Flip Channels Research Articles

Teleportation of Qubits in a Kicked Nonlinear Cavity with Ultra-short Pulses via Quantum Noisy Channels

AbstractIn this paper, we delve into the profound ramifications of noise on qubit teleportation between the esteemed figures of Alice and Bob, ruthlessly quantifying the negativity and distance of the transmitted information. Through the invocation of an audacious modification to the Hamiltonian of the Jaynes–Cummings model, incorporating the ferocious power of a kicked cavity and ultra-short laser pulses, we unleash a tempest that unrelentingly shapes the entanglement and quality of the teleported information. Moreover, we fearlessly venture into the treacherous territory of noisy channels, including the formidable adversaries of phase flip and double phase flip channels, as they mercilessly assail the teleported state, engendered by the tumultuous interaction within the unforgiving depths of the kicked cavity, only to be met with our resolute projection.

Metrological non-classical correlations and quantum coherence in hybrid (1/2,1) system under decoherence channels

Abstract Our research focuses on the interplay between thermal noise and decoherence channels on quantum coherence and nonclassical correlations in a hybrid ( 1 / 2 , 1 ) Heisenberg model. This hybrid system integrates the Dzyaloshinsky–Moriya interaction (DMI) and operates under the influence of an external magnetic field. We use local quantum Fisher information (LQFI) for correlation estimation and relative entropy of coherence for coherence measurement in the considered system. Our investigation encompasses various parameters of the hybrid system, the strength of the DMI and the intensity of the external magnetic field. Our findings underscore that elevated temperature compromises both nonclassical correlations and coherence. On the other hand, the robustness of the DMI mitigates the impact of thermal noise on quantum Fisher information correlations and relative entropy of coherence in the hybrid system. Additionally, we inspect the impact of decohering channels-specifically, dephasing, phase flip, and bit- and trit-flip channels-on thermal coherence and quantum correlations. The introduction of various decoherence processes into the hybrid qubit-qutrit system leads to a competition with thermal fluctuations, thereby giving rise to out-of-equilibrium states. Our results indicate that as the decoherence strength parameter (p) increases, both LQFI and relative entropy of coherence exhibit similar behaviors in the dephasing and phase flip channels. These resources gradually diminish, eventually disappearing entirely at p = 1. In the context of the bit- and trit-flip channels, quantum coherence displays notable distinctions compared to what is observed under dephasing and phase flip channels, revealing that coherence can be preserved if the DMI is strong and the intensity of the external magnetic field is reduced. These findings are important since it is crucial to first understand the decoherence process, arising from the interaction with the environment, and then to find ways to hinder this decoherence in order to avoid the complete loss of the quantum resources necessary to quantum information processing.

Quantum coherence and entanglement under the influence of decoherence

In this work, we delve into the dynamic traits of the relative entropy of quantum coherence (REQC) as the quantum system interacts with the different noisy channels, drawing comparisons with entanglement (concurrence). The research results demonstrate the broader prevalence and stronger robustness of the REQC as opposed to concurrence. It’s worth noting that the bit flip channel cannot uphold a constant nonzero frozen the REQC, besides, the concurrence follows a pattern of temporary reduction to zero, followed by recovery after a certain time span. More importantly, the REQC maintains its presence consistently until reaching a critical threshold, whereas concurrence experiences completely attenuation to zero under the influence of phase damping and amplitude damping channels.

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.

