© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Acta Physica Polonica A

Investigation of a Two-Qubit Decoherence by Using Bloch Vectors

Fahimeh Ahmadi, Safa Jami

Published May 1, 2014• 0 citations

Abstract

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.

DOI: 10.12693/aphyspola.125.1088

Related papers

Quantum decoherence of two qubits

Julius Helm, Walter T. Strunz

It is commonly stated that decoherence in open quantum systems is due to growing entanglement with an environment. In practice, however, surprisingly often decoherence may equally well be described by random unitary dynamics without invoking a quantum environment at all. For a single qubit, for instance, pure decoherence (or phase damping) is always of random unitary type. Here, we construct a simple example of true quantum decoherence of two qubits: we present a feasible phase damping channel of which we show that it cannot be understood in terms of random unitary dynamics. We give a very intuitive geometrical measure for the positive distance of our channel to the convex set of random unitary channels and find remarkable agreement with the so-called Birkhoff defect based on the norm of complete boundedness.

arXiv:0910.5364•Physical Review A•Oct 19, 2009•60 citations

Environment-assisted error correction of single-qubit phase damping

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

Open quantum system dynamics of random unitary type may in principle be fully undone. Closely following the scheme of environment-assisted error correction proposed by Gregoratti and Werner [J. Mod. Opt. 50, 915 (2003)], we explicitly carry out all steps needed to invert a phase-damping error on a single qubit. Furthermore, we extend the scheme to a mixed-state environment. Surprisingly, we find cases for which the uncorrected state is closer to the desired state than any of the corrected ones.

arXiv:1110.4806•Physical Review A•Dec 19, 2011•14 citations

Restoration of a quantum state in a dephasing channel via environment-assisted error correction

Xinyu Zhao, Samuel R. Hedemann, Ting Yu

In this paper, we propose an environment-assisted error correction scheme to fully recover a multiple-qubit state subject to a phase damping noise. We establish the theoretical framework and the operational procedure to restore an unknown initial quantum state for an $N$-qubit model interacting with either individual baths or a common bath. We give an explicit construction of the random unitary (RU) Kraus decomposition for an $N$-qubit model interacting with a common bath. We also demonstrate how to use only one unitary reversal operation to restore an arbitrary state with phase damping noise. In principle, the initial state can always be recovered with a success probability of 1. Interestingly, we found that non-RU decomposition can also be used to restore some particular entangled states. This may open a new path to restore a quantum entangled state beyond the standard RU scheme.

arXiv:1305.4627•Physical Review A•Aug 19, 2013•43 citations

Quantum coherence flow for a qubit evolving under the action of quantum channels

Mauro Buemo Pozzobom

Quantum Coherence (QC) has a fundamental role in Quantum Mechanics (QM). It has been studied since the emergence of QM. However, this quantum feature is easily destroyed when a physical system interacts with the environment. Also, recently the quantum coherence has been highlighted because of the possibility of using its as a resource in the Quantum Information Science (QIS). In this work we study the QC flow of a qubit (two-level system) interacting with the environment modeled by quantum channels of noise that are very common in QIS. These channels represent some physical systems and are widely used for error correction studies. We calculate the QC by the l1-norm, doing this for the different channels seeking to relate it to the entanglement, which is also another key topic in QM. We note that in the amplitude damping channel the total QC is equal to the sum of the local and non-local parts and that the non-local part is equivalent to entanglement. For the phase damping channel, entanglement does not cover all non-local QC. Here there is a gap between them that may depend on the time and on the initial state. Besides, for the bit, phase, and bit phase flip channels the possibility and the conditions for invariance of QC are considered. Also, we notice that for the depolarizing channel we can use the qubit as a catalyst for the creation of non-local QC and entanglement. We, as well, observed that even initial states incoherent can lead to transient quantum coherence between system and environment. We also showed that the emergence of entanglement does not necessarily imply the destruction of QC. Furthermore, we investigated whether QC is lost or changed into other types of correlations and besides which initial conditions allow making quantum coherence robust to decoherence.

