Environment-assisted error correction of single-qubit phase damping

Trendelkamp-Schroer, Benjamin; Helm, Julius; Strunz, Walter T.

doi:10.1103/physreva.84.062314

Cited by 15 publications

(21 citation statements)

References 26 publications

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“…On the other hand, in our EA-WMR scheme, given the four Kraus operators in Eq. (12)(13)(14)(15), it is clear that only K 1 is invertible, while other Kraus operators are singular. The smallest eigenvalue of…”

Section: Successful Probability For Wmr and Ea-wmr For Two Qubitsmentioning

confidence: 99%

“…Decoherence is a major obstacle in effectively implementing a quantum information processing task due to the inevitable interactions between quantum systems and their environments [1][2][3][4][5][6][7][8]. In the past few decades, several theoretical schemes, including dynamic decoupling control [9], feedback control [10], error correction codes [11], weak measurement reversal (WMR) [12,13] and environment-assisted error correction (EAEC) [14,15], to name a few, have been proposed to protect a quantum state from environmental noises. The EAEC scheme originally proposed by Gregoratti and Werner [14] has been studied in several interesting contexts [15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

“…In the past few decades, several theoretical schemes, including dynamic decoupling control [9], feedback control [10], error correction codes [11], weak measurement reversal (WMR) [12,13] and environment-assisted error correction (EAEC) [14,15], to name a few, have been proposed to protect a quantum state from environmental noises. The EAEC scheme originally proposed by Gregoratti and Werner [14] has been studied in several interesting contexts [15][16][17][18][19][20][21][22][23][24]. The underlying crucial idea in the EAEC scheme is to restore an unknown quantum state coupled to a noisy environment by performing a measurement on the environment followed by a quantum restoration operation on the system of interest conditioned on environment measurement outputs.…”

Section: Introductionmentioning

confidence: 99%

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Environment-assisted quantum state restoration via weak measurements

Wang

Zhao

2014

Phys. Rev. A

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In this paper, a new quantum state restoration scheme is proposed based on the environmentassisted error correction (EAEC) scheme. By introducing a weak measurement reversal (WMR) operation, we shall show how to recover an initial state of a quantum open system without invoking random unitary decompositions which are known to be absent in many important physical systems. We illustrate our new scheme and compare it with a scheme purely based on the WMR operation in the case of dissipative channel. In the proposed new scheme, the successful probability of recovering an unknown initial state can be significantly improved when the information obtained from an environment measurement is taken into account. Moreover, we show that the applicable range of our proposed scheme is wider than the EAEC scheme. Finally, the optimization of the successful probability for possible Kraus decompositions is discussed.

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Section: Successful Probability For Wmr and Ea-wmr For Two Qubitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Environment-assisted quantum state restoration via weak measurements

Wang

Zhao

2014

Phys. Rev. A

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“…Freedom to choose ξ allows us to optimize the measurement on the environment for certain tasks. Next we will discuss two of them: optimal bounds on entanglement dynamics [21,34] and environment assisted error correction [35,36].…”

mentioning

confidence: 99%

Parametrization and Optimization of Gaussian Non-Markovian Unravelings for Open Quantum Dynamics

et al. 2018

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We derive a family of Gaussian non-Markovian stochastic Schrödinger equations for the dynamics of open quantum systems. The different unravelings correspond to different choices of squeezed coherent states, reflecting different measurement schemes on the environment. Consequently, we are able to give a single shot measurement interpretation for the stochastic states and microscopic expressions for the noise correlations of the Gaussian process. By construction, the reduced dynamics of the open system does not depend on the squeezing parameters. They determine the non-Hermitian Gaussian correlation, a wide range of which are compatible with the Markov limit. We demonstrate the versatility of our results for quantum information tasks in the non-Markovian regime. In particular, by optimizing the squeezing parameters, we can tailor unravelings for improving entanglement bounds or for environment-assisted entanglement protection.

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“…The most important source is correlation between system and its surrounding that is a direct outcome of an open quantum system. Classical uctuations of elds are the second source of decoherence [5]. Decoherence is usually explained without quantum environment that these channels are denoted as random unitary (RU) channels.…”

Section: Introductionmentioning

confidence: 99%

Investigation of a Two-Qubit Decoherence by Using Bloch Vectors

Ahmadi¹,

Jami²

2014

Acta Phys. Pol. A

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The loss of the coherence happens due to the interaction between the desired system and its surroundings. Addressing decoherence is one of the main concepts in the study of quantum channels to access their potential for various scale. In this process the information of the system is penetrated into the environment. Therefore, the measurement of the environment could be used as the error correction method. Phase damping channels principally belong to random unitary channels and can be corrected by classical information. This paper presents a method to generate non-random unitary phase damping channels based on the Bloch vectors in two qubits systems. A phase damping channel which consisted of a two qubits system and a single qubit environment was investigated. The results demonstrated that the phase damping channels belong to random unitary dynamics if the three-dimensional tetrahedron volume spanned by the Bloch vectors in R 3 is not zero, or, the same hyperplane in R 3 was not pointed by the Bloch vectors. It is found that the Bell state belongs to random unitary class and can be corrected based on classical information obtained from environmental measurements.

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Environment-assisted error correction of single-qubit phase damping

Cited by 15 publications

References 26 publications

Environment-assisted quantum state restoration via weak measurements

Environment-assisted quantum state restoration via weak measurements

Parametrization and Optimization of Gaussian Non-Markovian Unravelings for Open Quantum Dynamics

Investigation of a Two-Qubit Decoherence by Using Bloch Vectors

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