Phase Flip Channel Research Articles

Fidelity Comparation of Two-Qubit Quantum Teleportation with Bit-Flip and Phase-Flip Channel

This study investigates the effect of noise on two-qubit quantum teleportation through a four-qubit entangled channel theoretically. Therefore, in this study a comparison of two states of teleportation through ideal and noisy channel was carried out. The noisy channel can have the effect of bit-flip channel and phase-flip channel. From these two effects, it is found that the channel transforms in-to a mixed state. If the noise is neglected, the channel is pure state. Then, this channel is measured and fidelity is calculated. The fidelity of an ideal environment is 1. This indicates that the teleportation was successfully sent and at the same time confirms the teleportation behavior under ideal conditions. In noisy environments, fidelity can be less than 1. Two factors in noisy environment that affect fidelity are noise factor (p) and the orginal parameter states (transmission coefficients). In this calculation, for the bit flip noise, we observed that as the values of the coefficient values of transmitted state increase, the fidelity value increases. Meanwhile, for the phase flip noise, we observed that as the values of the coefficient values of transmitted state increase, the fidelity value decreases.

Quantum differential privacy under noise channels

Quantum differential privacy is a way to protect privacy in quantum computing. It perturbs the final state of quantum computing by a specific quantum noise channel and makes the output useless to the attackers, so as to achieve privacy protection. In this paper, we study the quantum differential privacy under three channels: bit flip channel, phase flip channel and depolarizing channel. We calculate the privacy parameters for these three channels based on the proportional distance. We show the privacy protection capability by calculating the decay rates of the trace distances of two arbitrary quantum states before and after passing through the channels. Under the same privacy budget, we compare the fidelities, the trace distances between the real outputs and the outputs after entering the channels, and analyze the privacy protection performance of different quantum channels in detail.

Training a quantum measurement device to discriminate unknown non-orthogonal quantum states

Here, we study the problem of decoding information transmitted through unknown quantum states. We assume that Alice encodes an alphabet into a set of orthogonal quantum states, which are then transmitted to Bob. However, the quantum channel that mediates the transmission maps the orthogonal states into non-orthogonal states, possibly mixed. If an accurate model of the channel is unavailable, then the states received by Bob are unknown. In order to decode the transmitted information we propose to train a measurement device to achieve the smallest possible error in the discrimination process. This is achieved by supplementing the quantum channel with a classical one, which allows the transmission of information required for the training, and resorting to a noise-tolerant optimization algorithm. We demonstrate the training method in the case of minimum-error discrimination strategy and show that it achieves error probabilities very close to the optimal one. In particular, in the case of two unknown pure states, our proposal approaches the Helstrom bound. A similar result holds for a larger number of states in higher dimensions. We also show that a reduction of the search space, which is used in the training process, leads to a considerable reduction in the required resources. Finally, we apply our proposal to the case of the phase flip channel reaching an accurate value of the optimal error probability.

Entanglement recovery in noisy binary quantum information protocols via three-qubit quantum error correction codes

The task of preserving entanglement against noises is of crucial importance for both quantum communication and quantum information transfer. To this aim, quantum error correction (QEC) codes may be employed to compensate, at least partially, the detriments induced by environmental noise that can be modeled as a bit-flip or a phase-flip error channel. In this paper, we investigate the effects of the simple three-qubit QEC codes to restore entanglement and nonlocality in a two-qubit system and consider two practical applications: superdense coding and quantum teleportation. Though the considered three-qubit QEC codes are known to perfectly work in the presence of very small noise, we show that they can avoid the sudden death of entanglement and improve the performance of the addressed protocols also for larger noise amplitudes.

Quantum entanglement and coherence of tripartite W state for Dirac fields under noisy channels in non-inertial frames

We investigate quantum entanglement and coherence of tripartite W state for Dirac fields under phase damping, phase flip and bit flip channels, respectively, in non-inertial frames. Via π-tangle, we numerically compute tripartite entanglement of W state under three channels when two observers are accelerated. We also analytically derive l 1-norm quantum coherence of W state under the simultaneous influence of Unruh effect and noisy environments. For phase-damping and phase-flip channels, both the acceleration and noisy channels modulate the behaviour of the tripartitle entanglement and quantum coherence. They do not vanish even for infinite acceleration when only A's qubit is under noisy environment, in contrast with the case when two or more observers’ qubits are under noisy environment. In the case of the bit flip channel, the behavior of the tripartite entanglement is similar to the one of the phase flip channel, but quantum coherence remains unaffected by the environment.

