Showing papers on "Amplitude damping channel published in 2020"
TL;DR: This work proposes and demonstrates a general quantum algorithm to evolve open quantum dynamics on quantum computing devices that does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.
Abstract: Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.
93 citations
TL;DR: It is demonstrated that neural networkStates are capable of efficiently representing quantum codes for quantum information transmission and quantum error correction, supplying further evidence for the usefulness of neural network states to describe multipartite entanglement.
Abstract: We examine the usefulness of applying neural networks as a variational state ansatz for many-body quantum systems in the context of quantum information-processing tasks. In the neural network state ansatz, the complex amplitude function of a quantum state is computed by a neural network. The resulting multipartite entanglement structure captured by this ansatz has proven rich enough to describe the ground states and unitary dynamics of various physical systems of interest. In the present paper, we initiate the study of neural network states in quantum information-processing tasks. We demonstrate that neural network states are capable of efficiently representing quantum codes for quantum information transmission and quantum error correction, supplying further evidence for the usefulness of neural network states to describe multipartite entanglement. In particular, we show the following main results: a) Neural network states yield quantum codes with a high coherent information for two important quantum channels, the generalized amplitude damping channel and the dephrasure channel. These codes outperform all other known codes for these channels, and cannot be found using a direct parametrization of the quantum state. b) For the depolarizing channel, the neural network state ansatz reliably finds the best known codes given by repetition codes. c) Neural network states can be used to represent absolutely maximally entangled states, a special type of quantum error-correcting codes. In all three cases, the neural network state ansatz provides an efficient and versatile means as a variational parametrization of these highly entangled states.
53 citations
TL;DR: The generalized amplitude damping channel is 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.
Abstract: 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 analog 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 antidegradable. 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.
43 citations
TL;DR: The effect of six distinct noises on information loss is demonstrated, quantified through the fidelity measure and the loss of information is found to be minimum for amplitude damping channel and is maximum for the bit-flip channel.
22 citations
TL;DR: In this article, the robustness of entanglement in two qubits maximally entangled mixed states (MEMS) have been studied under quantum decoherence channels, where the concurrence has been used as an entangement measure.
Abstract: In the present article, the robustness of entanglement in two qubits maximally entangled mixed states (MEMS) have been studied under quantum decoherence channels. Here we consider bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels. To quantify the entanglement, the concurrence has been used as an entanglement measure. During this study interesting results have been found for sudden death and birth of entanglement under bit flip and bit-phase-flip channels. While amplitude damping channel produces entanglement sudden death and does not allow re-birth of entanglement. On the other hand, two qubits MEMS exhibit the robust character against the phase flip, phase damping and depolarization channels. The elegant behavior of all the quantum channels have been investigated with varying parameter of quantum state MEMS in different cases.
15 citations
TL;DR: Substantial progress is reported by deriving simple upper and lower bounds on the rates that can be achieved in asymptotic multipartite entanglement transformations, based on ideas of entanglements combing and state merging.
Abstract: The theory of the asymptotic manipulation of pure bipartite quantum systems can be considered completely understood: the rates at which bipartite entangled states can be asymptotically transformed into each other are fully determined by a single number each, the respective entanglement entropy. In the multipartite setting, similar questions of the optimally achievable rates of transforming one pure state into another are notoriously open. This seems particularly unfortunate in the light of the revived interest in such questions due to the perspective of experimentally realizing multipartite quantum networks. In this Letter, we report substantial progress by deriving simple upper and lower bounds on the rates that can be achieved in asymptotic multipartite entanglement transformations. These bounds are based on ideas of entanglement combing and state merging. We identify cases where the bounds coincide and hence provide the exact rates. As an example, we bound rates at which resource states for the cryptographic scheme of quantum secret sharing can be distilled from arbitrary pure tripartite quantum states. This result provides further scope for quantum internet applications, supplying tools to study the implementation of multipartite protocols over quantum networks.
14 citations
TL;DR: In this paper, a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension $d was introduced, and the entanglement assisted quantum and classical capacities for a rather wide class of maps were evaluated.
Abstract: The set of Multi-level Amplitude Damping (MAD) quantum channels is introduced as a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension $d$. In the special case of $d=3$, by exploiting degradability, data-processing inequalities, and channel isomorphism, we compute the associated quantum and private classical capacities for a rather wide class of maps, extending the set of solvable models known so far. We proceed then to the evaluation of the entanglement assisted, quantum and classical, capacities.