Ascertaining the influences of auxiliary qubits on the Einstein–Podolsky–Rosen steering and its directions

Einstein–Podolsky–Rosen (EPR) steering is an example of nontrivial quantum nonlocality and characteristic in the non-classical world. The directivity (or asymmetry) is a fascinating trait of EPR steering, and it is different from other quantum nonlocalities. Here, we consider the strategy in which two atoms compose a two-qubit X state, and the two atoms are owned by Alice and Bob, respectively. The atom of Alice suffers from a reservoir, and the atom of Bob couples with a bit flip channel. The influences of auxiliary qubits on EPR steering and its directions are revealed by means of the entropy uncertainty relation. The results indicate that EPR steering declines with growing time t when adding fewer auxiliary qubits. The EPR steering behaves as damped oscillation when introducing more auxiliary qubits in the strong coupling regime. In the weak coupling regime, the EPR steering monotonously decreases as t increases when coupling auxiliary qubits. The increases in auxiliary qubits are responsible for the fact that the steerability from Alice to Bob (or from Bob to Alice) can be more effectively revealed. Notably, the introductions of more auxiliary qubits can change the situation that steerability from Alice to Bob is certain to a situation in which steerability from Bob to Alice is certain.

Trade-offs between coherence and mixedness and their evolution under quantum noise channels

Generally quantum processes tend to mix the pure input states and degrade the original coherence. Such processes display exactly the trade-offs between the coherence and the mixedness. In this paper, we present trade-offs between the coherence measures (l2 norm of coherence, coherence via skew information, geometric measure of coherence) and the mixedness (normalized linear entropy mixedness, geometric measure of mixedness, mixedness via skew information). The evolution of these trade-offs are also investigated under four quantum noise channels: the bit flip, phase flip, depolarizing and amplitude damping channels.

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.

Invariance of success probability in Grover's quantum search under local noise with memory

We analyze the robustness of Grover's quantum search algorithm performed by a quantum register under a possibly time-correlated noise acting locally on the qubits. We model the noise as originating from an arbitrary but fixed unitary evolution, $U$, of some noisy qubits. The noise can occur with some probability in the interval between any pair of consecutive noiseless Grover evolutions. Although each run of the algorithm is a unitary process, the noise model leads to decoherence when all possible runs are considered. We derive a set of unitary $U$'s, called the 'good noises,' for which the success probability of the algorithm at any given time remains unchanged with varying the non-trivial total number ($m$) of noisy qubits in the register. The result holds irrespective of the presence of any time-correlations in the noise. We show that only when $U$ is either of the Pauli matrices $\sigma_x$ and $\sigma_z$ (which give rise to $m$-qubit bit-flip and phase-damping channels respectively in the time-correlation-less case), the algorithm's success probability stays unchanged when increasing or decreasing $m$. In contrast, when $U$ is the Pauli matrix $\sigma_y$ (giving rise to $m$-qubit bit-phase flip channel in the time-correlation-less case), the success probability at all times stays unaltered as long as the parity (even or odd) of the total number $m$ remains the same. This asymmetry between the Pauli operators stems from the inherent symmetry-breaking existing within the Grover circuit. We further show that the positions of the noisy sites are irrelevant in case of any of the Pauli noises. The results are illustrated in the cases of time-correlated and time-correlation-less noise. We find that the former case leads to a better performance of the noisy algorithm. We also discuss physical scenarios where our chosen noise model is of relevance.

Visually capture quantum nonlocalities through quantum steering ellipsoid

Quantum steering ellipsoid (QSE) can faithfully characterize arbitrary bipartite state, and provide a new method to visually investigate and capture various quantum nonlocalities. Note that the dissipation of quantum nonlocalities can be accelerated by the coupling between the system and the decoherence channel, which induces great challenges in detecting quantum nonlocalities. Herein, considering the scenario in which the subsystem of a two-qubit system is coupled with a decoherence channel, the quantum discord (QD) and concurrence are visually characterized and detected by employing the QSE. The results reveal that the QSE y and z semiaxes are responsible for the traits of the QD and concurrence under the bit flip channel. The x and y semiaxes dominate and visualize the QD and concurrence under the phase damping channel. Of particular note is that one can realize the detections of the QD and concurrence via the shape of the QSE. To be clearer, the disappearance of the QD can be ascertained according to a needle-shaped QSE or a vanishing QSE in the Bloch sphere. In contrast, one can witness the concurrence if the total semiaxis length is greater than one. Beyond this, our results visually reveal that quantum entanglement is a stronger quantum nonlocality than the QD from the perspective of geometry, and thus deepens the understanding of the quantum nonlocality.

