Generalized Amplitude Damping Channel Research Articles

On the eternal non-Markovianity of non-unital quantum channels

The eternally non-Markovian (ENM) Pauli channel is an example of a unital channel characterized by a negative decay rate for all time [Formula: see text]. Here, we consider the problem of constructing an analogous non-unital channel, and show in particular that a [Formula: see text]-dimensional generalized amplitude damping (GAD) channel cannot be ENM when the non-Markovianity originates solely from the non-unital part of the channel. We study specific ramifications of this result for qubit GAD. Specifically, we construct a quasi-ENM qubit GAD channel, characterized by a time [Formula: see text], such that the channel is non-Markovian (NM) only and for all time [Formula: see text]. We further point out that our negative result for the qudit GAD channel, namely, the impossibility of the eternal NM property, does not hold for a general qubit or higher-dimensional non-unital channel.

Protecting steered coherence in squeezed generalized amplitude damping channel with memory

We investigate the average steered coherence (ASC) and maximal steered coherence (MSC) of two qubits in a squeezed generalized amplitude damping channel modeled by a squeezed thermal bath with dissipation and memory. By considering the input Bell states, it is shown that while the dissipation and thermal effects induce decay of the ASC and MSC in the output states, the squeezing effect suppresses their decay in the strong (full) squeezing region for the input even-parity (odd-parity) Bell states. Besides, the memory effect due to correlated actions of the channel can also be exploited for suppressing decay of the ASC and MSC.

Enhancing the teleportation of quantum Fisher information under correlated generalized amplitude damping noise

The generalized amplitude damping (GAD) noise models the dynamical map of a qubit in contact with a non-zero temperature bosonic reservoir. When two qubits successively pass through the same GAD channel, correlation effects should be taken into account. Therefore, the dynamical map is modeled as correlated GAD (CGAD) noise. In this paper, we investigate the teleportation of quantum Fisher information (QFI) under CGAD noise. We first show that the correlation effects in CGAD noise can enhance the teleported QFI. We then present two probabilistic schemes to improve the teleportation of QFI in CGAD noise by weak measurement (WM) and environment-assisted measurement (EAM). We find the correlation effects of CGAD noise serve to improve the teleportation of QFI and increase the probability of success. Contrary to intuition, the thermal average photon number n does not always play a negative role in our probabilistic schemes. Although a larger n will cause the teleported QFI to decay faster, the corresponding probability of success will be higher. Finally, we introduce a quantity called average QFI to demonstrate that the EAM scheme is superior to the WM scheme with respect to QFI improvement under CGAD noise.

Genuine entanglement under squeezed generalized amplitude damping channels with memory

We study genuine entanglement among three qubits undergoing a noisy process that includes dissipation, squeezing, and decoherence. We obtain a general solution and analyze the asymptotic quantum states. We find that most of these asymptotic states can be genuinely entangled depending upon the parameters of the channel, memory parameter, and the parameters of the initial states. We study Greenberger–Horne–Zeilinger (GHZ) states and W states, mixed with white noise, and determine the conditions for them to be genuinely entangled at infinity. We find that for these mixtures, it is possible to start with a bi-separable state (with a specific mixture of white noise) and end with genuine entangled states. However, the memory parameter μ must be very high. We find that in contrast to the two-qubit case, none of the three-qubit asymptotic states for n → ∞ are genuinely entangled.

Scrutinizing joint remote state preparation under decoherence

This research examines the effect of an open system containing the squeezed generalized amplitude damping channel on the joint remote preparation quantum communication protocol using a maximally entangled two-qubit state. Our findings indicate that the fidelity of a quantum system in contact with a non-zero temperature thermal bath can be enhanced by varying the squeezing parameters. These parameters include the squeezing phase of the channel Phi and the amount of squeezing of the channel r.

Quantum Fisher information of phase estimation in the presence of indefinite causal order

Quantum Fisher information of phase estimation is studied for a single qubit which is influenced by the two generalized amplitude damping channels (GADCs) with indefinite causal order (ICO). The phase shift occurs between two consecutive applications of the GADCs. It is shown that the quantum Fisher information can be enhanced by the ICO of the quantum channels. Furthermore, even a completely incoherent state of the qubit is found to be useful for estimating the phase shift due to the ICO.

