A comparative study of protocols for secure quantum communication under noisy environment: single-qubit-based protocols versus entangled-state-based protocols

The effect of noise on various protocols of secure quantum communication has been studied. Specifically, we have investigated the effect of amplitude damping, phase damping, squeezed generalized amplitude damping, Pauli type as well as various collective noise models on the protocols of quantum key distribution, quantum key agreement, quantum secure direct quantum communication and quantum dialogue. From each type of protocol of secure quantum communication, we have chosen two protocols for our comparative study: one based on single-qubit states and the other one on entangled states. The comparative study reported here has revealed that single-qubit-based schemes are generally found to perform better in the presence of amplitude damping, phase damping, squeezed generalized amplitude damping noises, while entanglement-based protocols turn out to be preferable in the presence of collective noises. It is also observed that the effect of noise depends upon the number of rounds of quantum communication involved in a scheme of quantum communication. Further, it is observed that squeezing, a completely quantum mechanical resource present in the squeezed generalized amplitude channel, can be used in a beneficial way as it may yield higher fidelity compared to the corresponding zero squeezing case.     

On Concurrence and Entanglement of Rank Two Channels

Concurrence and further entanglement quanti.ers can be computed explicitly for channels of rank two if representable by just two Kraus operators. Almost all details are available for the subclass of rank two 1-qubit channels. There is a simple geometric picture beyond, explaining nicely the role of anti-linearity.Presented at the International Conference “Entanglement, Information & Noise”, Krzyżowa, Poland, June 14-20, 2004.     

Decoherence effects in the quantum qubit flip game using Markovian approximation

We are considering a quantum version of the penny flip game, whose implementation is influenced by the environment that causes decoherence of the system. In order to model the decoherence, we assume Markovian approximation of open quantum system dynamics. We focus our attention on the phase damping, amplitude damping and amplitude raising channels. Our results show that the Pauli strategy is no longer a Nash equilibrium under decoherence. We attempt to optimize the players’ control pulses in the aforementioned setup to allow them to achieve higher probability of winning the game compared with the Pauli strategy.     

Different dynamics of classical and quantum correlations under decoherence

The dynamics of classical and quantum correlations under nondissipative and dissipative decoherences are analytically and numerically investigated with both one-side measures and two-side measures. Specifically, two qubits under local amplitude damping decoherence and depolarizing decoherence channels are considered. We show that, under the action of amplitude damping decoherence, both the entanglement and correlations of the different types of initial states with same initial values, suffer different types of dynamics. Moreover, the transfers of the entanglement and correlations between the system and the environment for different types of initial states are also shown to be different. While for the action of depolarizing decoherence, there does not exist sudden change in the decay rates of both the classical and quantum correlations, which is different from some other nondissipative channels. Furthermore, the quantum dissonance can be found to keep unchanged under the action of depolarizing decoherence. Such different dynamic behaviors of different noisy quantum decoherence channels reveal distinct transmission performance of classical and quantum information.     

Variational-Based Reduced-Order Model in Dynamic Substructuring of Coupled Structures Through a Dissipative Physical Interface: Recent Advances

This paper deals with a variational-based reduced-order model in dynamic substructuring of two coupled structures through a physical dissipative flexible interface. We consider the linear elastodynamic of a dissipative structure composed of two main dissipative substructures perfectly connected through interfaces by a linking substructure. The linking substructure is flexible and is modeled in the context of the general linear viscoelasticity theory, yielding damping and stiffness operators depending on the frequency, while the two main dissipative substructures are modeled in the context of linear elasticity with an additional classical viscous damping modeling which is assumed to be independent of the frequency. We present recent advances adapted to such a situation, which is positioned with respect to an appropriate review that we carry out on the different methods used in dynamic substructuring. It consists in constructing a reduced-order model using the free-interface elastic modes of the two main substructures and, for the linking substructure, an appropriate frequency-independent elastostatic lifting operator and the frequency-dependent fixed-interface vector basis.     

Entanglement-breaking channels in infinite dimensions

In the first part of the paper we give a representation for entanglement-breaking channels in separable Hilbert space that generalizes the “Kraus decomposition with rank-one operators” and use it to describe complementary channels. We also note that coherent information for antidegradable channel is always nonpositive. In the second part, we give necessary and sufficient condition for entanglement breaking for the general quantum Gaussian channel. Application of this condition to one-mode channels provides several new cases where the additivity conjecture holds in the strongest form.     

