scholarly journals Simulation of Equatorial von Neumann Measurements on GHZ States Using Nonlocal Resources

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Jean-Daniel Bancal ◽  
Cyril Branciard ◽  
Nicolas Gisin
Keyword(s):  
Quantum System ◽  
Quantum State ◽  
Quantum Correlations ◽  
Communication Cost ◽  
Computational Power ◽  
Bloch Sphere ◽  
Classical Communication ◽  
Von Neumann ◽  
Ghz States ◽  
Von Neumann Measurements

Reproducing with elementary resources the correlations that arise when a quantum system is measured (quantum state simulation) allows one to get insight on the operational and computational power of quantum correlations. We propose a family of models that can simulate von Neumann measurements in thex−yplane of the Bloch sphere onn-partite GHZ states. For the tripartite and fourpartite states, the models use only bipartite nonlocal boxes; they can be translated into classical communication schemes with finite average communication cost.

Are quantum correlations symmetric?

2010 ◽  
Vol 10 (11&12) ◽  
pp. 901-910
Author(s):  
Karol Horodecki ◽  
Michal Horodecki ◽  
Pawel Horodecki
Keyword(s):  
Quantum State ◽  
Quantum Correlations ◽  
Operational Definition ◽  
Entangled State ◽  
Classical Communication ◽  
Measure Of Asymmetry ◽  
Bound Entanglement ◽  
Definition Of

We provide operational definition of asymmetry of entanglement: An entangled state contains asymmetric entanglement if its subsystems can not be exchanged (swapped) by means of local operations and classical communication. We show that in general states have asymmetric entanglement. This allows to construct nonsymmetric measure of entanglement, and a parameter that reports asymmetry of entanglement contents of quantum state. We propose asymptotic measure of asymmetry of entanglement, and show that states for which it is nonzero, contain necessarily bound entanglement.

scholarly journals Lagrangian description of Heisenberg and Landau–von Neumann equations of motion

2020 ◽  
Vol 35 (19) ◽  
pp. 2050161
Author(s):  
F. M. Ciaglia ◽  
F. Di Cosmo ◽  
A. Ibort ◽  
G. Marmo ◽  
L. Schiavone ◽  
...  
Keyword(s):  
Quantum System ◽  
Quantum State ◽  
Equations Of Motion ◽  
Quantum States ◽  
Heisenberg Equation ◽  
Lagrangian Description ◽  
Von Neumann ◽  
Fixed Reference ◽  
Von Neumann Equation ◽  
Algebra Of Operators

An explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau–von Neumann equation on the manifold of quantum states which are isospectral with respect to a fixed reference quantum state.

scholarly journals Distillation of secret key and entanglement from quantum states

2005 ◽  
Vol 461 (2053) ◽  
pp. 207-235 ◽  
Author(s):  
Igor Devetak ◽  
Andreas Winter
Keyword(s):  
Quantum Correlations ◽  
Quantum States ◽  
Von Neumann Entropy ◽  
Secret Key ◽  
Classical Communication ◽  
Von Neumann ◽  
Information Theoretic ◽  
Einstein Podolsky Rosen ◽  
Classical Quantum ◽  
The Difference

We study and solve the problem of distilling a secret key from quantum states representing correlation between two parties (Alice and Bob) and an eavesdropper (Eve) via one–way public discussion: we prove a coding theorem to achieve the ‘wire–tapper’ bound, the difference of the mutual information Alice–Bob and that of Alice–Eve, for so–called classical–quantum–quantum–correlations, via one–way public communication. This result yields information–theoretic formulae for the distillable secret key, giving ‘ultimate’ key rate bounds if Eve is assumed to possess a purification of Alice and Bob's joint state. Specializing our protocol somewhat and making it coherent leads us to a protocol of entanglement distillation via one–way LOCC (local operations and classical communication) which is asymptotically optimal: in fact we prove the so–called ‘hashing inequality’, which says that the coherent information (i.e. the negative conditional von Neumann entropy) is an achievable Einstein–Podolsky–Rosen rate. This result is known to imply a whole set of distillation and capacity formulae, which we briefly review.