The SWAP imposter: Bidirectional quantum teleportation and its performance

Bidirectional quantum teleportation is a fundamental protocol for exchanging quantum information between two parties. Specifically, two individuals make use of a shared resource state as well as local operations and classical communication (LOCC) to swap quantum states. In this work, we concisely highlight the contributions of our companion paper [A. U. Siddiqui and M. M. Wilde, arXiv:2010.07905 (2020)]. We develop two different ways of quantifying the error of nonideal bidirectional teleportation by means of the normalized diamond distance and the channel infidelity. We then establish that the values given by both metrics are equal for this task. Additionally, by relaxing the set of operations allowed from LOCC to those that completely preserve the positivity of the partial transpose, we obtain semidefinite programing lower bounds on the error of nonideal bidirectional teleportation. We evaluate these bounds for some key examples—isotropic states and when there is no resource state at all. In both cases, we find an analytical solution. The second example establishes a benchmark for classical versus quantum bidirectional teleportation. Another example that we investigate consists of two Bell states that have been sent through a generalized amplitude damping channel. For this scenario, we find an analytical expression for the error, as well as a numerical solution that agrees with the former up to numerical precision.

Protecting nonlocal quantum correlations in correlated squeezed generalized amplitude damping channel

Nonlocal quantum correlations, such as quantum entanglement, quantum steering, and Bell nonlocality, are crucial resources for quantum information tasks. How to protect these quantum resources from decoherence is one of the most urgent problems to be solved. Here, we investigate the evolution of these correlations in the correlated squeezed generalized amplitude damping (SGAD) channel and propose a scheme to protect them with weak measurement (WM) and quantum measurement reversal (QMR). Compared with the results of the uncorrelated SGAD channel, we find that when n=1, correlation and squeezing effects can prolong the survival time of quantum entanglement, Bell nonlocality, and quantum steering by about 152 times, 207 times, and 10 times, respectively. In addition, local WM and QMR can effectively recover the disappeared nonlocal quantum correlations either in uncorrelated or completely correlated SGAD channels. Moreover, we find that these initial nonlocal quantum correlations could be drastically amplified under the correlated channel. And the steering direction can be flexibly manipulated either by changing the channel parameters or the strength of WM and QMR. These results not only make a step forward in suppressing decoherence and enhancing quantum correlation in noise channels, but also help to develop relevant practical applications.

Dynamics of quantum Fisher information from a time-local non-Markovian master equation with decoherence rates and operators depending on the estimated parameter

We analyze the dynamics of the quantum Fisher information (QFI) in the case of a two-dimensional open quantum system obeying a time-local non-Markovian master equation in the canonical form, characterized by canonical decoherence rates and operators that depend on the parameter to be estimated. This last condition brings a framework in which the information about the parameter is structurally encoded not only in the open system, but also in the system-environment interaction or/and correlations, and in some environment properties. We derive analytical formulas for the decompositions of the QFI flow and of the purity dynamics in terms associated to the canonical decoherence rates. In contrast to the results presented in X.-M. Lu et al. [Phys. Rev. A 82, 042103 (2010)], we show that, in this extended framework, the QFI flow contains not only the subflows corresponding to the decoherence rates, but also supplementary terms which originate in the state dependence on the estimated parameter; moreover, the signs of the QFI subflows associated to the decoherence rates are not correlated to the signs of the rates. We show that a pertinent connection between the QFI flow and non-Markovianity can be realized using the canonical measures defined from the negative canonical decoherence rates. We employ this theoretical framework to explore the QFI flow and its subflows in two cases of quantum evolutions directed by master equations with decoherence rates or/and operators depending on the estimated parameter: (i) the Markovian nonunital time evolution of a qubit under the generalized amplitude damping channel; (ii) the non-Markovian time evolution of a two-dimensional electronic subsystem entangled with its vibrational environment in a molecule.

Learning entanglement breakdown as a phase transition by confusion

Quantum technologies require methods for preparing and manipulating entangled multiparticle states. However, the problem of determining whether a given quantum state is entangled or separable is known to be an NP-hard problem in general, and even the task of detecting entanglement breakdown for a given class of quantum states is difficult. In this work, we develop an approach for revealing entanglement breakdown using a machine learning technique, which is known as ‘learning by confusion’. We consider a family of quantum states, which is parameterized such that there is a single critical value dividing states within this family into separate and entangled. We demonstrate the ‘learning by confusion’ scheme allows us to determine the critical value. Specifically, we study the performance of the method for the two-qubit, two-qutrit, and two-ququart entangled state. In addition, we investigate the properties of the local depolarization and the generalized amplitude damping channel in the framework of the confusion scheme. Within our approach and setting the parameterization of special trajectories, we obtain an entanglement-breakdown ‘phase diagram’ of a quantum channel, which indicates regions of entangled (separable) states and the entanglement-breakdown region. Then we extend the way of using the ‘learning by confusion’ scheme for recognizing whether an arbitrary given state is entangled or separable. We show that the developed method provides correct answers for a variety of states, including entangled states with positive partial transpose. We also present a more practical version of the method, which is suitable for studying entanglement breakdown in noisy intermediate-scale quantum devices. We demonstrate its performance using an available cloud-based IBM quantum processor.

