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Physical Review A

On-demand control of coherence transfer between interacting qubits surrounded by a dissipative environment

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

Published Jan 31, 2014• 7 citations
Publisher

Abstract

On-demand measurement-based schemes to control coherence transfer between interacting qubits inside a dissipative environment are considered. The measurements employed are of the types of quantum weak measurement and quantum reversal measurement of which one is carried out at the beginning of the system evolution $t=0$ and the other at a later intended time $t>0.$ The relevant questions are which type of measurement should be performed at $t=0$ and which type at $t>0$, as well as which strength of the second measurement should be chosen in dependence on the strength of the first measurement to optimally achieve a demand? We answer such questions in this work as to meet two concrete demands, namely, to make optimal (i) the transfer of coherence from the $s$th qubit to the $r$th qubit and (ii) the preservation of coherence at the $s$th qubit. Particularly, independent of the coherence degree of the $s$th qubit at $t=0,$ the coherence degree of either the $r$th qubit or the $s$th qubit at any $t>0$ can be made arbitrarily close to the maximum value equal to 1/2, but at the cost of vanishingly reduced success probability. As an application, we discuss the coherence transfer between two qubits of a bipartite system. We also analyze the influence of the controlling schemes for optimal coherence transfer on the degree of entanglement created at $t>0$ between the two qubits.

DOI
10.1103/physreva.89.013852

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On-demand measurement-based schemes to control coherence transfer between interacting qubits inside a dissipative environment are considered. The measurements employed are of the types of quantum weak measurement and quantum reversal measurement of which one is carried out at the beginning of the system evolution t=0t=0t=0 and the other at a later intended time t>0.t>0.t>0. The relevant questions are which type of measurement should be performed at t=0t=0t=0 and which type at t>0t>0t>0, as well as which strength of the second measurement should be chosen in dependence on the strength of the first measurement to optimally achieve a demand? We answer such questions in this work as to meet two concrete demands, namely, to make optimal (i) the transfer of coherence from the sssth qubit to the rrrth qubit and (ii) the preservation of coherence at the sssth qubit. Particularly, independent of the coherence degree of the sssth qubit at t=0,t=0,t=0, the coherence degree of either the rrrth qubit or the sssth qubit at any t>0t>0t>0 can be made arbitrarily close to the maximum value equal to 1/2, but at the cost of vanishingly reduced success probability. As an application, we discuss the coherence transfer between two qubits of a bipartite system. We also analyze the influence of the controlling schemes for optimal coherence transfer on the degree of entanglement created at t>0t>0t>0 between the two qubits.
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.
We investigate the protection of quantum correlations of two qubits in independent vacuum reservoirs by means of weak measurements. It is found that the weak measurement can reduce the amount of quantum correlation for one type of initial state at the beginning in a non-Markovian environment and meanwhile it can reduce the occurrence time of entanglement sudden death (ESD) in the process of time evolution. In a Markovian environment, the quantum entanglements of the two kinds of initial states decay rapidly and the weak measurement can further weaken the quantum entanglement, therefore in this case the entanglement cannot be optimized in the evolution process.
When a quantum system interacts with its environment, the so-called decoherence effect will normally destroy the coherence in the quantum state and the entanglement between its subsystems. We propose a feedback control strategy based on quantum weak measurements to protect coherence and entanglement of the quantum state against environmental disturbance. For a one-qubit quantum system under amplitude damping and dephasing decoherence channels, our strategy can preserve the coherence based on the measured information about the population difference between its two levels. For a two-qubit quantum system disentangled by independent amplitude damping and dephasing decoherence channels, the designed feedback control can preserve coherence between the ground state and the highest excited states by tuning the coupling strength between the two qubits, and at the same time minimize the loss of entanglement between the two qubits. As a consequence of dynamic symmetry, the generalization of these results derives the concept of control-induced decoherence-free observable subspace, for which several criteria are provided.
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.
We investigate the quantum control of two qubits interacting with a Markovian environment and evolving as an XXX state. The control is implemented via a simple applied field, whose profile is determined by means of the piecewise time-independent quantum control method. The goal is to make either the population or the system concurrence to follow a specified tracking control trajectory. By considering the system under the influence of three kinds of noise---phase damping, amplitude damping, or a combination of both---we unveil the conditions (like energy balance) under which the quantum control is properly achieved and fidelity (monitored through the trace distance) is kept satisfactorily high, even if the qubits interact differently with the dissipative medium. We further find that the effects of phase damping, a type of noise which notoriously destroys coherence and entanglement, can be mitigated if during the control the system is also exposed to amplitude damping. Of potential interest for the usage of entanglement as resource for quantum information, our results indicate that distinct entanglement measures and coherence can be maintained relatively high (even at long times) as a consequence of the tracking quantum control process.
We consider a bipartite open quantum system constituted by two interacting qubitsAAAandBBB, assuming that the former is coupled to the environment and is directly affected by coherent control, while the latter does not interact directly with the environment and the control fields. We are interested in the controllability properties of the subsystemBBB. In this paper, we give a first analysis of the problem and provide some negative answers