterion for bipartite DS states. Finally, we focus onN-partite DS qubits, where PPT is known to be necessary and sufficient for separability. In this case, we present a family of almost DS states that are PPT with respect to each partition but nevertheless entangled.

scholarly journals The type-independent resource theory of local operations and shared randomness

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 262 ◽  
Author(s):  
David Schmid ◽  
Denis Rosset ◽  
Francesco Buscemi
Keyword(s):  
Quantum Theory ◽  
Quantum Information Processing ◽  
Full Range ◽  
Quantum States ◽  
Resource Theory ◽  
Independent Manner ◽  
Common Cause ◽  
Entanglement Witnesses ◽  
Different Types ◽  
Common Resource

In space-like separated experiments and other scenarios where multiple parties share a classical common cause but no cause-effect relations, quantum theory allows a variety of nonsignaling resources which are useful for distributed quantum information processing. These include quantum states, nonlocal boxes, steering assemblages, teleportages, channel steering assemblages, and so on. Such resources are often studied using nonlocal games, semiquantum games, entanglement-witnesses, teleportation experiments, and similar tasks. We introduce a unifying framework which subsumes the full range of nonsignaling resources, as well as the games and experiments which probe them, into a common resource theory: that of local operations and shared randomness (LOSR). Crucially, we allow these LOSR operations to locally change the type of a resource, so that players can convert resources of any type into resources of any other type, and in particular into strategies for the specific type of game they are playing. We then prove several theorems relating resources and games of different types. These theorems generalize a number of seminal results from the literature, and can be applied to lessen the assumptions needed to characterize the nonclassicality of resources. As just one example, we prove that semiquantum games are able to perfectly characterize the LOSR nonclassicality of every resource of any type (not just quantum states, as was previously shown). As a consequence, we show that any resource can be characterized in a measurement-device-independent manner.

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