Bounding the quantum capacity with flagged extensions

In this article we consider flagged extensions of convex combination of quantum channels, and find general sufficient conditions for the degradability of the flagged extension. An immediate application is a bound on the quantum Q and private P capacities of any channel being a mixture of a unitary map and another channel, with the probability associated to the unitary component being larger than 1/2. We then specialize our sufficient conditions to flagged Pauli channels, obtaining a family of upper bounds on quantum and private capacities of Pauli channels. In particular, we establish new state-of-the-art upper bounds on the quantum and private capacities of the depolarizing channel, BB84 channel and generalized amplitude damping channel. Moreover, the flagged construction can be naturally applied to tensor powers of channels with less restricting degradability conditions, suggesting that better upper bounds could be found by considering a larger number of channel uses.

Evaluating the advantage of adaptive strategies for quantum channel distinguishability

Recently, the resource theory of asymmetric distinguishability for quantum strategies was introduced by [Wang et al., Phys. Rev. Research 1, 033169 (2019)]. The fundamental objects in the resource theory are pairs of quantum strategies, which are generalizations of quantum channels that provide a framework to describe an arbitrary quantum interaction. In the present paper, we provide semi-definite program characterizations of the one-shot operational quantities in this resource theory. We then apply these semi-definite programs to study the advantage conferred by adaptive strategies in discrimination and distinguishability distillation of generalized amplitude damping channels. We find that there are significant gaps between what can be accomplished with an adaptive strategy versus a non-adaptive strategy.

Analysis of Decoherence in Linear and Cyclic Quantum Walks

We theoretically analyze the case of noisy Quantum walks (QWs) by introducing four qubit decoherence models into the coin degree of freedom of linear and cyclic QWs. These models include flipping channels (bit flip, phase flip and bit-phase flip), depolarizing channel, phase damping channel and generalized amplitude damping channel. Explicit expressions for the probability distribution of QWs on a line and on a cyclic path are derived under localized and delocalized initial states. We show that QWs which begin from a delocalized state generate mixture probability distributions, which could give rise to useful algorithmic applications related to data encoding schemes. Specifically, we show how the combination of delocalzed initial states and decoherence can be used for computing the binomial transform of a given set of numbers. However, the sensitivity of QWs to noisy environments may negatively affect various other applications based on QWs.

Optimal measurement-based feedback control on noisy quantum systems

A quantum system will both lose and gain excitation through interaction with the environment in a non-zero temperature environment. In this paper, we investigate how a feedback control scheme utilizing weak measurement stabilizes a quantum state which suffers from an environment with finite temperature. Our study has shown that compared with the conventional ‘do-nothing’ and ‘Helstrom’ schemes, this method is much more useful for suppressing decoherence in a generalized amplitude damping (GAD) noise channel. Additionally, for a quantum state, we give the expression of optimum measurement strength, correction angle and the general analytic expression for the optimum fidelity. Additionally, the maximum value of the fidelity improvement can be achieved by controlling the measurement strength, correction angle and the special initial state of the system. More importantly, we find that this approach can not only be helpful for suppressing decoherence in the GAD channel, but can also play a significant role in the amplitude damping noise channel. This phenomenon reveals that in non-zero temperature noise channels, the feedback control scheme via weak measurement can be better for stabilizing a quantum state.

Relating heat and entanglement in strong-coupling thermodynamics.

Explaining the influence of strong coupling in the dynamics of open quantum systems is one of the most challenging issues in the rapidly growing field of quantum thermodynamics. By using a particular definition of heat, we develop an approach to study the thermodynamics in the strong-coupling regime, which takes into account quantum resources such as coherence and entanglement. We apply the method to calculate the time-dependent thermodynamic properties of a system and an environment interacting via the generalized amplitude-damping channel. The results indicate that the transient imbalance between heat dissipated and heat absorbed that occurs in the process is responsible for the generation of system-environment entanglement.