几种确定型量子程序的可达和终止验证

讨论了单量子比特空间中,比特翻转、相位翻转、去极化、幅值阻尼和相位阻尼等量子信道作为特殊的非确定型量子程序—确定型量子程序,从计算基态运行时程序的可达集合和它们终止及发散的情况。研究表明:这些量子信道从计算基态运行时,有的量子程序的终止和发散与刻画量子信道的参数有紧密的联系,而有的量子程序的终止和发散与刻画量子信道的参数没有联系。     

Three-player quantum Kolkata restaurant problem under decoherence

Effect of quantum decoherence in a three-player quantum Kolkata restaurant problem is investigated using tripartite entangled qutrit states. Different qutrit channels such as, amplitude damping, depolarizing, phase damping, trit-phase flip and phase flip channels are considered to analyze the behaviour of players payoffs. It is seen that Alice’s payoff is heavily influenced by the amplitude damping channel as compared to the depolarizing and flipping channels. However, for higher level of decoherence, Alice’s payoff is strongly affected by depolarizing noise. Whereas the behaviour of phase damping channel is symmetrical around 50% decoherence. It is also seen that for maximum decoherence (p = 1), the influence of amplitude damping channel dominates over depolarizing and flipping channels. Whereas, phase damping channel has no effect on the Alice’s payoff. Therefore, the problem becomes noiseless at maximum decoherence in case of phase damping channel. Furthermore, the Nash equilibrium of the problem does not change under decoherence.     

Discretization of the Wave Equation Using Continuous Elements in Time and a Hybridizable Discontinuous Galerkin Method in Space

We provide an error analysis of two methods for time stepping the wave equation. These are based on the Hybridizable Discontinuous Galerkin (HDG) method to discretize in space, and the continuous Galerkin method to discretize in time. Two variants of HDG are proposed: a dissipative method based on the standard numerical flux used for elliptic problems, and a non-dissipative method based on a new choice of the flux involving time derivatives. The analysis of the fully discrete problem is based on simplified arguments using projections rather than explicit interpolants used in previous work. Some numerical results are shown that illuminate the theory.     

The Jamiołkowski Isomorphism and a Simplified Proof for the Correspondence Between Vectors Having Schmidt Number <Emphasis Type="Italic">k</Emphasis> and <Emphasis Type="Italic">k</Emphasis>-Positive Maps

Positive maps which are not completely positive are used in quantum information theory as witnesses for convex sets of states, in particular as entanglement witnesses and, more generally, as witnesses for states having Schmidt number not greater than k. Such maps and witnesses are related to k-positive maps, and their properties may be investigated by making use of the Jamiołkowski isomorphism. In this article we review the properties of this isomorphism, noting that there are actually two related mappings bearing that name. As a new result, we give a simplified proof for the correspondence between vectors having Schmidt number k and k-positive maps and thus for the Jamiołkowski criterion for complete positivity. Another consequence is a special case of a result by Choi, namely that k-positivity implies complete positivity, if k is the dimension of the smaller one of the Hilbert spaces on which the operators act.     

Decoherence and entanglement degradation of a qubit-qutrit system in non-inertial frames

We study the effect of decoherence on a qubit-qutrit system under the influence of global, local and multilocal decoherence in non-inertial frames. We show that the entanglement sudden death can be avoided in non-inertial frames in the presence of amplitude damping, depolarizing and phase damping channels at lower level of decoherence. However, degradation of entanglement is seen due to Unruh effect. It is seen that for lower values of decoherence, the depolarizing channel heavily degrades the entanglement as compared to the amplitude damping and phase damping channels. Entanglement sudden birth is also seen in case of depolarizing channel. However, for higher values of decoherence parameters, amplitude damping channel dominantly degrades the entanglement of the hybrid system. Entanglement sudden death is not seen for any value of acceleration of the accelerated observer “Rob” in case of phase damping channel. Further more, a symmetrical behaviour of negativity is seen for depolarizing channel.     

Quantum discord protection of a two-qutrit V-type atomic system from decoherence by partially collapsing measurements

In this paper, by exploiting the weak measurement and quantum measurement reversal procedure, we propose a scheme to show how one can protect the geometric quantum discord (GQD) of a two-qutrit V-type atomic system each of which interacts with a dissipative reservoir independently. We examine the scheme for the GQD of the initial two-qutrit Werner and Horodecki states for different classes of weak measurement strengths. It is found out that the presented protocol enables us to suppress decoherence due to the amplitude damping channel and preserve the quantum discord of the two-qutrit system successfully.     

Dynamics of relative entropy of coherence under Markovian channels

We study the relative entropy of coherence under the effect of certain one-qubit channels that are Markovian and noisy. The cohering power and decohering power of phase damping, amplitude damping, flip and depolarizing channels are analytically calculated. For phase damping channel, the decohering power on the \(x,\ y,\) and z bases is the same. The same phenomenon is observed for the flip and depolarizing channels. Further, we show that weak measurement and its reversal can be employed to suppress the decohering power of the amplitude damping channel.     