Genuine three qubit Einstein–Podolsky–Rosen steering under decoherence: revealing hidden genuine steerability via pre-processing

The behaviour of genuine EPR steering of three qubit states under various environmental noises is investigated. In particular, we consider the two possible steering scenarios in the tripartite setting: (1 $$\rightarrow $$ 2), where Alice demonstrates genuine steering to Bob-Charlie and (2 $$\rightarrow $$ 1), where Alice-Bob together demonstrate genuine steering to Charlie. In both these scenarios, we analyse the genuine steerability of the generalized Greenberger–Horne–Zeilinger (gGHZ) states or the W-class states under the action of noise modelled by amplitude damping (AD), phase flip (PF), bit flip (BF) and phase damping (PD) channels. In each case, we consider three different interactions with the noise depending upon the number of parties undergoing decoherence. We observed that the tendency to demonstrate genuine steering decreases as the number of parties undergoing decoherence increases from one to three. We have observed several instances where the genuine steerability of the state revives after collapsing if one keeps on increasing the damping. However, hidden genuine steerability of a state cannot be revealed solely from the action of noise. So, the parties having a characterized subsystem perform local pre-processing operations depending upon the steering scenario and the state shared with the dual intent of revealing hidden genuine steerability or enhancing it.

Probing Genuine Multipartite Einstein–Podolsky–Rosen Steering and Entanglement Under an Open Tripartite System

Einstein–Podolsky–Rosen steering is a peculiar quantum nonlocal correlation and has unique physical characteristics and a wide application prospect. Even more importantly, multipartite steerable states have more vital applications in the future quantum information field. Thus, in this work, we explored the dynamics characteristics of both genuine multipartite steering (GMS) and genuine multipartite entanglement (GME) and the relations of both under an open tripartite system. Specifically, the tripartite decoherence system may be modeled by the three parties of a tripartite state that undergo the noisy channels. The conditions for genuine entangled and steerable states can be acquired for the initial tripartite state. The results showed that decoherence noises can degrade the genuine multipartite entanglement and genuine multipartite steering and even induce its death. Explicitly, GME and GMS disappear with the increase in the decoherence strength under the phase damping channel. However, GME and GMS rapidly decay to death with the increase in the channel-noise factor and then come back to life soon after in the bit flip channel. Additionally, the results indicate that GMS is born of GME, but GME does not imply GMS, which means that the set of genuine multipartite steerable states is a strict subset of the set of genuine multipartite entangled states. These conclusions may be useful for discussing the relationship of quantum nonlocal correlations (GME and GMS) in the decoherence systems.

Dynamical quantum phase transitions in a noisy lattice gauge theory

Lattice gauge theories form an intriguing class of theories highly relevant to both high-energy particle physics and low-energy condensed matter physics with the rapid development of engineered quantum devices providing new tools to study, e.g., dynamics of such theories. The massive Schwinger model is known to exhibit intricate properties of more complicated theories and has recently been shown to undergo dynamical quantum phase transitions out of equilibrium. With current technology, noise is inevitable and potentially fatal for a successful quantum simulation. This paper studies the dynamics subject to noise of a $(1+1)\mathrm{D}\phantom{\rule{4pt}{0ex}}\mathrm{U}(1)$ quantum link model following a quench of the sign of the mass term. We find that not only is the system capable of handling noise at rates realistic in NISQ-era devices, promising the possibility to study the target dynamics with current technology, but the effect of noise can be understood in terms of simple models. Specifically the gauge-breaking nature of bit flip channels results in exponential dampening of state amplitudes, and thus observables, which does not affect the structures of interest. This is especially important as it demonstrates that the gauge theory can be successfully studied with devices that only exhibit approximate gauge invariance.

