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arXiv:0705.3952 · Journal of Physics A Mathematical and Theoretical

Amplitude damping for single-qubit system with single-qubit mixed-state environment

Eylee Jung, Mi-Ra Hwang, You Hwan Ju, Daniel K. Park, Hung-Soo Kim, Min-Soo Kim, Jin-Woo Son

Published Jan 15, 2008• 5 citations
arXivHTMLPDF

Abstract

We study a generalized amplitude damping channel when environment is initially in the single-qubit mixed state. Representing the affine transformation of the generalized amplitude damping by a three-dimensional volume, we plot explicitly the volume occupied by the channels simulatable by a single-qubit mixed-state environment. As expected, this volume is embedded in the total volume by the channels which is simulated by two-qubit enviroment. The volume ratio is approximately 0.08 which is much smaller than 3/8, the volume ratio for generalized depolarizing channels.

DOI
10.1088/1751-8113/41/4/045306

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We study a generalized amplitude damping channel when environment is initially in the single-qubit mixed state. Representing the affine transformation of the generalized amplitude damping by a three-dimensional volume, we plot explicitly the volume occupied by the channels simulatable by a single-qubit mixed-state environment. As expected, this volume is embedded in the total volume by the channels which is simulated by two-qubit enviroment. The volume ratio is approximately 0.08 which is much smaller than 3/8, the volume ratio for generalized depolarizing channels.
We analyze the class of single-qubit channels with the environment modeled by a one-qubit mixed state. The set of affine transformations for this class of channels is computed analytically, employing the canonical form for the two-qubit unitary operator. We demonstrate that 38\frac{3}{8}83​ of the generalized depolarizing channels can be simulated by the one-qubit mixed-state environment by explicitly obtaining the shape of the volume occupied by this class of channels within the tetrahedron representing the generalized depolarizing channels. Further, as a special case, we show that the two-Pauli channel cannot be simulated by a one-qubit mixed-state environment.
Abstract Due to interaction with the environment, a quantum state is subjected to decoherence which becomes one of the major problems in many quantum systems. Amplitude damping is one of the most important decoherence processes. Here, we show that general two-qubit mixed states undergoing amplitude damping can be almost completely restored using a reversal procedure. This reversal procedure through CNOT and Hadamard gates could also protect the entanglement of two-qubit mixed states from general amplitude damping. We also propose a robust recovery scheme to protect the quantum states when the decay parameters or the input quantum states are not completely known.
Several instructions need to be considered in order to transfer classical error correction techniques to the quantum regime. The quantum error correction field has been developed to face these issues. One of the common source of errors in quantum systems is environment decoherence. Due to interaction with the environment, the quantum states of a system entangle with the environment and are subject to decoherence. In this thesis, we mainly focused on the amplitude damping which is one of the most important models of decoherence processes. We showed that general two-qubit mixed states undergoing an amplitude damping, can be almost completely restored using a reversal procedure. This reversal procedure through CNOT and Hadamard gates could also protect the entanglement of two-qubit mixed states from general amplitude damping. Concurrence and fidelity are two measurements used in order to examine how our proposed scheme performs. Furthermore, to give generality to our scheme, we proposed a robust recovery scheme to protect the quantum states when the decay parameters or the input quantum states are not completely known.
Abstract It is known that the inevitable interaction of the entangled qubits with their environments may result in the degradation of quantum correlation. We study the decoherence of two remote qubits under general local single- and two-sided amplitude-damping channel (ADC). By using concurrence, quantum discord and Clauser–Horne–Shimony–Holt (CHSH) inequality, we find that the relation between the residual quantum correlations and the initial ones are different. Recently, Wang et al. [Int. J. Theor. Phys. 54 (2015) 5] showed that there exist a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction and quantum discord, respectively. Here we find that both in single- and two-sided ADC, only the evolution of CHSH inequality with the initial parameter is proportional to that of the initial nonlocality. That means the initial state with maximally nonlocality will retain its role in the evolution. It implies that the evolution of nonlocality may reveal the characteristics of quantum state better. Furthermore, we discuss the evolutions of the three different quantum measurements with the initial parameter under generalized amplitude damping channel (GADC) and find that they are all proportional to that of the initial state.
We propose a scheme to enhance entanglement from amplitude damping or correlated amplitude damping decoherence. We show that entanglement sudden death time can be prolonged by the initial single-qubit operation combined with local filtering operation. For the amplitude damping channel case, we give the optimal single-qubit operation for arbitrary pure state [Formula: see text]. For the correlated amplitude damping channel case, we find that single-qubit operation on the initial state can not only enhance the final entanglement but also avoid entanglement sudden death. Compared to the previous schemes, the optimal operations and local filtering operations used in our scheme are independent with the decay parameters of the environment.