•Aug 23, 2016•0 citations

Characterization of decoherence from an environmental perspective

Julius Helm, Walter T. Strunz, Stephan Rietzler +1 more

For the case of phase damping (pure decoherence) we investigate the extent to which environmental traits are imprinted on an open quantum system. The dynamics is described using the quantum channel approach. We study what the knowledge of the channel may reveal about the nature of its underlying dynamics and, conversely, what the dynamics tell us about how to consistently model the environment. We find that, for a Markov phase-damping channel(i.e., a channel compatible with a time-continuous Markovian evolution), the environment may adequately be represented by a mixture of only a few coherent states. For arbitrary Hilbert space dimension $N\ensuremath{\geqslant}4$ we refine the idea of quantum phase damping, for which we show a means of identification. Symmetry considerations are used to identify decoherence-free subspaces of the system.

arXiv:1012.4685•Physical Review A•Apr 18, 2011•32 citations

Quantum decoherence under phase damping in non-inertial frames

Min-Zhe Piao, Xin Ji

We investigate the quantum decoherence of Dirac fields in a non-inertial system under phase damping channel. The quantum decoherence and the loss of entanglement generated by Unruh radiation will influence each other, and the entanglement disappears only as time tends to infinity whether one or two qubits of system is coupled to the environment.

Journal of Modern Optics•Oct 12, 2011•14 citations

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.

It is commonly stated that decoherence in open quantum systems is due to growing entanglement with an environment. In practice, however, surprisingly often decoherence may equally well be described by random unitary dynamics without invoking a quantum environment at all. For a single qubit, for instance, pure decoherence (or phase damping) is always of random unitary type. Here, we construct a simple example of true quantum decoherence of two qubits: we present a feasible phase damping channel of which we show that it cannot be understood in terms of random unitary dynamics. We give a very intuitive geometrical measure for the positive distance of our channel to the convex set of random unitary channels and find remarkable agreement with the so-called Birkhoff defect based on the norm of complete boundedness.

In this paper, we propose an environment-assisted error correction scheme to fully recover a multiple-qubit state subject to a phase damping noise. We establish the theoretical framework and the operational procedure to restore an unknown initial quantum state for an

N

-qubit model interacting with either individual baths or a common bath. We give an explicit construction of the random unitary (RU) Kraus decomposition for an

N

-qubit model interacting with a common bath. We also demonstrate how to use only one unitary reversal operation to restore an arbitrary state with phase damping noise. In principle, the initial state can always be recovered with a success probability of 1. Interestingly, we found that non-RU decomposition can also be used to restore some particular entangled states. This may open a new path to restore a quantum entangled state beyond the standard RU scheme.

Quantum Coherence (QC) has a fundamental role in Quantum Mechanics (QM). It has been studied since the emergence of QM. However, this quantum feature is easily destroyed when a physical system interacts with the environment. Also, recently the quantum coherence has been highlighted because of the possibility of using its as a resource in the Quantum Information Science (QIS). In this work we study the QC flow of a qubit (two-level system) interacting with the environment modeled by quantum channels of noise that are very common in QIS. These channels represent some physical systems and are widely used for error correction studies. We calculate the QC by the l1-norm, doing this for the different channels seeking to relate it to the entanglement, which is also another key topic in QM. We note that in the amplitude damping channel the total QC is equal to the sum of the local and non-local parts and that the non-local part is equivalent to entanglement. For the phase damping channel, entanglement does not cover all non-local QC. Here there is a gap between them that may depend on the time and on the initial state. Besides, for the bit, phase, and bit phase flip channels the possibility and the conditions for invariance of QC are considered. Also, we notice that for the depolarizing channel we can use the qubit as a catalyst for the creation of non-local QC and entanglement. We, as well, observed that even initial states incoherent can lead to transient quantum coherence between system and environment. We also showed that the emergence of entanglement does not necessarily imply the destruction of QC. Furthermore, we investigated whether QC is lost or changed into other types of correlations and besides which initial conditions allow making quantum coherence robust to decoherence.

For the case of phase damping (pure decoherence) we investigate the extent to which environmental traits are imprinted on an open quantum system. The dynamics is described using the quantum channel approach. We study what the knowledge of the channel may reveal about the nature of its underlying dynamics and, conversely, what the dynamics tell us about how to consistently model the environment. We find that, for a Markov phase-damping channel(i.e., a channel compatible with a time-continuous Markovian evolution), the environment may adequately be represented by a mixture of only a few coherent states. For arbitrary Hilbert space dimension $N\ensuremath{\geqslant}4$ we refine the idea of quantum phase damping, for which we show a means of identification. Symmetry considerations are used to identify decoherence-free subspaces of the system.