Dephasing Channel Research Articles

Electron spin relaxation due to charge noise

We study decoherence of an electron spin qubit in a quantum dot due to charge noise. We find that at the lowest order in spin-orbit interaction, the pure dephasing channel is suppressed for both $1/f$ charge noise and Johnson noise, so that charge noise leads to a pure relaxation channel of decoherence. Because of the weaker magnetic field dependence, the spin relaxation rate due to charge noise could dominate over phonon noise at low magnetic fields in a gate-defined GaAs or Si quantum dot or an InAs self-assembled quantum dot. Furthermore, in a large InAs self-assembled quantum dot, spin relaxation due to phonon noise could be suppressed in high magnetic fields due to the suppression of the coupling matrix element, so that the spin relaxation due to charge noise could dominate in both low and high magnetic fields. Numerically, in a 1 T magnetic field, the spin relaxation time due to typical charge noise is about 100 s in Si, $0.1$ s in GaAs for a gate-defined quantum dot with a 1 meV confinement, and 10 $\ensuremath{\mu}$s (or 1 s) in InAs self-assembled quantum dot with a 4 meV (or 30 meV) confinement.

Entanglement sudden death in the presence of quantum decoherence in non-inertial frames: beyond the single-mode approximation

The entanglement behavior of Dirac field under quantum decoherence in the non-inertial frames is studied beyond the single-mode approximation. Two kinds of damping processes, amplitude damping channel and dephasing channel, are investigated as the sources of decoherence. The decoherence and Unruh effect will lead to entanglement degradation. This study demonstrates that as two observers experience the decoherence, the entanglement sudden death will occur in amplitude damping channel. Our study shows that the entanglement sudden death will occur in the presence of Unruh effect accompanying the decoherence. In addition, our results show that the amplitude damping channel has more remarkable impacts than the dephasing channel.

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

In this paper, we propose an explicit 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 state beyond the standard RU scheme.

Nonequilibrium Landau-Zener-Stueckelberg spectroscopy in a double quantum dot

We study theoretically nonequilibrium Landau-Zener-Stueckelberg (LZS) dynamics in a driven double quantum dot (DQD) including dephasing and, importantly, energy relaxation due to environmental fluctuations. We derive effective nonequilibrium Bloch equations. These allow us to identify clear signatures for LZS oscillations observed but not recognized as such and to identify the full environmental fluctuation spectra acting on a DQD in experiments [Petersson, Petta, Lu, and Gossard, Phys. Rev. Lett. 105, 246804 (2010)]. We find that the dominant dephasing and relaxation channels vary while driving. In detail, super-Ohmic fluctuations, typically due to phonons, are the main relaxation channel for a detuned DQD while dephasing is due to slow noise. In contrast, at zero detuning Ohmic fluctuations dominate dephasing and relaxation.

Invariant quantum discord in qubit–qutrit systems under local dephasing

We investigate the dynamics of quantum discord and entanglement for a class of mixed qubit–qutrit states assuming that only the qutrit is under the action of a dephasing channel. We demonstrate that even though the entanglement in the qubit–qutrit state disappears in a finite time interval, the partial coherence left in the system enables quantum discord to remain invariant throughout the time evolution.

Non-Markovianity of local dephasing channels and time-invariant discord

We study non-Markovianity and information flow for qubits experiencing local dephasing with an Ohmic class spectrum. We demonstrate the existence of a temperature-dependent critical value of the Ohmicity parameter $s$ for the onset of non-Markovianity and give a physical interpretation of this phenomenon by linking it to the form of the reservoir spectrum. We demonstrate that this link holds also for more general spectra. We unveil a class of initial states for which discord is forever frozen at a positive value. We connect time-invariant discord to non-Markovianity and propose a physical system in which it could be observed.

DYNAMICS OF QUANTUM CORRELATIONS IN TWO-QUBIT SYSTEMS WITHIN NON-MARKOVIAN ENVIRONMENTS

Knowledge of the dynamical behavior of correlations with no classical counterpart, like entanglement, nonlocal correlations and quantum discord, in open quantum systems is of primary interest because of the possibility to exploit these correlations for quantum information tasks. Here we review some of the most recent results on the dynamics of correlations in bipartite systems embedded in non-Markovian environments that, with their memory effects, influence in a relevant way the system dynamics and appear to be more fundamental than the Markovian ones for practical purposes. Firstly, we review the phenomenon of entanglement revivals in a two-qubit system for both independent environments and a common environment. We then consider the dynamics of quantum discord in non-Markovian dephasing channel and briefly discuss the occurrence of revivals of quantum correlations in classical environments.