Quantum speedup dynamics process in Schwarzschild space–time

Quantum speed limit time (QSLT) can be used to characterize the intrinsic minimal time interval for a quantum system evolving from an initial state to a target state. We investigate the QSLT of the open system in Schwarzschild space–time. We show that, in some typical noisy channels, the Hawking effect can accelerate the evolution of the system. For an initial entangled state, the evolution speed of the system can be enhanced in the depolarizing, bit flip, and bit-phase flip channels as the Hawking temperature increases, which are in sharp contrast to the phase flip channel. Moreover, the optimal initial entanglement exists in other noise channels except the phase flip channel, which minimizes the QSLT of the system and thus leads to the maximum evolution speed of the system.

Deterministic remote state preparation of arbitrary three-qubit state through noisy cluster-GHZ channel

We propose a novel scheme for remote state preparation of an arbitrary three-qubit state with unit success probability, utilizing a nine-qubit cluster-GHZ state without introducing auxiliary qubits. Furthermore, we proceed to investigate the effects of different quantum noises (e.g., amplitude-damping, phase-damping, bit-flip and phase-flip noises) on the systems. The fidelity results of three-qubit target state are presented, which are usually used to illustrate how close the output state is to the target state. To compare the different effects between the four common types of quantum noises, the fidelities under one specific identical target state are also calculated and discussed. It is found that the fidelity of the phase-flip noisy channel drops the fastest through the four types of noisy channels, while the fidelity is found to always maintain at 1 in bit-flip noisy channel.

Quantum discord for multiqubit systems

We evaluate analytically the quantum discord for a large family of multiqubit states. It is interesting to note that the quantum discord of three-qubits and five-qubits is the same, as is the quantum discord of two-qubits and six-qubits. We discover that the quantum discord of this family states can be concluded into three categories. The level surfaces of the quantum discord in the three categories is shown through images. Furthermore, we investigated the dynamic behavior of quantum discord under decoherence. For the odd partite systems, we prove the frozen phenomenon of quantum discord doesn't exist under the phase flip channel, while it can be found in the even partite systems.

Error rates and resource overheads of repetition cat qubits

We estimate and analyze the error rates and the resource overheads of the repetition cat qubit approach to universal and fault-tolerant quantum computation. The cat qubits stabilized by two-photon dissipation exhibit an extremely biased noise where the bit-flip error rate is exponentially suppressed with the mean number of photons. In a recent work, we suggested that the remaining phase-flip error channel could be suppressed using a 1D repetition code. Indeed, using only bias-preserving gates on the cat-qubits, it is possible to build a universal set of fault-tolerant logical gates at the level of the repetition cat qubit. In this paper, we perform Monte-Carlo simulations of all the circuits implementing the protected logical gates, using a circuit-level error model. Furthermore, we analyze two different approaches to implement a fault-tolerant Toffoli gate on repetition cat qubits. These numerical simulations indicate that very low logical error rates could be achieved with a reasonable resource overhead, and with parameters that are within the reach of near-term circuit QED experiments.

Probing quantum Fisher information of an open Dirac system with Hawking effect in the Schwarzschild black hole

The unavoidable interaction of a real quantum system with the environment leads to the degradation of quantum coherence. Consequently, this paper investigates how such interaction can influence the quantum Fisher information (QFI) with the Hawking effect in the Schwarzschild black hole. We have considered two models of quantum decoherence: amplitude damping and phase damping channels; both can be experimentally induced. We found that Quantum information is more robust to phase flip channel than to the amplitude damping channel. It is observed that under the influence of phase damping channel, Quantum information does not depend on Hawking temperature making the parameter estimation immune to the Hawking effect but susceptible to decoherence. We found that QFI dwindles with increasing Hawking temperature and becomes more attenuated with decoherence which implies that the parameter estimation can be achieved with higher precision when the black hole is not evaporating.

Coherent-driving-assisted quantum speedup in Markovian channels* *Project supported by the Shandong Provincial Natural Science Foundation, China (Grant No. ZR2020MA086) and the National Natural Science Foundation of China (Grant Nos. 61675115 and 11974209).