9 citations
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TL;DR: In this paper, a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension $d was introduced, and the entanglement assisted quantum and classical capacities for a rather wide class of maps were evaluated.
Abstract: The set of Multi-level Amplitude Damping (MAD) quantum channels is introduced as a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension $d$. In the special case of $d=3$, by exploiting degradability, data-processing inequalities, and channel isomorphism, we compute the associated quantum and private classical capacities for a rather wide class of maps, extending the set of solvable models known so far. We proceed then to the evaluation of the entanglement assisted, quantum and classical, capacities.
9 citations
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TL;DR: In this article, the authors consider flagged extensions of channels that can be written as convex combination of other channels, and find general sufficient conditions for the degradability of the flagged extension.
Abstract: In this article we consider flagged extensions of channels that can be written as convex combination of other channels, and find general sufficient conditions for the degradability of the flagged extension. An immediate application is a bound on the quantum and private capacities of any channel being a mixture of a unitary operator and another channel, with the probability associated to the unitary operator 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.
7 citations
TL;DR: In this paper, the authors studied the relaxation dynamics of coherences of different order present in a system of two coupled nuclear spins and used a previously designed model for intrinsic noise present in such systems which considers the Lindblad master equation for Markovian relaxation.
Abstract: 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.
6 citations
TL;DR: In this article, a comparison of several entanglement distribution schemes in the context of special relativity is made, considering three types of entangled photon states: polarization, single photon, and Laguerre-Gauss mode entangled states.
Abstract: In recent years there has been a great deal of focus on a globe-spanning quantum network, including linked satellites for applications ranging from quantum key distribution to distributed sensors and clocks. In many of these schemes, relativistic transformations may have deleterious effects on the purity of the distributed entangled pairs. In this paper, we make a comparison of several entanglement distribution schemes in the context of special relativity. We consider three types of entangled photon states: polarization, single photon, and Laguerre-Gauss mode entangled states. All three types of entangled states suffer relativistic corrections, albeit in different ways. These relativistic effects become important in the context of applications such as quantum clock synchronization, where high fidelity entanglement distribution is required.
TL;DR: In this article, the authors present a theoretical scheme and its experimental proof of principle for an open quantum system undergoing Markovian and non-Markovian evolutions by diagnosing them with the relative entropy of coherence of two polarization qubits playing the roles of system and ancilla.
Abstract: We present a theoretical scheme and its experimental proof of principle for an open quantum system undergoing Markovian and non-Markovian evolutions. We exhibit these two regimes by diagnosing them with the relative entropy of coherence of two polarization qubits playing the roles of system and ancilla. These are initially prepared in a polarization maximally entangled state of a photon pair produced by spontaneous parametric down-conversion. We induce Markovian and non-Markovian regimes in the system's dynamics with the help of two auxiliary qubits, experimentally implemented by optical paths in a layout of Sagnac and Mach-Zehnder interferometers. We replicate system-environment interactions by means of an amplitude damping channel and a suitably designed inversion of it. In our scheme, one needs only two experimentally accessible parameters to achieve Markovian and non-Markovian regimes.
TL;DR: This work proposes a simple quantum error-correcting code for the detected amplitude damping channel that requires only two qubits and implements the encoding, the channel, and the recovery on an optical platform, the IBM Q System, and a nuclear magnetic resonance system.
Abstract: Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high fidelity. Here we propose a simple quantum error-correcting code for the detected amplitude damping channel. The code requires only two qubits. We implement the encoding, the channel, and the recovery on an optical platform, the IBM Q System, and a nuclear magnetic resonance system. For all of these systems, the error correction advantage appears when the damping rate exceeds some threshold. We compare the features of these quantum information processing systems used and demonstrate the advantage of quantum error correction on current quantum computing platforms.
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TL;DR: A small linear increase from zero in some eigenvalue of a density operator makes the derivative of its von-Neumann entropy logarithmic, a $\log$-singularity, and methods for checking non-additivity and positivity of the coherent information of a noisy quantum channel are developed.
