Second-order coding rates for pure-loss bosonic channels

A pure-loss bosonic channel is a simple model for communication over free-space or fiber-optic links. More generally, phase-insensitive bosonic channels model other kinds of noise, such as thermalizing or amplifying processes. Recent work has established the classical capacity of all of these channels, and furthermore, it is now known that a strong converse theorem holds for the classical capacity of these channels under a particular photon-number constraint. The goal of the present paper is to initiate the study of second-order coding rates for these channels, by beginning with the simplest one, the pure-loss bosonic channel. In a second-order analysis of communication, one fixes the tolerable error probability and seeks to understand the back-off from capacity for a sufficiently large yet finite number of channel uses. We find a lower bound on the maximum achievable code size for the pure-loss bosonic channel, in terms of the known expression for its capacity and a quantity called channel dispersion. We accomplish this by proving a general “one-shot” coding theorem for channels with classical inputs and pure-state quantum outputs which reside in a separable Hilbert space. The theorem leads to an optimal second-order characterization when the channel output is finite-dimensional, and it remains an open question to determine whether the characterization is optimal for the pure-loss bosonic channel.     

The quantum dynamic capacity formula of a quantum channel

The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an ??ab initio?? approach, using only the most basic tools in the quantum information theorist??s toolkit: the Alicki-Fannes?? inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon theory literature. We also demonstrate that the ??quantum dynamic capacity formula?? characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula reduces the computation of the trade-off surface to a tractable, textbook problem in Pareto trade-off analysis, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.     

Schemes for remotely preparing an arbitrary four-qubit \chi -state

Two schemes via different entangled resources as the quantum channel are proposed to realize remote preparation of an arbitrary four-particle \(\chi \) -state with high success probabilities. To design these protocols, some useful and general measurement bases are constructed, which have no restrictions on the coefficients of the prepared states. It is shown that through a four-particle projective measurement and two-step three-particle projective measurement under the novel sets of mutually orthogonal basis vectors, the original state can be prepared with the probability 50 and 100 %, respectively. And for the first scheme, the special cases of the prepared state that the success probability reaches up to 100 % are discussed by the permutation group. Furthermore, the present schemes are extended to the non-maximally entangled quantum channel, and the classical communication costs are calculated.     

Perfect Parallel Repetition Theorem for Quantum Xor Proof Systems

We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier’s verdict is a function of the XOR of the two bits received. We show that, when the provers are allowed to coordinate their behavior using a shared entangled quantum state, a perfect parallel repetition theorem holds in the following sense. The prover’s optimal success probability for simultaneously playing a collection of XOR proof systems is exactly the product of the individual optimal success probabilities. This property is remarkable in view of the fact that, in the classical case (where the provers can only utilize classical information), it does not hold. The theorem is proved by analyzing parities of XOR proof systems using semidefinite programming techniques, which we then relate to parallel repetitions of XOR games via Fourier analysis.      

On the second-order asymptotics for entanglement-assisted communication

The entanglement-assisted classical capacity of a quantum channel is known to provide the formal quantum generalization of Shannon’s classical channel capacity theorem, in the sense that it admits a single-letter characterization in terms of the quantum mutual information and does not increase in the presence of a noiseless quantum feedback channel from receiver to sender. In this work, we investigate second-order asymptotics of the entanglement-assisted classical communication task. That is, we consider how quickly the rates of entanglement-assisted codes converge to the entanglement-assisted classical capacity of a channel as a function of the number of channel uses and the error tolerance. We define a quantum generalization of the mutual information variance of a channel in the entanglement-assisted setting. For covariant channels, we show that this quantity is equal to the channel dispersion and thus completely characterize the convergence toward the entanglement-assisted classical capacity when the number of channel uses increases. Our results also apply to entanglement-assisted quantum communication, due to the equivalence between entanglement-assisted classical and quantum communication established by the teleportation and super-dense coding protocols.     

Probabilistic teleportation via multi-parameter measurements and partially entangled states

In this paper, a novel scheme for probabilistic teleportation is presented with multi-parameter measurements via a non-maximally entangled state. This is in contrast to the fact that the measurement kinds for quantum teleportation are usually particular in most previous schemes. The detail implementation producers for our proposal are given by using of appropriate local unitary operations. Moreover, the total success probability and classical information of this proposal are calculated. It is demonstrated that the success probability and classical cost would be changed with the multi-measurement parameters and the entanglement factor of quantum channel. Our scheme could enlarge the research range of probabilistic teleportation.     

