scholarly journals Characterization of Quantum Correlations with Local Dimension Constraints and Its Device-Independent Applications

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Miguel Navascués ◽  
Gonzalo de la Torre ◽  
Tamás Vértesi
Keyword(s):  
Quantum Correlations ◽  
Local Dimension

scholarly journals Quantum limit of genuine tripartite correlations by bipartite extremality

2020 ◽  
Vol 18 (04) ◽  
pp. 2050014
Author(s):  
Hiroyuki Ozeki ◽  
Satoshi Ishizaka
Keyword(s):  
Probability Space ◽  
Quantum Correlations ◽  
Quantum Limit ◽  
Sufficient Criterion ◽  
Extremal Points ◽  
Chsh Inequality ◽  
Nonlocal Correlations ◽  
Necessary And Sufficient

The characterization of the extremal points of the set of quantum correlations has attracted wide interest. In the simplest bipartite Bell scenario, a necessary and sufficient criterion for identifying extremal correlations has recently been conjectured, but extremality of tripartite correlations is not well known. In this study, we analyze tripartite extremal correlations in terms of the conjectured bipartite extremal criterion, and we demonstrate that the bipartite part of some extremal correlations satisfies the bipartite criterion, even though they violate Svetlichny’s inequality, and therefore are considered (stronger) genuine tripartite nonlocal correlations. This phenomenon arises from the fact that the conjectured extremal criterion is automatically satisfied when the violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality exceeds a certain threshold, the value of which is given by the maximum CHSH violation at the edges of the probability space. This also suggests the possibility that the extremality of bipartite correlations can be certified by verifying whether the CHSH violation exceeds the threshold.

scholarly journals Bounds on Mixed State Entanglement

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 62 ◽  
Author(s):  
Bruno Leggio ◽  
Anna Napoli ◽  
Hiromichi Nakazato ◽  
Antonino Messina
Keyword(s):  
Mixed State ◽  
General Framework ◽  
Quantum Correlations ◽  
Thermal Entanglement ◽  
Mixed States ◽  
Clear Explanation ◽  
Finite Dimensionality ◽  
Partial Transpose ◽  
The Subject

In the general framework of d 1 × d 2 mixed states, we derive an explicit bound for bipartite negative partial transpose (NPT) entanglement based on the mixedness characterization of the physical system. The derived result is very general, being based only on the assumption of finite dimensionality. In addition, it turns out to be of experimental interest since some purity-measuring protocols are known. Exploiting the bound in the particular case of thermal entanglement, a way to connect thermodynamic features to the monogamy of quantum correlations is suggested, and some recent results on the subject are given a physically clear explanation.

scholarly journals Universal non-Markovianity detection in hybrid open quantum systems

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Jiří Svozilík ◽  
Raúl Hidalgo-Sacoto ◽  
Ievgen I. Arkhipov
Keyword(s):  
Quantum System ◽  
Wigner Function ◽  
Open Quantum Systems ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Continuous Variables ◽  
Open Quantum ◽  
Hybrid Quantum Systems

Abstract A universal characterization of non-Markovianity for any open hybrid quantum systems is presented. This formulation is based on the negativity volume of the generalized Wigner function, which serves as an indicator of the quantum correlations in any composite quantum systems. It is shown, that the proposed measure can be utilized for any single or multi-partite quantum system, containing any discrete or continuous variables. To demonstrate its power in revealing non-Markovianity in such quantum systems, we additionally consider a few illustrative examples.

scholarly journals Characterization of quantum and classical correlations in the Earth’s curved space-time

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Tonghua Liu ◽  
Shuo Cao ◽  
Shumin Wu
Keyword(s):  
Relativistic Effects ◽  
Quantum Correlations ◽  
Space Time ◽  
Kerr Metric ◽  
Curved Space ◽  
The Earth ◽  
Rotation Of The Earth ◽  
Earth Orbits ◽  
Quantum And Classical Correlations

Abstract The preparation of quantum systems and the execution of quantum information tasks between distant users are always affected by gravitational and relativistic effects. In this work, we quantitatively analyze how the curved space-time background of the Earth affects the classical and quantum correlations between photon pairs that are initially prepared in a two-mode squeezed state. More specifically, considering the rotation of the Earth, the space-time around the Earth is described by the Kerr metric. Our results show that these state correlations, which initially increase for a specific range of satellite’s orbital altitude, will gradually approach a finite value with increasing height of satellite’s orbit (when the special relativistic effects become relevant). More importantly, our analysis demonstrates that the changes of correlations generated by the total gravitational frequency shift could reach the level of $$<0.5\%$$ < 0.5 % within the satellite’s height at geostationary Earth orbits.