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.

Robustness of two-qubit and three-qubit states in correlated quantum channels

We investigate how the correlated actions of quantum channels affect the robustness of entangled states. We consider the Bell-like state and random two-qubit pure states in the correlated depolarizing, bit flip, bit-phase flip, and phase flip channels. It is found that the robustness of two-qubit pure states can be noticeably enhanced due to the correlations between consecutive actions of these noisy channels, and the Bell-like state is always the most robust one. We also consider the robustness of three-qubit pure states in correlated noisy channels. For the correlated bit flip and phase flip channels, the result shows that although the most robust and most fragile states are locally unitary equivalent, they exhibit different robustness in different correlated channels, and the effect of channel correlations on them is also significantly different. However, for the correlated depolarizing and bit-phase flip channels, the robustness of two special three-qubit pure states is exactly the same. Moreover, compared with the random three-qubit pure states, they are neither the most robust states nor the most fragile states.

Robustness of multipartite entangled states for fermionic systems under noisy channels in non-inertial frames

We investigate robustness of bipartite and tripartite entangled states for fermionic systems in non-inertial frames, which are under noisy channels. We consider two Bell states and two Greenberger-Horne-Zeilinger (GHZ) states, which possess initially the same amount of entanglement, respectively. By using genuine multipartite (GM) concurrence, we analytically derive the equations that determine the difference between the robustness of these locally unitarily equivalent states under the amplitude-damping channel. We find that tendency of the robustness for two GHZ states evaluated by using three-tangle τ and GM concurrence as measures of genuine tripartite entanglement is equal to each other. We also find that the robustness of two Bell states is equal to each other under the depolarizing, phase damping and bit flip channels, and that the same is true for two GHZ states.

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.

Complete Complementarity Relations in System–environment Decoherent Dynamics

We investigate the system-environment information flow from the point of view ofcomplete complementarity relations. We consider some commonly used noisy quantum channels:Amplitude damping, phase damping, bit flip, bit-phase flip, phase flip, depolarizing, and correlatedamplitude damping. By starting with an entangled bipartite pure quantum state, with the linearentropy being the quantifier of entanglement, we study how entanglement is redistributed and turnedinto general correlations between the degrees of freedom of the whole system. For instance, it ispossible to express the entanglement entropy in terms of the multipartite quantum coherence or interms of the correlated quantum coherence of the different partitions of the system. In addition,we notice that for the depolarizing and bit-phase flip channels the wave and particle aspects candecrease or increase together. Besides, by considering the environment as part of a pure quantumsystem, the linear entropy is shown to be not just a measure of mixedness of a particular subsystem,but a correlation measure of the subsystem with rest of the world.

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.

The n-th Decay Rate of Coherence for Bell-diagonal States Under Quantum Channels

We study the degree to which the coherence of quantum states is affected by noise. We give the definition of the n-th decay rate and investigate the coherence of Bell-diagonal states under n iterations of channels. We derive explicit formulas of the n-th decay rates based on l1 norm of coherence, relative entropy of coherence and skew information-based coherence. It is found that the larger n is, the faster the n-th decay rate decreases as the parameter p of Bell-diagonal states increases. Moreover, for any fixed n, with the increase of p, Bell-diagonal states can be completely incoherent under generalized amplitude damping (GAD) channels, depolarization (DEP) channels and phase flip (PF) channels, while this is not the case for bit flip (BF) channels and bit-phase flip (BPF) channels. We also investigate the geometry of the relative entropy of coherence and skew information-based coherence of Bell-diagonal states under different channels when the n-th decay rate is one, i.e., the coherence is frozen. It is shown that compared with BF and BPF channels, when n is large enough, the coherence of Bell-diagonal states will not be frozen under GAD, DEP and PF channels. For skew information-based coherence, similar properties of coherence freezing are found.