Sequential, successive, and simultaneous decoders for entanglement-assisted classical communication

Bennett et al. showed that allowing shared entanglement between a sender and receiver before communication begins dramatically simplifies the theory of quantum channels, and these results suggest that it would be worthwhile to study other scenarios for entanglement-assisted classical communication. In this vein, the present paper makes several contributions to the theory of entanglement-assisted classical communication. First, we rephrase the Giovannetti–Lloyd–Maccone sequential decoding argument as a more general “packing lemma” and show that it gives an alternate way of achieving the entanglement-assisted classical capacity. Next, we show that a similar sequential decoder can achieve the Hsieh–Devetak–Winter region for entanglement-assisted classical communication over a multiple access channel. Third, we prove the existence of a quantum simultaneous decoder for entanglement-assisted classical communication over a multiple access channel with two senders. This result implies a solution of the quantum simultaneous decoding conjecture for unassisted classical communication over quantum multiple access channels with two senders, but the three-sender case still remains open (Sen recently and independently solved this unassisted two-sender case with a different technique). We then leverage this result to recover the known regions for unassisted and assisted quantum communication over a quantum multiple access channel, though our proof exploits a coherent quantum simultaneous decoder. Finally, we determine an achievable rate region for communication over an entanglement-assisted bosonic multiple access channel and compare it with the Yen-Shapiro outer bound for unassisted communication over the same channel.     

以最大slice态为信道的受控量子远程控制

利用三量子最大slice态作为量子信道,提出了单量子酉算子的受控远程执行的两个协议.首先,利用双向量子隐形传态(BQST),给出了一个任意单量子酉算子的受控隐形传输方案.结果 表明,通过非最大纠缠信道,发送者能够在遥远的接受者的量子系统上远程地执行一个任意单量子酉算子.如果发送者和控制者对各自量子执行恰当的投影测量,那...     

多参数测量的分层量子态分享

融合了分层量子态分享及多参数测量思想，提出了一个研究不同最大纠缠量子信道的分层量子态分享可能性的新框架，并以4-粒子团簇态作为量子信道为例说明了该框架是可行的，指出该例是现有协议的推广。考虑到最大纠缠态的保持对现有技术的挑战，将上述框架推广到非最大纠缠信道的情形，且以4-粒子非最大纠缠团簇态为例，验证了这个推广框架用于研究不同非最大纠缠信道的分层量子态分享是可行的。进一步，分析了验证实例的成功概率（经典耗费）与测量参数或量子纠缠参数间的依赖关系，说明了可以根据量子信道的参数来调整测量基的参数，达到调节成功概率或经典耗费，满足真实世界中不同需求之目的。     

基于多参数测量的双向受控隐形传态

融合了双向隐形传态、受控隐形传态、概率隐形传态及多参数测量思想,提出了一个新的双向受控概率隐形传态协议。在该协议中,以五粒子非最大纠缠团簇态为信道,发送者采用多参数通用测量,接收者引入辅助粒子,并在控制者的允许下,利用测量信息施行适当酉变换,就能以一定概率同时交换他们的量子态。分析了成功概率（经典耗费）与量子纠缠参数及测量参数间的依赖关系,说明了该协议可以根据量子信道的参数来调整多参数测量的参数,达到调节成功概率或经典耗费,满足真实世界中多种不同需求的目的。此外,该协议是经典双向受控隐形传态的推广。     

Secrecy results for compound wiretap channels

We derive a lower bound on the secrecy capacity of a compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. [1], thus establishing a full coding theorem in this case. We achieve this with a stronger secrecy criterion and the maximum error probability criterion, and with a decoder that is robust against the effect of randomization in the encoding. This relieves us from the need of decoding the randomization parameter, which is in general impossible within this model. Moreover, we prove a lower bound on the secrecy capacity of a compound wiretap channel without channel state information and derive a multiletter expression for the capacity in this communication scenario.     

Efficient joint remote preparation of an arbitrary two-qubit state via cluster and cluster-type states

In this paper, we present a possible improvement of the successful probability of joint remote state preparation via cluster states following some ideals from probabilistic joint remote state preparation (Wang et al. in Opt Commun, 284:5835, 2011). The success probability can be improved from $1/4$ to 1 via the same quantum entangled channel by adding some classical information and performing some unitary operations. Moreover, we also discussed the scheme for joint remote preparation via cluster-type states. Compared with other schemes, our schemes have the advantage of having high successful probability for joint preparation of an arbitrary two-qubit state via cluster states and cluster-type states.     

任意二粒子纠缠态的受控量子通信

为了解决任意二量子通信问题,首先给出了五粒子和七粒子纠缠态的构造方法,并提供了它们的量子线路图。其次,以该五粒子纠缠态为量子信道,提出一个任意二粒子未知量子态的受控隐形传态协议。该协议在监察者Charlie的控制下,Alice进行四粒子投影测量和经典通信,Bob采用简单酉变换就能以100%的概率成功重构一个任意二粒子纠缠态。最后,利用七粒子纠缠态为量子信道,提出了任意二粒子纠缠态的联合受控远程制备方案。在此方案中,发送者Alice用自己掌握被制备态的部分信息构造测量基,发送者Bob采用前馈测量策略,接收者Diana在监控者Charlie的帮助下,通过简单幺正变换就能确定性地恢复原始态。     

On classical capacities of infinite-dimensional quantum channels

A coding theorem for entanglement-assisted communication via an infinite-dimensional quantum channel with linear constraints is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and χ-capacity of constrained channels are obtained, and conditions for their coincidence are given. Sufficient conditions for continuity of the entanglement-assisted classical capacity as a function of a channel are obtained. Some applications of the obtained results to analysis of Gaussian channels are considered. A general (continuous) version of the fundamental relation between coherent information and the measure of privacy of classical information transmission via an infinite-dimensional quantum channel is proved.     