THERMAL DISCORD AND NEGATIVITY IN A TWO-SPIN-QUTRIT SYSTEM UNDER DIFFERENT MAGNETIC FIELDS

2013 ◽  
Vol 11 (08) ◽  
pp. 1350070 ◽  
Author(s):  
XIAO-JING LI ◽  
HUI-HUI JI ◽  
XI-WEN HOU
Keyword(s):  
Magnetic Fields ◽  
Quantum Discord ◽  
Strong Field ◽  
Quantum Correlations ◽  
Mixed States ◽  
Classical Correlation ◽  
Lower Temperature ◽  
Qubit States ◽  
Quantum And Classical Correlations

The characterization of quantum discord (QD) has been well understood only for two-qubit states and is little known for mixed states beyond qubits. In this work, thermal quantum discord is studied for a qutrit system in different magnetic fields, where classical correlation and entanglement negativity are calculated for comparison. It is shown that the discord is more robust against temperature than the negativity. For a suitable region of magnetic field and its direction, the discord is non-zero while the negativity is zero. When the system is at a lower temperature, these three quantities, however, display a similar behavior for the varied field and direction, and their discontinuities come from crossovers between different ground states in the system. Moreover, the inequality between the quantum and classical correlations depends upon the system parameters as well as the temperature. In particular, both correlations are equal at a suitable field, direction, and temperature. Remarkably, such an equality remains for a strong field in the antiparallel direction, while both correlations in two-qubit systems are identical for any antiparallel field and temperature. These are useful for quantum information and understanding quantum correlations in qutrit mixed states.

scholarly journals Quantum Networks and Symmetries

2021 ◽  
Author(s):  
Kiara Hansenne ◽  
Zhen-Peng xu ◽  
Tristan Kraft ◽  
Otfried Gühne
Keyword(s):  
Quantum Correlations ◽  
Quantum States ◽  
Network Structures ◽  
Large Network ◽  
Quantum Networks ◽  
Graph States ◽  
Versatile Tool ◽  
Entangled Quantum States ◽  
Basic Network

Abstract Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress of the field, but so far only results for small basic network structures or pure quantum states are known. Here we show that symmetries provide a versatile tool for the analysis of correlations in quantum networks. We provide an analytical approach to characterize correlations in large network structures with arbitrary topologies. As examples, we show that entangled quantum states with a bosonic or fermionic symmetry can not be generated in networks; moreover, cluster and graph states are not accessible. Our methods can be used to design certification methods for the functionality of specific links in a network and have implications for the design of future network structures.

scholarly journals Bond dimension witnesses and the structure of homogeneous matrix product states

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 50 ◽  
Author(s):  
Miguel Navascues ◽  
Tamas Vertesi
Keyword(s):  
Ground State ◽  
Quantum Correlations ◽  
Matrix Product ◽  
Solid State Physics ◽  
Matrix Product States ◽  
Matrix Algebras ◽  
Finite Dimensional ◽  
Homogeneous Matrix ◽  
Local Operators

For the past twenty years, Matrix Product States (MPS) have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via site-independent tensors and a boundary condition. Exploiting a connection with the theory of matrix algebras, we derive two structural properties shared by all hMPS, namely: a) there exist local operators which annihilate all hMPS of a given bond dimension; and b) there exist local operators which, when applied over any hMPS of a given bond dimension, decouple (cut) the particles where they act from the spin chain while at the same time join (glue) the two loose ends back again into a hMPS. Armed with these tools, we show how to systematically derive `bond dimension witnesses', or 2-local operators whose expectation value allows us to lower bound the bond dimension of the underlying hMPS. We extend some of these results to the ansatz of Projected Entangled Pairs States (PEPS). As a bonus, we use our insight on the structure of hMPS to: a) derive some theoretical limitations on the use of hMPS and hPEPS for ground state energy computations; b) show how to decrease the complexity and boost the speed of convergence of the semidefinite programming hierarchies described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of finite-dimensional quantum correlations.

scholarly journals ON BELL INEQUALITY VIOLATIONS WITH HIGH-DIMENSIONAL SYSTEMS

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1807-1823 ◽  
Author(s):  
ADETUNMISE C. DADA ◽  
ERIKA ANDERSSON
Keyword(s):  
Quantum Information ◽  
Information Science ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
High Dimensional ◽  
Separable State ◽  
Local Dimension ◽  
Quantum Information Science ◽  
Fundamental Physics

Quantum correlations resulting in violations of Bell inequalities have generated a lot of interest in quantum information science and fundamental physics. In this paper, we address some questions that become relevant in Bell-type tests involving systems with local dimension greater than 2. For CHSH-Bell tests within 2D subspaces of such high-dimensional systems, it has been suggested that experimental violation of Tsirelson's bound indicates that more than 2D entanglement was present. We explain that the overstepping of Tsirelson's bound is due to violation of fair sampling, and can in general be reproduced by a separable state, if fair sampling is violated. For a class of Bell-type inequalities generalized to d-dimensional systems, we then consider what level of violation is required to guarantee d-dimensional entanglement of the tested state, when fair sampling is satisfied. We find that this can be used as an experimentally feasible test of d-dimensional entanglement for up to quite high values of d.

Sign in / Sign up

Export Citation Format

Share Document