Abstract: A small linear increase from zero in some eigenvalue of a density operator makes the derivative of its von-Neumann entropy logarithmic. We call this logarithmic derivative a $\log$-singularity and use it develop methods for checking non-additivity and positivity of the coherent information $\mathcal{Q}^{(1)}$ of a noisy quantum channel. One concrete application of our method leads to a novel type of non-additivity where a zero quantum capacity qubit amplitude damping channel in parallel with a simple qutrit channel is shown to have larger $\mathcal{Q}^{(1)}$ than the sum of $\mathcal{Q}^{(1)}$'s of the two individual channels. Another application shows that any noisy quantum channel has positive $\mathcal{Q}^{(1)}$ if its output dimension is larger than its complementary output (environment) dimension and this environment dimension equals the rank of some output state obtained from a pure input state. Special cases of this result prove $\mathcal{Q}^{(1)}$ is positive for a variety of channels, including the complement of a qubit channel, and a large family of incomplete erasure channels where the positivity of $\mathcal{Q}^{(1)}$ comes as a surprise.
TL;DR: The results show that the correlation between environmental noises plays a positive role in enhancing the entanglement of assistance, and in particular, it also works very well for very large decoherence strength of channel.
Abstract: Entanglement of assistance from multipartite to fewer partites (e.g., bipartite) entangled state via measurements is an important way for generating entanglement. Here, we study the dynamics of entanglement of assistance from a tripartite W-like state to a bipartite Bell-like state under correlated amplitude damping channel using weak measurement and quantum measurement reversal. Our results show that the correlation between environmental noises plays a positive role in enhancing the entanglement of assistance, and in particular, it also works very well for very large decoherence strength of channel. More importantly, we find that an almost maximal two-qubit entangled state in the total region of decoherence strength can be obtained from the originally W-like state with a better success probability. The proposed scheme provides an active way in combating the amplitude damping noises, which may have potential applications in quantum communication and distributed quantum computation.
TL;DR: In this article, the relative entropy of coherence of the output state of two qubits X states with 5 parameters was calculated when one subsystem or two subsystems goes through the amplitude damping channel n times.
Abstract: In this paper, we calculate relative entropy of coherence of the output state of two qubits X states with 5 parameters when one subsystem or two subsystems goes through the amplitude damping channel n times. We find that relative entropy of coherence of the output state decreases as the parameter g of the amplitude damping channel continuously changes from zero to one no matter how much n is. The curvature of relative entropy of coherence for the output state loosely increases gradually as n increases. Furthermore when n is larger, frozen coherence can appear as the parameter g of the amplitude damping channel increases.
TL;DR: The simultaneous dense coding (SDC) protocol when the noise on consecutive uses of the channel has some partial correlations is studied to evaluate the influence of the correlated noise.
Abstract: In this paper, we study the simultaneous dense coding (SDC) protocol when the noise on consecutive uses of the channel has some partial correlations. Three typical kinds of correlated noise are studied, i.e., the correlated depolarizing channel, the correlated dephasing channel and the correlated amplitude damping channel. Three success probabilities of SDC are calculated to evaluate the influence of the correlated noise. The analytical expressions of the success probabilities as functions of the noise strength and the correlation level are given.
TL;DR: In this paper, the authors investigated the speedup evolution of the system under the influence of the Unruh effect, where one of the observers (e.g., Bob) is uniformly accelerated.
Abstract: We investigate the speedup evolution of the system under the influence of the Unruh effect, where one of the observers (e.g., Bob) is uniformly accelerated. We show that acceleration can be beneficial to the evolution speed of the system, even in the presence of noise. Here two distinct dissipation mechanisms are considered, one where the total system is in a noise channel and the second where only Bob’s qubit is in a noisy channel. Interestingly, for the total system in the amplitude damping channel and depolarizing channel, the evolution speed of the system may increase monotonously with the increase of acceleration, which is in stark contrast to the case where only Bob’s qubit undergoing a noise channel. We find that the reason behind these behaviors are due to the competition mechanism between the Unruh effect and the dissipation effect, illustrated by the analytical formula of quantum speed limit time derived under quasi-inertial frame and strong dissipation regime.
TL;DR: In this article, the average fidelity and quantum correlations accurately depend on types of noise acting on quantum channels, such as amplitude damping, phase damping and depolarizing, and the authors showed that the quantum channels are more useful for teleportation when the shared qubits are affected by noisy channels such as AD channel and phase flip.
