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Physical Review A

Stochastic resonance of quantum discord

Chee‐Kong Lee, L. C. Kwek, Jianshu Cao

Published Dec 19, 2011• 8 citations
Publisher

Abstract

We study the stochastic resonance of quantum discord (``discord resonance'') in coupled quantum systems and make a comparison with the stochastic resonance of entanglement (``entanglement resonance''). It is found that the discord resonance is much more robust against dephasing noise and thermal effects than the entanglement resonance. We also show that, unlike the entanglement resonance, the level of dissipation at which the discord resonance occurs is not sensitive to dephasing noise. These results suggest that it is easier to detect the discord resonance in actual experiments, where the dephasing noise and temperature are difficult to control.

DOI
10.1103/physreva.84.062113

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We study the stochastic resonance of quantum discord (discord resonance'') in coupled quantum systems and make a comparison with the stochastic resonance of entanglement (entanglement resonance''). It is found that the discord resonance is much more robust against dephasing noise and thermal effects than the entanglement resonance. We also show that, unlike the entanglement resonance, the level of dissipation at which the discord resonance occurs is not sensitive to dephasing noise. These results suggest that it is easier to detect the discord resonance in actual experiments, where the dephasing noise and temperature are difficult to control.
We calculate the dissipative dynamics of two-qubit quantum discord under Markovian environments. We analyze various dissipative channels such as dephasing, depolarizing, and generalized amplitude damping, assuming independent perturbation, in which each qubit is coupled to its own channel. Choosing initial conditions that manifest the so-called sudden death of entanglement, we compare the dynamics of entanglement with that of quantum discord. We show that in all cases where entanglement suddenly disappears, quantum discord vanishes only in the asymptotic limit, behaving similarly to individual decoherence of the qubits, even at finite temperatures. Hence, quantum discord is more robust than the entanglement against to decoherence so that quantum algorithms based only on quantum discord correlations may be more robust than those based on entanglement.
We calculate the dissipative dynamics of two-qubit quantum discord under Markovian environments. We analyze various dissipative channels such as dephasing, depolarizing, and generalized amplitude damping, assuming independent perturbation, in which each qubit is coupled to its own channel. Choosing initial conditions that manifest the so-called sudden death of entanglement, we compare the dynamics of entanglement with that of quantum discord. We show that in all cases where entanglement suddenly disappears, quantum discord vanishes only in the asymptotic limit, behaving similarly to individual decoherence of the qubits, even at finite temperatures. Hence, quantum discord is more robust than the entanglement against decoherence so that quantum algorithms based only on quantum discord correlations may be more robust than those based on entanglement.
"We review the theoretical and the experimental researches aimed at quantifying or identifying quantum correlations in liquid-state nuclear magnetic resonance (NMR) systems at room temperature. We first overview, at the formal level, a method to determine the quantum discord and its classical counterpart in systems described by a deviation matrix. Next, we describe an experimental implementation of that method. Previous theoretical analysis of quantum discord decoherence had predicted the time dependence of the discord to change suddenly under the influence of phase noise. The experiment attests to the robustness of the effect, sufficient to confirm the theoretical prediction even under the additional influence of a thermal environment. Finally, we discuss an observable witness for the quantumness of correlations in two-qubit systems and its first NMR implementation. Should the nature, not the amount, of the correlation be under scrutiny, the witness offers the most attractive alternative."
The dynamics of quantum discord for a class of qutrit-qutrit states under depolarizing and dephasing noise are investigated using the geometric measure of quantum discord. We find that in the quantum discord for these states, a sudden change near the transition point exists from a bound-entangled to a free-entangled state, and that the sudden change point remains unchanged in later evolution under depolarizing noise. Moreover, the behavior of quantum discord is independent of the parameter of the given initial states in many regions.
We analyze the classical and quantum correlation properties of the standard and so-called quasiclassical depolarizing channel with correlated noise and non-Markovian dephasing channel, specifically we use the quantum discord, entanglement, and measurement-induced disturbance (MID) to measure the quantum correlations. For the depolarizing channel, we find that the memory effect has more influence on the MID and quantum discord than entanglement. For the dephasing channel, we show that the non-Markovian dephasing channel is more robust than Markovian dephasing channel against decoherence. We also find that at first MID and quantum discord take different values, and then after a specific time they will take almost the same value and both decay monotonically in the same way.
Measurements of quantum systems disturb their states. To quantify this nonclassical characteristic, Zurek and Ollivier [Phys. Rev. Lett. 88, 017901 (2001)] introduced the quantum discord, a quantum correlation that can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers the exponential speed-up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy. We also identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.