scholarly journals QUANTUM DISCORD FOR MULTIPARTITE COHERENT STATES INTERPOLATING BETWEEN WERNER AND GREENBERGER–HORNE–ZEILINGER STATES

2012 ◽  
Vol 10 (05) ◽  
pp. 1250060 ◽  
Author(s):  
M. DAOUD ◽  
R. AHL LAAMARA
Keyword(s):  
Quantum System ◽  
Ground State ◽  
Coherent States ◽  
Quantum Discord ◽  
Temporal Evolution ◽  
Conditional Entropy ◽  
Quantum Correlations ◽  
Ghz States ◽  
Werner States ◽  
Explicit Expressions

The quantum discord is used as measure of quantum correlations for two families of multipartite coherent states. The first family interpolates between generalized GHZ states and generalized Werner states. The second one is an interpolation between generalized GHZ and the ground state of the multipartite quantum system. Two inequivalent ways to split the system in a pair of qubits are introduced. The explicit expressions of quantum quantum discord in multipartite coherent states are derived. Its evaluation uses the Koashi–Winter relation in optimizing the conditional entropy. The temporal evolution of quantum correlations (quantum discord and entanglement) is also discussed.

Bell inequality for quNits with binary measurements

2003 ◽  
Vol 3 (2) ◽  
pp. 157-164
Author(s):  
H. Bechmann-Pasquinucci ◽  
N. Gisin
Keyword(s):  
Quantum Cryptography ◽  
Bell Inequality ◽  
The Other ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Von Neumann ◽  
Chsh Inequality ◽  
Intermediate States ◽  
Von Neumann Measurements

We present a generalized Bell inequality for two entangled quNits. On one quNit the choice is between two standard von Neumann measurements, whereas for the other quNit there are N^2 different binary measurements. These binary measurements are related to the intermediate states known from eavesdropping in quantum cryptography. The maximum violation by \sqrt{N} is reached for the maximally entangled state. Moreover, for N=2 it coincides with the familiar CHSH-inequality.

Non-Markovianity leading to coherence revivals in an open quantum system

2020 ◽  
pp. 2050040
Author(s):  
Y. Yugra ◽  
F. De Zela
Keyword(s):  
Quantum Information ◽  
Quantum System ◽  
Open Quantum System ◽  
Open Systems ◽  
Quantum Correlations ◽  
Experimental Proof ◽  
Optical Setup ◽  
Open Quantum ◽  
All Optical ◽  
Proof Of Principle

Coherence and quantum correlations have been identified as fundamental resources for quantum information tasks. As recently shown, these resources can be interconverted. In multipartite systems, entanglement represents a prominent case among quantum correlations, one which can be activated from coherence. All this makes coherence a key resource for securing the operational advantage of quantum technologies. When dealing with open systems, decoherence hinders full exploitation of quantum resources. Here, we present a protocol that allows reaching the maximal achievable amount of coherence in an open quantum system. By implementing our protocol, or suitable variants of it, coherence losses might be fully compensated, thereby leading to coherence revivals. We provide an experimental proof of principle of our protocol through its implementation with an all-optical setup.

scholarly journals Reading a Qubit Quantum State with a Quantum Meter: Time Unfolding of Quantum Darwinism and Quantum Information Flux

2019 ◽  
Vol 26 (04) ◽  
pp. 1950023
Author(s):  
Salvatore Lorenzo ◽  
Mauro Paternostro ◽  
G. Massimo Palma
Keyword(s):  
Quantum Information ◽  
Harmonic Oscillator ◽  
Quantum System ◽  
Quantum State ◽  
Common Theme ◽  
Quantum Harmonic Oscillator ◽  
Collision Model ◽  
Single Qubit ◽  
Quantum Darwinism

Quantum non-Markovianity and quantum Darwinism are two phenomena linked by a common theme: the flux of quantum information between a quantum system and the quantum environment it interacts with. In this work, making use of a quantum collision model, a formalism initiated by Sudarshan and his school, we will analyse the efficiency with which the information about a single qubit gained by a quantum harmonic oscillator, acting as a meter, is transferred to a bosonic environment. We will show how, in some regimes, such quantum information flux is inefficient, leading to the simultaneous emergence of non-Markovian and non-darwinistic behaviours.

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