Abstract: In quantum information theory, the effects of quantum noise on teleportation are undeniable. Hence, we investigate the effect of noisy channels including amplitude damping, phase damping, depolarizing and phase flip on the teleported state between Alice and Bob where they share an entangled state by using atom-field interaction state. We analyze the fidelity and quantum correlations as a function of decoherence rates and time scale of a state to be teleported. We observe that the average fidelity and quantum correlations accurately depend on types of noise acting on quantum channels. It is found that atom-field interaction states are affected by amplitude damping channel are more useful for teleportation than when the shared qubits are affected by noisy channels such as AD channel and phase flip. We also observe that if the quantum channels are subject to phase flip noise, the average fidelity reproduces initial quantum correlations to possible values. On the other hand, not only all the noisy quantum channels do not always destroy average fidelity but also they can yield the highest fidelity in noisy conditions. In the current demonstration, our results provide that the average fidelity can have larger than 2/3 in front of the noise of named other channels with increasing decoherence strength. Success in quantum states transfer in the present noise establishes the importance of studying noisy channels.
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TL;DR: In this paper, the authors developed quantum circuits for optimal simulation of Markovian and non-Markovian open quantum systems using ancilla qubits to simulate the environment, and memory effects are induced by storing information about the system on extra qubits.
Abstract: Digital quantum simulation on quantum systems require algorithms that can be implemented using finite quantum resources. Recent studies have demonstrated digital quantum simulation of open quantum systems on Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we develop quantum circuits for optimal simulation of Markovian and Non-Markovian open quantum systems. The circuits use ancilla qubits to simulate the environment, and memory effects are induced by storing information about the system on extra qubits. We simulate the amplitude damping channel and dephasing channel as examples of the framework and infer (Non-)Markovianity from the (non-)monotonic behaviour of the dynamics. Further, we develop a method to optimize simulations by decomposing complex open quantum dynamics into smaller parts, that can be simulated using a small number of qubits. We show that this optimization reduces quantum space complexity from $O(l)$ to $O(1)$ for simulating the environment.
TL;DR: In this article, the authors study the dynamics of quantum correlation measures such as entanglement and measurement-induced nonlocality (MIN) as a function of decoherence parameters.
Abstract: 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 states 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 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.
TL;DR: In this article, the authors studied the relaxation dynamics of coherences of different orders present in a system of two coupled nuclear spins and used a previously designed model for intrinsic noise present in such systems which considers the Lindblad master equation for Markovian relaxation.
Abstract: In this work, we studied the relaxation dynamics of coherences of different orders 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 (CPD) channel acting simultaneously on both spins in conjunction with a generalised amplitude damping channel acting independently on both spins. The differential relaxation of multiple-quantum coherences can be ascribed to the action of a CPD channel acting simultaneously on both the spins.
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TL;DR: In this paper, the authors show how to reduce the de-coherence induced by a large class of multi-parameter qubit channels which have one invariant pure state.
Abstract: The problem of combating de-coherence by weak measurements has already been studied for the amplitude damping channel and for specific input states. We show how such a process can reduce the de-coherence induced by a large class of multi-parameter qubit channels which have one invariant pure state. These channels are unitarily equivalent to a channel represented by at most three Kraus operators embodying four real parameters. The figure of merit that we use is the average input-output fidelity which we show can be increased up to 30 percents by tuning of the weak measurement parameter.
TL;DR: In this paper, the average gate fidelities of one-and two-qubit gates were analyzed in a measurement-based quantum computation considering non-Markovian environments.
Abstract: We study the exact open system dynamics of one- and two-qubit gates during a measurement-based quantum computation considering non-Markovian environments. We obtain analytical solutions for the average gate fidelities and analyze them for amplitude damping and phase damping channels. We show, for both channels, that the average fidelity is identical for the $X$ gate and $Z$ gate and very similar for the $\ensuremath{\pi}/4$ gate when considering the amplitude damping channel. Also, we show that fast application of the projective measurements does not necessarily imply high gate fidelity nor does slow application necessarily imply low gate fidelity. Indeed, for highly non-Markovian environments, it is of utmost importance to know the best time to perform the measurements, since a huge variation in the gate fidelity may occur given this scenario. Furthermore, we show that whereas for amplitude damping the knowledge of the dissipative map is sufficient to determine the best measurement times, i.e., the best times at which measures are taken, the same is not necessarily true for phase damping. For the latter, the time of the set of measures becomes crucial since a phase error in one qubit can fix the phase error that takes place in another. Finally, we show that these peculiar results disappear if all qubits are subjected to Markovian processes.