Local cloning of multipartite entangled states

No cloning theorem is a very fundamental issue in quantum mechanics. But the issue is much more involved if we consider quantum state shared among two or more than two parties and allow only local operation and classical communication. In the context of the fact that no known bipartite entangled state can be cloned by local operation and classical communication (LOCC) without assistance of extra entangled state, the cloning of unknown orthogonal entangled state becomes meaningful when there is some supply of free entanglement. With restriction on supply of free entanglement, various cases have been studied. In this paper, we try to give an overview of the subject and results that have been obtained across the literature along with a new result on probabilistic LOCC cloning of four Bell states.     

Multiparty-controlled joint remote state preparation

In this work, we present a novel and efficient information-processing way, multiparty-controlled joint remote state preparation (MCJRSP), to transmit quantum information from many senders to one distant receiver via the control of many agents in a network. We firstly put forward a scheme regarding MCJRSP for an arbitrary single-particle state via Greenberg–Horne–Zeilinger entangled states, and then extend to generalize an arbitrary two-particle state scenario. Notably, different from conventional joint remote state preparation, the desired states cannot be recovered but all of agents collaborate together. Besides, both successful probability and classical information cost are worked out, the relations between success probability and the employed entanglement are revealed, the case of many-particle states is generalized briefly, and the experimental feasibility of our schemes is analysed via an all-optical framework at last. And we argue that our proposal might be of importance to long-distance communication in prospective quantum networks.     

Joint remote preparation of four-qubit cluster-type states with multiparty

For N+1-sender independently share the classical knowledge of a quantum state, a new scheme for joint remote preparation of four-particle cluster-type states using only two partially two-particle entangled states as quantum channel is presented. In our scheme, each of the senders is just required to perform a bipartite projective measurement, and the receiver adopts some appropriate unitary operation to obtain the original state with certain probability. We also discuss four type information-splitting methods which can make the receiver obtain the unknown state. The classical communication cost is also calculated.     

Quantum coding in non-inertial frames

The quantum and classical correlations are quantified by means of the coherent and mutual information, respectively, where we use the single-mode approximation. It is shown that the users can communicate in an optimal way for small values of accelerations. The capacity of accelerated channel is investigated for different classes of initial states. It is shown that the capacities of the traveling channels depend on the frame in which the accelerated channels are observed in and the initial shared state between the partners. In some frames, the capacities decay as the accelerations of both qubit increase. The decay rate is larger if the partners initially share a maximum entangled state. The possibility of using the accelerated quantum channels to perform quantum coding protocol is discussed. The amount of decoded information is quantified for different cases, where it decays as the partner’s accelerations increase to reach its minimum bound. This minimum bound depends on the initial shared states, and it is large for maximum entangled state.     

Scheme for entanglement concentration of unknown partially entangled three-atom W states in cavity QED

We propose a practical scheme to concentrate entanglement in a pair of unknown partially entangled three-atom W states in cavity quantum electrodynamics (QED). In the scheme, Alice, Bob, and Charlie at three distant parties can obtain one maximally entangled three-atom W state with the certain success probability from two identical partially entangled three-atom W states by local operations and classical communication. We propose the detailed process of entanglement concentration and analyze the experimental feasibility of the scheme.     

Efficient entanglement purification via quantum communication bus

A scheme is proposed to implement entanglement purification for two remote less entangled photons using robust continuous variable coherent modes, called as quantum communication bus (qubus), rather than consuming expensive ancilla single-photon sources. The qubus beams in the coherent states provide for the natural communication in the purification protocol, instead of the classical communication between the distant photons. Weak cross-Kerr nonlinearities, qubus beams and quantum non-demolition (QND) photon-number-resolving measurement are utilized for implementing deterministic entanglement purification. The core element to realize the QND measurement is Kerr nonlinearity. The necessary QND measurement in the present scheme is not an extra, very difficult, addition to the present protocol, but is taken care of by a phase measurement. The entanglement purification protocol (EPP) can obtain a maximally entangled pair with only one step, instead of improving the fidelity of less entangled pairs by performing continuous indefinite iterative purification procedure. The total success probability and fidelity of the present purification scheme can approach unit in principle. In addition, we investigate photon loss of the qubus beams during the transmission and decoherence effects in the entanglement purification caused by such a photon loss.