Mocking up a Dephasing Channel with a Minimal-Sized Environment

In order to model the most general quantum operation on a d-dimensional system, a d2-dimensional environment is usually needed. We focus on the quantum dephasing process and find that this channel can be modeled by an environment with the size of at most d dimensions. An experimentally accessible matrix D is defined to characterize the dephasing channel and the minimal number of Kraus operators of the channel from the matrix I) for mocking up the dephasing channel is presented in the minimal-sized environment. An experimental simulation of dephasing channels by means of nuclear magnetic resonance techniques is carried out to justify the idea.

Quantum discord of Bell cat states under amplitude damping

The evolution of pairwise quantum correlations of Bell cat states under amplitude damping is examined using the concept of quantum discord which goes beyond entanglement. A closed expression of the quantum discord is explicitly derived. We used the Koashi–Winter relation, a relation which facilitates the optimization process of the conditional entropy. We also discuss the temporal evolution of bipartite quantum correlations under a dephasing channel and compare the behaviors of quantum discord and entanglement whose properties are characterized through the concurrence.

Geometric measure of pairwise quantum discord for superpositions of multipartite generalized coherent states

We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl–Heisenberg, SU(2) and SU(1,1) coherent states which interpolate between Werner and Greenberger–Horne–Zeilinger states.

The quantum dynamic capacity formula of a quantum channel

The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an “ab initio” approach, using only the most basic tools in the quantum information theorist’s toolkit: the Alicki-Fannes’ inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon theory literature. We also demonstrate that the “quantum dynamic capacity formula” characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula reduces the computation of the trade-off surface to a tractable, textbook problem in Pareto trade-off analysis, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.

Comparison of different measures for quantum discord under non-Markovian noise

Two geometric measures for quantum discord were recently proposed by Modi et al (2010 Phys. Rev. Lett. 104 080501) and Dakić et al (2010 Phys. Rev. Lett. 105 190502). We study the similarities and differences for total quantum correlations of Bell-diagonal states using these two geometry-based quantum discord and the original quantum discord. We show that, under non-Markovian dephasing channels, quantum discord and one of the geometric measures remain constant for a finite amount of time, but not the other geometric measure. However, all the three measures share a common sudden change point. Our study on critical point of sudden transition might be useful for keeping long-time total quantum correlations under decoherence.

Factorization law for entanglement evolution of two qubits in non-Markovian pure dephasing channels

The entanglement evolution of two qubits in local, two-sided non-Markovian pure dephasing channels is investigated. It is found that for the two-sided pure dephasing channel case, when the qubits are initially prepared in a general class of states, whether pure or mixed, the entanglement can be expressed as the products of initial entanglement and the channelsʼ action on the maximally entangled state. This provide us a good approximation to characterize the entanglement dynamics of arbitrary states to some extent.

FROZEN DISCORD IN NON-MARKOVIAN DEPHASING CHANNELS

We investigate the dynamics of quantum and classical correlations in a system of two qubits under local colored-noise dephasing channels. The time evolution of a single qubit interacting with its own environment is described by a memory kernel non-Markovian master equation. The memory effects of the non-Markovian reservoirs introduce new features in the dynamics of quantum and classical correlations compared to the white noise Markovian case. Depending on the geometry of the initial state, the system can exhibit frozen discord and multiple sudden transitions between classical and quantum decoherence [L. Mazzola, J. Piilo and S. Maniscalco, Phys. Rev. Lett. 104 (2010) 200401]. We provide a geometric interpretation of those phenomena in terms of the distance of the state under investigation to its closest classical state in the Hilbert space of the system.