The dynamics of Bell nonlocality for three-qubit system in independent reservoirs

The Bell nonlocality for initially general W states undergoing independent generalized amplitude damping channels are investigated. We examine in detail the effect of adding the number of qubits in the reservoir on delay of the Bell nonlocality dynamics. We show that the Bell nonlocality can be obviously enhanced in suppressing decoherence with the help of auxiliary qubits in the reservoir. In particular, the sudden death of Bell nonlocality can be perfectly bypassed, and corresponding condition has been also demonstrated for initially standard W state. We also provide two ways to produce the interesting quantum beats for the tripartite Bell nonlocality and entanglement. The obtained results may have some potential interests in the quantum decoherence field.

Robustness of Measurement–Induced Correlations Under Decoherence Effect

In this article, we study the dynamics of quantum correlation measures such as entanglement and measurement–induced nonlocality (MIN). Starting from an arbitrary Bell-diagonal mixed state under Markovian local noise such as bit-phase flip, depolarizing and generalized amplitude damping channel, we provide the decays of the entanglement measured by concurrence and quantum correlation captured by different forms of MIN (trace distance, Hilbert–Schmidt norm and relative entropy) as a function of the decoherence parameters. The effect of local noises on the dynamical behaviors of quantum correlation is also observed. We show the existence of specific and important features of MIN such as revival, noise robustness and sudden change with respect to decoherence parameter. It is observed that all the noises cause sudden death of entanglement for partially entangled states. Further, we show the existence of separable quantum states with non-zero quantum correlations in terms of MIN.

Pursuing the Fundamental Limits for Quantum Communication

The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information coherently. In this paper, we derive single-letter upper bounds on the quantum and private capacities of quantum channels. The quantum capacity of a quantum channel is always no larger than the quantum capacity of its extended channels, since the extensions of the channel can be considered as assistance from the environment. By optimizing the parametrized extended channels with specific structures such as the flag structure, we obtain new upper bounds on the quantum capacity of the original quantum channel. Furthermore, we extend our approach to estimating the fundamental limits of private communication and one-way entanglement distillation. As notable applications, we establish improved upper bounds to the quantum and private capacities for fundamental quantum channels of interest in quantum information, some of which are also the sources of noise in superconducting quantum computing. In particular, our upper bounds on the quantum capacities of the depolarizing channel and the generalized amplitude damping channel are strictly better than previously best-known bounds for certain regimes.

Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase damping and amplitude damping noise channels

In this work, we studied the relaxation dynamics of coherences of different order present in a system of two coupled nuclear spins. We used a previously designed model for intrinsic noise present in such systems which considers the Lindblad master equation for Markovian relaxation. We experimentally created zero-, single- and double- quantum coherences in several two-spin systems and performed a complete state tomography and computed state fidelity. We experimentally measured the decay of zero- and double- quantum coherences in these systems. The experimental data fitted well to a model that considers the main noise channels to be a correlated phase damping channel acting simultaneously on both spins in conjunction with a generalized amplitude damping channel acting independently on both spins. The differential relaxation of multiple-quantum coherences can be ascribed to the action of a correlated phase damping channel acting simultaneously on both the spins.

Information-theoretic aspects of the generalized amplitude-damping channel

The generalized amplitude damping channel (GADC) is one of the sources of noise in superconducting-circuit-based quantum computing. It can be viewed as the qubit analogue of the bosonic thermal channel, and it thus can be used to model lossy processes in the presence of background noise for low-temperature systems. In this work, we provide an information-theoretic study of the GADC. We first determine the parameter range for which the GADC is entanglement breaking and the range for which it is anti-degradable. We then establish several upper bounds on its classical, quantum, and private capacities. These bounds are based on data-processing inequalities and the uniform continuity of information-theoretic quantities, as well as other techniques. Our upper bounds on the quantum capacity of the GADC are tighter than the known upper bound reported recently in [Rosati et al., Nat. Commun. 9, 4339 (2018)] for the entire parameter range of the GADC, thus reducing the gap between the lower and upper bounds. We also establish upper bounds on the two-way assisted quantum and private capacities of the GADC. These bounds are based on the squashed entanglement, and they are established by constructing particular squashing channels. We compare these bounds with the max-Rains information bound, the mutual information bound, and another bound based on approximate covariance. For all capacities considered, we find that a large variety of techniques are useful in establishing bounds.