As is well known, the quantum evolution speed of quantum state can never be accelerated in the Markovian regime without any operators on the system. The Hamiltonian corrections induced by the action of coherent driving forces are often used to fight dissipative and decoherence mechanisms in experiments. For this reason, considering three noisy channels (the phase-flip channel, the amplitude damping channel and the depolarizing channel), we propose a scheme of speedup evolution of an open system by controlling an external unitary coherent driving operator on the system. It is shown that, in the presence of the coherent driving, no-speedup evolution can be transformed into quantum speedup evolution in the Markovian dynamics process. Additionally, under the fixed coherent driving strength in the above three noisy channels, the best way to achieve the most degree of quantum speedup for the system has been acquired by rotating the system with appropriate driving direction angles, respectively. Finally, we conclude that the reason for this acceleration is not the non-Markovian dynamical behavior of the system but due to the oscillation of geometric distance between the initial state and the target final state.

Dynamics of quantum correlations for different types of noisy channels

The effect of noise channels (amplitude damping, phase damping, depolarizing and phase flip) on the behaviors of quantum correlations such as quantum discord (QD), super quantum discord (SQD) within an atom-field interaction with environments are investigated. Generation and preservation of the quantum entanglement between the qubit and field have played an important role for both fundamental quantum theories and experiments. This topic motivates us to explore the role of noise channels on quantum correlations in the Jaynes–Cummings model. Our analytical results show that the entanglement and quantum correlation dynamics is strongly related to the decoherenc strength and type of noisy channel. One purpose of this work is to answer the following question: is it possible the effects of noise channels on entangled states lead to birth of entanglement and quantum correlations or do they just have a destructive effects? We show that, the noise of all above channels do not lead to a sudden vanishing of quantum correlations. But the noise of phase flip channel reproduces initial quantum correlations. Furthermore, we find that entanglement and QD are more fragile to environmental noises than the SQD. For this reason, it seems that our results can be beneficial to deeply understanding the weak measurement and quantum correlation in quantum information resource.

Quantum simulation of quantum relativistic diffusion via quantum walks

Two models are first presented, of a one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with random coin unitaries. It is then shown that both these models admit a common limit in the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two of the three standard error channels for a two-level quantum system. This, as one may call it, Dirac Lindblad equation, provides a model of quantum relativistic spatial diffusion, which is evidenced both analytically and numerically. This model of spatial diffusion has the intriguing specificity of making sense only with original unitary models which are relativistic in the sense that they have chirality, on which the noise is introduced: the diffusion arises via the by-construction (quantum) coupling of chirality to the position. For a particle with vanishing mass, the model of quantum relativistic diffusion introduced in the present work, reduces to the well-known telegraph equation, which yields propagation at short times, diffusion at long times, and exhibits no quantumness. Finally, the results are extended to temporal noises which depend smoothly on position.

Suppressing the information losses of accelerated qubit–qutrit system

Protecting the accelerated information coherence and suppressing of its decay due to the acceleration is achieved by using different noisy channels. The behavior of three different types of information; Fisher, nonlocal and local information of qubit–qutrit system is discussed. It is shown that, the estimation rate of the acceleration parameter is maximized if both subsystems are accelerated and interacted locally with their noise channels. However, if the largest subsystem is accelerated, then the estimation rate is minimized. The rate of change of the nonlocal information depends on which subsystem is accelerated. The results display that the local information is almost unaltered during the acceleration process, that is, the information is frozen. We show that the phase-flip channel represents the weak channel, where its suppressing of the decay due to the acceleration is smaller than the dephasing and depolarize of channels.

Joint remote state preparation (JRSP) of two-qubit equatorial state in quantum noisy channels

This letter reports the influence of noisy channels on JRSP of two-qubit equatorial state. We present a protocol for JRSP of two-qubit equatorial state. Afterward, we investigate the effects of five quantum noises on the protocol. We find that the system loses some of its properties as consequence of unwanted interactions with environment. For instance, within the domain 0<λ<0.65, the information lost via transmission of qubits in amplitude channel is most minimal, while for 0.65<λ≤1, the information lost in phase flip channel becomes the most minimal. Also, for any given λ, the information transmitted through depolarizing channel has the least chance of success.

