skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Evolution of pairwise entanglement in a coupled n-body system

Abstract

We study the exact evolution of two noninteracting qubits, initially in a Bell state, in the presence of an environment, modeled by a kicked Ising spin chain. Dynamics of this model range from integrable to chaotic and we can handle numerics for a large number of qubits. We find that the entanglement (as measured by concurrence) of the two qubits has a close relation to the purity of the pair, and closely follows an analytic relation derived for Werner states. As a collateral result we find that an integrable environment causes quadratic decay of concurrence as well as of purity, while a chaotic environment causes linear decay. Both quantities display recurrences in an integrable environment.

Authors:
 [1];  [2];  [3];  [4]
  1. Instituto de Fisica, University of Mexico (UNAM) (Mexico)
  2. (UNAM) (Mexico)
  3. Centro de Ciencias Fisicas, University of Mexico (UNAM) (Mexico)
  4. (Mexico)
Publication Date:
OSTI Identifier:
20786650
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.73.012305; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; BELL THEOREM; CHAOS THEORY; DECAY; EVOLUTION; IMPURITIES; INTEGRAL CALCULUS; ISING MODEL; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUBITS; SPIN

Citation Formats

Pineda, Carlos, Centro de Ciencias Fisicas, University of Mexico, Seligman, Thomas H., and Centro Internacional de Ciencias, Cuernavaca. Evolution of pairwise entanglement in a coupled n-body system. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Pineda, Carlos, Centro de Ciencias Fisicas, University of Mexico, Seligman, Thomas H., & Centro Internacional de Ciencias, Cuernavaca. Evolution of pairwise entanglement in a coupled n-body system. United States. doi:10.1103/PHYSREVA.73.0.
Pineda, Carlos, Centro de Ciencias Fisicas, University of Mexico, Seligman, Thomas H., and Centro Internacional de Ciencias, Cuernavaca. Sun . "Evolution of pairwise entanglement in a coupled n-body system". United States. doi:10.1103/PHYSREVA.73.0.
@article{osti_20786650,
title = {Evolution of pairwise entanglement in a coupled n-body system},
author = {Pineda, Carlos and Centro de Ciencias Fisicas, University of Mexico and Seligman, Thomas H. and Centro Internacional de Ciencias, Cuernavaca},
abstractNote = {We study the exact evolution of two noninteracting qubits, initially in a Bell state, in the presence of an environment, modeled by a kicked Ising spin chain. Dynamics of this model range from integrable to chaotic and we can handle numerics for a large number of qubits. We find that the entanglement (as measured by concurrence) of the two qubits has a close relation to the purity of the pair, and closely follows an analytic relation derived for Werner states. As a collateral result we find that an integrable environment causes quadratic decay of concurrence as well as of purity, while a chaotic environment causes linear decay. Both quantities display recurrences in an integrable environment.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 1,
volume = 73,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}
  • The generation of entanglement between two identical, interacting quantum dots - initially in ground states--by a coherent field and the subsequent time evolution of the entanglement are studied by calculating the concurrence between the two dots. The results predict that while it is possible to generate entanglement (or entanglement of formation, as defined for a mixed state) between the two dots, at no time do the dots become fully entangled to each other or is a maximally entangled Bell state ever achieved. We also observe that the degree of entanglement increases with an increase in the photon number inside themore » cavity and a decrease in the dot-photon coupling. The behavior of the two-dot system, initially prepared in an entangled state and interacting with thermal light, is also studied.« less
  • We show that spin squeezing implies pairwise entanglement for arbitrary symmetric multiqubit states. If the squeezing parameter is less than or equal to 1, we demonstrate a quantitative relation between the squeezing parameter and the concurrence for the even and odd states. We prove that the even states generated from the initial state with all qubits being spin down, via the one-axis twisting Hamiltonian, are spin squeezed if and only if they are pairwise entangled. For the states generated via the one-axis twisting Hamiltonian with an external transverse field for any number of qubits greater than 1 or via themore » two-axis countertwisting Hamiltonian for any even number of qubits, the numerical results suggest that such states are spin squeezed if and only if they are pairwise entangled.« less
  • Considering the dynamics of a two-qubit entangled system in the decoherence environment, we investigate the stability of pairwise entanglement under decoherence. We find that for different decoherence models, there exists some special class of entangled states of which the pairwise entanglement is the most stable. The lifetime of the entanglement in these states is larger than other states with the same initial entanglement. In addition, we also investigate the dynamics of pairwise entanglement in the ground state of spin models such as Heisenberg and XXY models.
  • We analyze quantum entanglement of Stokes light and atomic electronic polarization excited during single-pass, linear-regime, stimulated Raman scattering in terms of optical wave-packet modes, and atomic-ensemble spatial modes. The output of this process is confirmed to be decomposable into multiple discrete, Bosonic mode pairs, each pair undergoing independent evolution into a two-mode squeezed state. For this we extend the Bloch-Messiah reduction theorem, previously known for discrete linear systems [S. L. Braunstein, Phys. Rev. A 71, 055801 (2005)]. We present typical mode functions in the case of one-dimensional scattering in an atomic vapor. We find that in the absence of dispersion,more » one mode pair dominates the process, leading to a simple interpretation of entanglement in this continuous-variable system. However, many mode pairs are excited in the presence of dispersion-induced temporal walkoff of the Stokes, as witnessed by the photon-count statistics. We also consider the readout of the stored atomic polarization using the anti-Stokes scattering process. We prove that the readout process can also be decomposed into multiple mode pairs, each pair undergoing independent evolution analogous to a beam-splitter transformation. We show that this process can have unit efficiency under realistic experimental conditions. The shape of the output light wave packet can be predicted. In the case of unit readout efficiency it contains only excitations originating from a specified atomic excitation mode.« less