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International Journal of Quantum Information

QUANTUM CORRELATIONS IN THE "q-DEFORMED" WERNER STATE

Бо Лю, Kang Xue, Gangcheng Wang, Chunfang Sun, Lidan Gou, Guijiao Du

Published Mar 1, 2013• 3 citations
Publisher

Abstract

We investigate quantum discord of the "q-deformed" Werner state via Yang–Baxterization approach. There are two parameters q and u in this "q-deformed" Werner state. The parameter u, which plays an important role in some typical models, is related to the probability of the "q-deformed" two-qubit spin singlet state in this study. The "q-deformed" parameter q is related to the single loop through d = q + q-1. When topological parameter d approaches 2 (i.e. q → 1), the "q-deformed" Werner state degenerates into the well-known Werner state. The results show that topological parameter d has great influence on quantum correlations of the "q-deformed" Werner state. When we fix the parameter u, the quantum correlations decrease with increasing the single loop d. When d approaches +∞ (i.e. q → 0+or +∞), quantum discord, geometric measure of quantum discord and entanglement all tend to 0. While d approaches 2 (i.e. q → 1), all of them just have the same results with the Werner state.

DOI
10.1142/s0219749913500184

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We investigate quantum discord of the "q-deformed" Werner state via Yang–Baxterization approach. There are two parameters q and u in this "q-deformed" Werner state. The parameter u, which plays an important role in some typical models, is related to the probability of the "q-deformed" two-qubit spin singlet state in this study. The "q-deformed" parameter q is related to the single loop through d = q + q-1. When topological parameter d approaches 2 (i.e. q → 1), the "q-deformed" Werner state degenerates into the well-known Werner state. The results show that topological parameter d has great influence on quantum correlations of the "q-deformed" Werner state. When we fix the parameter u, the quantum correlations decrease with increasing the single loop d. When d approaches +∞ (i.e. q → 0+or +∞), quantum discord, geometric measure of quantum discord and entanglement all tend to 0. While d approaches 2 (i.e. q → 1), all of them just have the same results with the Werner state.
Quantum correlations among parts of a composite quantum system are a fundamental resource for several applications in quantum information. In general, quantum discord can measure quantum correlations. In that way, we investigate the quantum discord of the two-qubit system constructed from the Yang—Baxter Equation. The density matrix of this system is generated through the unitary Yang—Baxter matrix R̆. The analytical expression and numerical result of quantum discord and geometric measure of quantum discord are obtained for the Yang—Baxter system. These results show that quantum discord and geometric measure of quantum discord are only connect with the parameter θ, which is the important spectral parameter in Yang—Baxter equation.
Quantum correlations among different parts of a composite quantum system are the fundamental resource of several applications in quantum information. In general, quantum discord can measure quantum correlations. In that way, the quantum correlations in the Yang-Baxter spin-1/2 chain mode are investigated. In the second part of the paper, the Yang-Baxter spin-1/2 chain modes are constructed from the Yang-Baxter equation. First, we analyze the two matrix representations of Temperly-Lieb algebra. Second, the two solutions of the Yang-Baxter equation are generated using the Yang-Baxterization. Finally, we can change the usual two-particle spin-1/2 chain to the Yang-Baxter spin-1/2 chain modes by means of the unitary Yang-Baxter matrix-R. In the third part, the density matrices of the two chain modes are generated in the thermal equilibrium state in a canonical ensemble. According to the definition of the geometric measure of quantum discord, the analytical expressions of the geometric measure of quantum discord, in the temperature and the external magnetic field, are obtained for the Yang-Baxter spin-1/2 chain modes. When the temperature and the magnetic field intensity increase, the geometric measure of quantum discord decreases. Under the specific conditions, the result of the second chain mode is similar to that of the first one. Then we obtain the numerical results of quantum discord, the geometric measure of quantum discord, and concurrence. It is found that the concurrence can quickly decrease to the value of zero when the temperature is greater than the value of one. At the same time, quantum discord and the geometric measure of quantum discord are not of the value of zero. Thus the quantum discord and the geometric measure of quantum discord can go beyond the concept of entanglement and obtain the “quantumness” of the correlations between the two parts of a system for the Yang-Baxter spin-1/2 chain modes. They are very good quantum resources for quantum information and quantum computing.
Quantum Discord of fff-Deformed Bipartite Entangled Oscillators
Quantum correlations in compound systems are of great importance, and they are fundamental resource for the development of quantum computation protocols and quantum information. In this work we construct bipartite pure coherent states using the fff-deformed oscillator formalism and the Barut-Girardello deformation function. Also we construct the extension of these systems to mixed states using Werner like states. For the states constructed, we study the dependence of the entanglement and quantum discord upon the deformation and mixed parameters.
We investigate the dynamic behaviors of quantum discord for a central two-qubit system coupled to an XY\mathit{XY}XY-spin-chain environment. In the weak-coupling regime, we show that the quantum discord for the two central qubits can become minimized rapidly close to the critical point of a quantum phase transition. By considering the two qubits that are initially prepared in the Werner state, we study the evolution of the quantum discord and that of entanglement under the same conditions. Our results imply that entanglement can disappear completely after a finite time, while the quantum discord decreases and tends to be a stable value according to the initial-state parameter for a very-long-time interval. In this sense, the quantum discord is more robust than entanglement for the quantum system exposed to the environment. The relation between the quantum correlations and the classical correlation is also shown for two particular cases.
Abstract Using the single-mode approximation we study the quantum correlations of a free Dirac field on the Werner state in the noninertial frame. We present analytical quantum discord D and its geometric measurement D G . We notice that the quantum discord still exists for the system ρ ARI even in the acceleration limit. We also calculate the entanglement of formation (EOF) and the geometric measure of entanglement ( E G ) to compare the behaviors of the entanglement with the quantum discord. The entanglement is nonzero for the fidelity of the Werner state with a Bell state F > 0.5, while the quantum discord is equal to zero only for F = 0.25. We also observe that the quantum discord is more robust to the change of acceleration than the entanglement, which is more sensitive to the acceleration.
We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.