Total Pairwise Quantum Correlation and Entanglement in a Mixed-Three-Spin Ising-XY Model with Added Dzyaloshinskii—Moriya Interaction under Decoherence

We investigate the behavior of geometric global quantum discord (GGQD) and concurrence (C) between half-spins of a mixed-three-spin (1/2, 1, 1/2) system with the Ising-XY model for which spins (1, 1/2) have the Ising interaction and half-spins (1/2, 1/2) have both XY and the Dzyaloshinskii—Moriya interactions together, under the decoherence action. A single-ion anisotropy property with coefficient ζ is assumed for the spin-integer. This system which includes an analytical Hamiltonian is considered at the front of an external homogeneous magnetic field B in thermal equilibrium. Finally, we compare GGQD and C and express some interesting phase flip reactions of the total quantum correlation and pairwise entanglement between spins (1/2, 1/2). Generally, we conclude that the concurrence and GGQD have different behaviors under the phase flip channel.

On the quantum discord of general X states

Quantum discord Q is a function of density matrix elements. The domain of such a function in the case of two-qubit system with X density matrix may consist of three subdomains at most: two ones where the quantum discord is expressed in closed analytical forms (Q_{\pi/2} and Q_0) and an intermediate subdomain for which, to extract the quantum discord Q_\theta, it is required to solve in general numerically a one-dimensional minimization problem to find the optimal measurement angle \theta\in(0,\pi/2). Hence the quantum discord is given by a piecewise-analytic-numerical formula Q=\min{Q_{\pi/2}, Q_\theta, Q_0}. Equations for determining the boundaries between these subdomains are obtained. The boundaries consist of bifurcation points. The Q_{\theta} subdomains are discovered in the generalized Horodecki states, in the dynamical phase flip channel model, in the anisotropic spin systems at thermal equilibrium, in the heteronuclear dimers in an external magnetic field. We found that transitions between Q_{\theta} subdomain and Q_{\pi/2} and Q_0 ones occur suddenly but continuously and smoothly, i.e., nonanalyticity is hidden and can be observed in higher derivatives of discord function.

Controlling the coherence in a pure dephasing model for arbitrary prescibed time span

We present an open-loop unitary strategy to control the coherence in a pure dephasing model (related to the phase-flip channel) that is able to recover, for whatever prescribed time span, the initial coherence at the end of the control process. The strategy's key idea is to steer the quantum state to the subset of invariant states and keep it there the necessary time, using a fine tuned control Hamiltonian.

The Quantum Correlations of the Werner State Under Quantum Decoherence

This paper examines the quantum correlations of the Werner state and demonstrates the relationship between the quantum discord and entanglement under decoherence. We also identify that when the discord takes the maximal value for a given state, and discuss the boundary value for entanglement and discord. As we all know that, in an ideal environment, the quantum discord is always larger than the entanglement of formation for almost all entangled states. But, the analysis in the article exposes that the entanglement may show stronger anti-interference than quantum discord in the noisy channel. In addition, the emphasis is also placed on the problem of the relation between the geometric discord (D g ) and the entanglement of formation (EOF) which is customarily used as a measure of entanglement. At the same time, we also investigate the inequality 2D g ≥ N 2 and find that it is still be satisfied under the phase flip channel.

Characterization of a spatial light modulator as a polarization quantum channel

Spatial light modulators are versatile devices employed in a vast range of applications to modify the transverse phase or amplitude profile of an incident light beam. Most experiments are designed to use a specific polarization which renders optimal sensitivity for phase or amplitude modulation. Here we take a different approach and apply the formalism of quantum information to characterize how a phase modulator affects a general polarization state. In this context, the spatial modulators can be exploited as a resource to couple the polarization and the transverse spatial degrees of freedom. Using a quasi-monochromatic single photon beam obtained from a pair of twin photons generated by spontaneous parametric down conversion, we performed quantum process tomography in order to obtain a general analytic model for a quantum channel that describes the action of the device on the polarization qubits. We illustrate the application of these concepts by demonstrating the implementation of a controllable phase flip channel. This scheme can be applied in a straightforward manner to characterize the resulting polarization states of different types of phase or amplitude modulators and motivates the combined use of polarization and spatial degrees of freedom in innovative applications.