Displaced rotations of coherent states

We propose an approach with displaced states that can be used for rotations of coherent states. Our approach is based on representation of arbitrary one-mode pure state in free-travelling fields, in particular superposition of coherent states (SCSs), in terms of displaced number states with arbitrary amplitude of displacement. Optical scheme is developed for construction of displacing Hadamard gate for the coherent states. It is based on alternation of single photon additions and displacement operators (in general case, N-singe photon additions and N ? 1-displacements are required) with seed coherent state to generate both even and odd displaced squeezed SCSs regardless of number of used photon additions. The optical scheme is sensitive to the seed coherent state provided that other parameters of the scheme are invariable. Output states approximate with high fidelity either even squeezed SCS or odd SCS shifted relative each other by some value. It enables to construct local rotations for coherent states, in particular, Hadamard gate being mainframe element for quantum computation with coherent states. The effects deteriorating quality of output states are considered.     

Quantum coherence of two-qubit over quantum channels with memory

Using the axiomatic definition of the quantum coherence measure, such as the \(l_{1}\) norm and the relative entropy, we study the phenomena of two-qubit system quantum coherence through quantum channels where successive uses of the channels are memory. Different types of noisy channels with memory, such as amplitude damping, phase damping, and depolarizing channels effect on quantum coherence have been discussed in detail. The results show that quantum channels with memory can efficiently protect coherence from noisy channels. Particularly, as channels with perfect memory, quantum coherence is unaffected by the phase damping as well as depolarizing channels. Besides, we also investigate the cohering and decohering power of quantum channels with memory.     

Generation and protection of steady-state quantum correlations due to quantum channels with memory

We have proposed a scheme of the generation and preservation of two-qubit steady-state quantum correlations through quantum channels where successive uses of the channels are correlated. Different types of noisy channels with memory, such as amplitude damping, phase damping, and depolarizing channels, have been taken into account. Some analytical or numerical results are presented. The effect of channels with memory on dynamics of quantum correlations has been discussed in detail. The results show that steady-state entanglement between two initial qubits whose initial states are prepared in a specific family states without entanglement subject to amplitude damping channel with memory can be generated. The entanglement creation is related to the memory coefficient of channel \(\mu \). The stronger the memory coefficient of channel \( \mu \) is, the more the entanglement creation is, and the earlier the separable state becomes the entangled state. Besides, we compare the dynamics of entanglement with that of quantum discord when a two-qubit system is initially prepared in an entangled state. We show that entanglement dynamics suddenly disappears, while quantum discord dynamics displays only in the asymptotic limit. Furthermore, two-qubit quantum correlations can be preserved at a long time in the limit of \(\mu \rightarrow 1\).     

Vague综合评判方法

给出了一种基于Vague集的模糊综合评判方法,利用Vague集的运算得到全部候选方案的总体模糊评判值,通过两两比较建立可能度矩阵,得到候选方案集的排序向量,从而实现对候选方案的最优选择。通过实例表明,该方法切实可行,可以很好地帮助用户从多个候选方案中选择最适合的方案。     

Quantum information at the interface of light with atomic ensembles and micromechanical oscillators

This article reviews recent research towards a universal light-matter interface. Such an interface is an important prerequisite for long distance quantum communication, entanglement assisted sensing and measurement, as well as for scalable photonic quantum computation. We review the developments in light-matter interfaces based on room temperature atomic vapors interacting with propagating pulses via the Faraday effect. This interaction has long been used as a tool for quantum nondemolition detections of atomic spins via light. It was discovered recently that this type of light-matter interaction can actually be tuned to realize more general dynamics, enabling better performance of the light-matter interface as well as rendering tasks possible, which were before thought to be impractical. This includes the realization of improved entanglement assisted and backaction evading magnetometry approaching the Quantum Cramer-Rao limit, quantum memory for squeezed states of light and the dissipative generation of entanglement. A separate, but related, experiment on entanglement assisted cold atom clock showing the Heisenberg scaling of precision is described. We also review a possible interface between collective atomic spins with nano- or micromechanical oscillators, providing a link between atomic and solid state physics approaches towards quantum information processing.     

Air-damped microresonators with enhanced quality factor

It is known that the dissipative damping force due to the air film trapped between the bottom of surface micromachined resonators and the substrate on which they are fabricated decreases in magnitude as the separation between the two increases. The practical outcome of this is that microresonators located close to a substrate will have higher damping and a lower quality factor Q. In order to further investigate this effect and compare experimental findings with theory, a new test device that enables modulation of the damping interaction between a surface micromachined resonator and the substrate has been fabricated. The device consists of a surface micromachined polysilicon microresonator, which is self-elevated out of the plane of the substrate using a bimorph beam. A second, identical microresonator lying parallel to the plane of the substrate has also been fabricated. Both devices have been fabricated using the polysilicon multiuser microelectromechanical systems (MEMS) processes (polyMUMPs). The resonator-to-substrate separation of the elevated resonator is varied by changing the temperature of the bimorph beam, and the Q factors for different separations have been measured. Experimental results show that the elevated microresonators have Q values which are 65% higher than the in-plane microresonators. These experimental findings show good agreement with the theoretical model of damping used.