03.10.+m Entanglement measures

Trace-distance measure of coherence

Date: 
2015-11-10 - 2016-01-12
Author(s): 

Swapan Rana, Preeti Parashar, Maciej Lewenstein

Reference: 

Phys. Rev. A 93, 012110

We show that trace distance measure of coherence is a strong monotone for all qubit and, so called, X states.

Practical Entanglement Estimation for Spin-System Quantum Simulators

Date: 
2015-07-09 - 2016-03-09
Author(s): 

O. Marty, M. Cramer, and M. B. Plenio

Reference: 

Phys. Rev. Lett. 116, 105301

We present practical methods to measure entanglement for quantum simulators that can be realized with trapped ions, cold atoms, and superconducting qubits. Focusing on long- and short-range Ising-type Hamiltonians, we introduce schemes that are applicable under realistic experimental conditions including mixedness due to, e.g., noise or temperature. In particular, we identify a single observable whose expectation value serves as a lower bound to entanglement and that may be obtained by a simple quantum circuit.

Violation of Bell inequalities in larger Hilbert spaces: robustness and challenges

Date: 
2016-01-08
Author(s): 

W. Weiss, G. Benenti, G. Casati, I. Guarneri, T. Calarco, M. Paternostro, S. Montangero

Reference: 

New J. Phys. 18 013021 (2016)
http://dx.doi.org/10.1088/1367-2630/18/1/013021

We explore the challenges posed by the violation of Bell-like inequalities by d-dimensional systems exposed to imperfect state-preparation and measurement settings. We address, in particular, the limit of high-dimensional systems, naturally arising when exploring the quantum-to-classical transition. We show that, although suitable Bell inequalities can be violated, in principle, for any dimension of given subsystems, it is in practice increasingly challenging to detect such violations, even if the system is prepared in a maximally entangled state.

A note on the gap between rank and border rank

Date: 
2015-04-21
Author(s): 

Jeroen Zuiddam

Reference: 

arXiv:1504.05597 [math.AC]

We study the tensor rank of a certain algebra. As a result we find a sequence of tensors with a large gap between rank and border rank, and thus a counterexample to a conjecture of Rhodes. We also obtain a new lower bound on the tensor rank of powers of the generalized W-state.

Quantifying entanglement with scattering experiments

Date: 
2013-10-03
Author(s): 

O. Marty, M. Epping, H. Kampermann, D. Bruß, M.B. Plenio and M. Cramer

Reference: 

Physical Review B 89, 125117 (2014)

We show how the entanglement contained in states of spins arranged on a lattice may be quantified with observables arising in scattering experiments. We focus on the partial differential cross-section obtained in neutron scattering from magnetic materials but our results are sufficiently general such that they may also be applied to, e.g., optical Bragg scattering from ultracold atoms in optical lattices or from ion chains.

Dissociation and annihilation of multipartite entanglement structure in dissipative quantum dynamics

Date: 
2013-12-23
Author(s): 

Sergey N. Filippov, Alexey A. Melnikov and Mário Ziman

Reference: 

Phys. Rev. A 88, 062328 (2013)

We study the dynamics of the entanglement structure of a multipartite system experiencing a dissipative evolution. We characterize the processes leading to a particular form of output-system entanglement and provide a recipe for their identification via concatenations of particular linear maps with entanglement-breaking operations. We illustrate the applicability of our approach by considering local and global depolarizing noises acting on general multiqubit states.

Matrix product states with long-range localizable entanglement

Date: 
2012-12-14
Author(s): 

T. B. Wahl, D. Pérez-García, and J. I. Cirac

Reference: 

URL: http://link.aps.org/doi/10.1103/PhysRevA.86.062314
DOI: 10.1103/PhysRevA.86.062314
PACS: 03.67.Mn, 03.65.Ud, 75.10.Pq, 71.10.Hf

We derive a criterion to determine when a translationally invariant matrix product state (MPS) has long-range localizable entanglement, where that quantity remains finite in the thermodynamic limit. We give examples fulfilling this criterion and eventually use it to obtain all such MPS with bond dimension 2 and 3.

An optimization library for evaluating convex-roof entanglement measures

Date: 
2011-09-03
Author(s): 

B. Roethlisberger, J. Lehmann, and D. Loss

Reference: 

Comput. Phys. Comm. 183, 155

We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures.

Entangling two distant oscillator with a quantum reservoir

Date: 
2011-09-08
Author(s): 

A. Wolf, G. de Chiara, E. Kajari, E. Lutz, G. Morigi

Reference: 

arXiv:1102.1838v1
Europhys. Lett. 95, 60008 (2011)
doi:10.1209/0295-5075/95/60008

The generation of entanglement between two oscillators that interact via a common reservoir is theoretically studied. The reservoir is modeled by a one-dimensional harmonic crystal initially in thermal equilibrium. Starting from a separable state, the oscillators can become entangled after a transient time, that is of the order of the thermalization time scale. This behavior is observed at finite temperature even when the oscillators are at a distance significantly larger than the crystal's interparticle spacing.

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