Quantum discord in the ground and thermal states of spin clusters

Quantum discord (QD) is a general measure of bipartite quantum correlations with a potential role in quantum information processing tasks. Spin clusters serve as ideal candidates for the implementation of some of the associated protocols. In this paper, we consider a symmetric spin trimer and a tetramer which describe a number of known molecular magnets and compute the QD in the ground and thermal states of the clusters. The variations of the QD as a function of an anisotropy parameter, magnetic field and temperature are investigated. We obtain a number of interesting results such as a finite value of the QD in the trimer ground state for which the pairwise entanglement is known to be zero, differences in the nature of some of the variations in the ferromagnetic and antiferromagnetic cases, and discontinuous jumps in the magnitude of the QD at first-order quantum phase transition points. A remarkable feature that is observed is that the QD completely vanishes only in the asymptotic limit of temperature T → ∞. We further study the dynamics of the QD and the pairwise entanglement at T = 0 under the effect of a dephasing channel describing the interaction of the reduced spin cluster state with independent local environments. The QD is found to vanish asymptotically as t → ∞. In the case of the spin trimer, the pairwise entanglement has a zero value at all times and reaches a zero value in a finite time in the case of the tetramer.

Influence of decoherence of entanglement on deterministic remote state preparation

We investigate the influence of decoherence of entanglement on the deterministic remote state preparation. Firstly, the determinability and the depletion of entanglement bits and classical bits are obtained. Then two kinds of decoherent channels (depolarizing and dephasing) are analyzed. For the depolarizing channel, the fidelity is related only to the depolarization and the latitude of target quantum bits on the Bloch sphere, but is independent of longitude. For the dephasing channel, the fidelity is not affected by the quantum channel and only related to the latitude of target quantum bits.

Channel capacities of an exactly solvable spin-star system

We calculate the entanglement-assisted and unassisted channel capacities of an exactly solvable spin star system, which models the quantum dephasing channel. The capacities for this non-Markovian model exhibit a strong dependence on the coupling strengths of the bath spins with the system, the bath temperature, and the number of bath spins. For equal couplings and bath frequencies, the channel becomes periodically noiseless.

Role of chaos in quantum communication through a dynamical dephasing channel

In this article we treat the subject of chaotic environments with few degrees of freedom in quantum communication by investigating a conservative dynamical map as a model of a dephasing quantum channel. When the channel's dynamics is chaotic, we investigate the model's semi-classical limit and show that the entropy exchange grows at a constant rate which depends on a single parameter (the interaction strength), analogous to stochastic models of dephasing channels. We analyze memory effects in the channel and present strong physical arguments to support that the present model is forgetful in the chaotic regime while memory effects in general cannot be ignored when channel dynamics is regular. In order to render the nonchaotic channel forgetful, it becomes necessary to apply a reset to the channel and this reset can efficiently be modeled by application of a chaotic map. We may then refer to encoding theorems (valid in the case of forgetful channels) to present evidence of a transition from noiseless to noisy channel due to the environment's transition from regular to chaotic dynamics.

Trade-off capacities of the quantum Hadamard channels

Coding theorems in quantum Shannon theory express the ultimate rates at which a sender can transmit information over a noisy quantum channel. More often than not, the known formulas expressing these transmission rates are intractable, requiring an optimization over an infinite number of uses of the channel. Researchers have rarely found quantum channels with a tractable classical or quantum capacity, but when such a finding occurs, it demonstrates a complete understanding of that channel's capabilities for transmitting classical or quantum information. Here we show that the three-dimensional capacity region for entanglement-assisted transmission of classical and quantum information is tractable for the Hadamard class of channels. Examples of Hadamard channels include generalized dephasing channels, cloning channels, and the Unruh channel. The generalized dephasing channels and the cloning channels are natural processes that occur in quantum systems through the loss of quantum coherence or stimulated emission, respectively. The Unruh channel is a noisy process that occurs in relativistic quantum information theory as a result of the Unruh effect and bears a strong relationship to the cloning channels. We give exact formulas for the entanglement-assisted classical and quantum communication capacity regions of these channels. The coding strategy for each of these examples is superior to a na\"{\i}ve time-sharing strategy, and we introduce a measure to determine this improvement.

Property of Quantum Correlations with Correlated Noise

We analyze the classical and quantum correlation properties of the standard and so-called quasiclassical depolarizing channel with correlated noise and non-Markovian dephasing channel, specifically we use the quantum discord, entanglement, and measurement-induced disturbance (MID) to measure the quantum correlations. For the depolarizing channel, we find that the memory effect has more influence on the MID and quantum discord than entanglement. For the dephasing channel, we show that the non-Markovian dephasing channel is more robust than Markovian dephasing channel against decoherence. We also find that at first MID and quantum discord take different values, and then after a specific time they will take almost the same value and both decay monotonically in the same way.