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Physical Review A

Enhancing entanglement of two qubits undergoing independent decoherences by local pre- and postmeasurements

Zhong‐Xiao Man, Yun‐Jie Xia, Nguyen Ba An

Published Nov 19, 2012• 70 citations
Publisher

Abstract

We consider two entangled qubits, each of which is coupled to its own reservoir, so that their entanglement degrades with time. To enhance the qubits' entanglement at a time during the evolution we propose a proper combination of pre- and postmeasurements to be performed locally on individual qubits. The premeasurements are weak measurements, but the postmeasurements may be either quantum measurement reversals or weak measurements again, depending on the situation at the time they are applied. Given the parameters of the initial qubits' state, the premeasurements' strength, and the evolution time, we establish the optimal conditions for the postmeasurements so that the qubits' entanglement becomes the largest possible. Actually, by our scheme, less entangled qubits can evolve into more entangled ones with a finite probability, or even into a near-maximally entangled state but with a vanishingly low probability. We also examine the entanglement distribution among different pairs of subsystems involved and find out that the pairwise concurrence dynamics in our scheme differs strikingly from that in the situation without any control actions.

DOI
10.1103/physreva.86.052322

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We consider two entangled qubits, each of which is coupled to its own reservoir, so that their entanglement degrades with time. To enhance the qubits' entanglement at a time during the evolution we propose a proper combination of pre- and postmeasurements to be performed locally on individual qubits. The premeasurements are weak measurements, but the postmeasurements may be either quantum measurement reversals or weak measurements again, depending on the situation at the time they are applied. Given the parameters of the initial qubits' state, the premeasurements' strength, and the evolution time, we establish the optimal conditions for the postmeasurements so that the qubits' entanglement becomes the largest possible. Actually, by our scheme, less entangled qubits can evolve into more entangled ones with a finite probability, or even into a near-maximally entangled state but with a vanishingly low probability. We also examine the entanglement distribution among different pairs of subsystems involved and find out that the pairwise concurrence dynamics in our scheme differs strikingly from that in the situation without any control actions.
Addressing various types of decoherence is of paramount importance for employing entanglement in quantum information processing and quantum computing. In this paper, we propose two schemes to manipulate entanglement of two qubits stored in a common environment by means of combined weak measurements and quantum measurement reversals. We derive the explicit conditions for the measurement strengths under which at any time and for any initial states the qubits' entanglement can be protected quite well with a reasonable finite success probability. Moreover, the two schemes enable us in principle to achieve the maximal entanglement or to restore the initial state (entanglement) of the qubits.
Qubits A, B and C, initially prepared in a like-GHZ state, are distributed to three remote receivers through a decoherence environment. A weak measurement is firstly performed on each qubit before experiencing the decoherence channel, and then the receivers carry out a quantum measurement reversal on individual qubit after receiving them. The qubits’ entanglement is evaluated by means of negativity. The results show the pre- and post-measurements’ strength has an important influence on tripartite entanglement for the initially given state, and proper pre- and post-measurements’ strength always effectively improves tripartite entanglement, which is significant to protect entanglement from decoherence.
We study the entanglement trapping of two entangled qubits, each of which is in its own photonic band gap, based on the weak measurement and quantum measurement reversal. An almost maximal entanglement of the two-qubit system can be trapped by using a certain weak measurement strength. Furthermore, we find that the optimal entanglement enhancing is not only dependent on the weak measurement strength but also on the different initial states. The outcomes in our scheme are completely different from that without any measurement on the studied system.
The entanglement of two qubits, each defined as an effective two-level, spin 1/2 system, is investigated for the case that the qubits interact via a Heisenberg XY interaction and are subject to decoherence due to population relaxation and thermal effects. For zero temperature, the time-dependent concurrence is studied analytically and numerically for some typical initial states, including a separable (unentangled) initial state. An analytical formula for non-zero steady state concurrence is found for any initial state, and optimal parameter values for maximizing steady state concurrence are given. The steady state concurrence is found analytically to remain non-zero for low, finite temperatures. We also identify the contributions of global and local coherence to the steady state entanglement.
We study the entanglement dynamics of a two-qubit system, each of which is embedded into its local reservoir, and the entanglement distribution among all the bipartite subsystems including qubit-qubit, qubit-reservoir, and reservoir-reservoir. It is found that the entanglement can be stably distributed among all components and particularly it also satisfies an identity firstly given by Yonac, Yu and Eberly (J. Phys. B 40, S45 (2007)) for a double J-C model without decoherence. While the explicit distribution of the entanglement is dependent of the detail of the model, even the approximation used, the identity remains unchanged. Our unified treatment includes the previous results in the literature as special cases. The result reveals the profound nature of the entanglement and should have significant implications for quantum information processing. below) has been satisfied at any time. This may be not surprising since the double J-C model has no decoherence and any initial information can be preserved in the time evolution. However, it would be surprising if the identity is still valid in the presence of the decoherence, in which a non-equilibrium relaxation process is involved. In this paper, we show that it is indeed true for such a system consisted of two qubits locally interacting with two reser- voirs. We find that the distribution of the entanglement among the bipartite subsystems is dependent of the ex- plicit property of the environment and its coupling with the qubit. The rich dynamical behaviors obtained pre- viously in the literature can be regarded as the special cases of our present result or Markovian approximation. Particularly, we find that the entanglement can stably distribute among all the bipartite subsystems if the qubit and its environment can form a bound state and the non- Markovian effect is important. Irrespective of how dis- tributes the entanglement, it is found that the identity about the entanglement in the whole system can be sat- isfied at any time, which reveals the profound physics of the entanglement dynamics. We consider two qubits interacting with two uncorre- lated vacuum reservoirs. Due to the dynamical indepen- dence between the two local subsystems, we can firstly solve the single subsystem, then apply the result obtained to the double-qubit case. The Hamiltonian of each local subsystem is (16)
We present an approach to the study of entanglement decay which focuses on collective properties. As an example, we investigate the entanglement decay of a two-qubit system produced by local identical reservoirs acting on the qubits for three experimentally and theoretically relevant cases. We study the probability distributions of disentanglement times, a quantity independent of the measure used to quantify entanglement, and the time-dependent probability distribution of concurrence. Analytical results are obtained for initially uniformly distributed pure states. The calculation of these probability distributions gives a complete insight into how different decoherence channels affect the entanglement initially contained in the set of two-qubit pure states. Numerical results are reported for randomly distributed initial mixed states. Although the paper focuses in Markovian noisy channels, we show that our results also describe nonautonomous and non-Markovian channels.