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.     

How quantum is a quantum ensemble?

In the Hilbert space operator formalism of quantum mechanics, a single quantum state, which is represented by a density operator, can be regarded as classical in the sense that it can always be diagonalized. However, a quantum ensemble, which is represented by a family of quantum states together with a probability distribution specifying the probability of the occurrence of each state, cannot be diagonalized simultaneously in generic cases, and possesses intrinsic quantum features as long as the involved quantum states are not commutative. The natural question arises as how to quantify its quantumness. By virtue of a canonical correspondence between quantum ensembles and classical-quantum bipartite states, we propose an intuitive entropic quantity which captures certain quantum features of quantum ensembles, and compare it with that defined as the gap between the Holevo quantity and the accessible information. Implications for quantum cryptography and relations to quantum channel capacities are indicated. Some illustrative examples are worked out.     

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.     

Comparative explorations of the revival and robustness for quantum dynamics under decoherence channels

In this paper, we demonstrate the revival and robustness of quantum dynamics under local decoherent evolutions through investigating the dynamical behaviors of quantum correlation. The results show that in depolarizing channel, quantum discord damps faster and revivals after a dark interval of time, while the others will revival immediately at the critical point. In addition, in hybrid channel the declining initial condition can speed up the attenuation of quantum discord within a limited time, while it can enable trace distance discord and Bures distance discord to damp more smoothly. In this sense, quantum discord is typically less robust against decoherence than the others. Interestingly, nonlocality shows different decay rates in the vicinity of critical point. Additionally, we lastly provide a physical interpretation concerning these phenomena.     

On Classification of Quantum Channels

Quantum mutual entropy and quantum capacity are rigorously defined by Ohya, and they are quite useful in the study of quantum communication processes. Mathematical models of optical communication processes are described by a quantum channel and optical states, and quantum capacity is one of the most important criteria to measure the efficiency of information transmission. In actual optical communication, a laser beam is used for a signal, and it is denoted mathematically by a coherent state. Further, optical communication using a squeezed state, which is expected to be more efficient than that using a coherent state is proposed. In this paper, we define several quantum channels, that is, a squeezed channel and a coherent channel and so on. We compare them by calculating quantum capacity.     

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.     

Superactivation of quantum channels is limited by the quantum relative entropy function

In this work we prove that the possibility of superactivation of quantum channel capacities is determined by the mathematical properties of the quantum relative entropy function. Before our work this fundamental and purely mathematical connection between the quantum relative entropy function and the superactivation effect was completely unrevealed. We demonstrate the results for the quantum capacity; however the proposed theorems and connections hold for all other channel capacities of quantum channels for which the superactivation is possible.     

Hadamard quantum broadcast channels

We consider three different communication tasks for quantum broadcast channels, and we determine the capacity region of a Hadamard broadcast channel for these various tasks. We define a Hadamard broadcast channel to be such that the channel from the sender to one of the receivers is entanglement-breaking and the channel from the sender to the other receiver is complementary to this one. As such, this channel is a quantum generalization of a degraded broadcast channel, which is well known in classical information theory. The first communication task we consider is classical communication to both receivers, the second is quantum communication to the stronger receiver and classical communication to other, and the third is entanglement-assisted classical communication to the stronger receiver and unassisted classical communication to the other. The structure of a Hadamard broadcast channel plays a critical role in our analysis: The channel to the weaker receiver can be simulated by performing a measurement channel on the stronger receiver’s system, followed by a preparation channel. As such, we can incorporate the classical output of the measurement channel as an auxiliary variable and solve all three of the above capacities for Hadamard broadcast channels, in this way avoiding known difficulties associated with quantum auxiliary variables.     

Multi-server blind quantum computation over collective-noise channels

Blind quantum computation (BQC) enables ordinary clients to securely outsource their computation task to costly quantum servers. Besides two essential properties, namely correctness and blindness, practical BQC protocols also should make clients as classical as possible and tolerate faults from nonideal quantum channel. In this paper, using logical Bell states as quantum resource, we propose multi-server BQC protocols over collective-dephasing noise channel and collective-rotation noise channel, respectively. The proposed protocols permit completely or almost classical client, meet the correctness and blindness requirements of BQC protocol, and are typically practical BQC protocols.     

Simulation of quantum key distribution in a secure star topology optimization in quantum channel

The field of quantum cryptography is mostly theoretical therefore in this paper we represent its implementation by means of virtual scenarios. The central issue in cryptography is the secure transmission of the key between nodes. Thus, in this paper we establish a secure channel using Quantum Key Distribution (QKD) for the transfer of the key material between the nodes and help to identify an eavesdropper in the channel. A graphical representation of the quantum channel traffic at the ideal state and also during network disruption has been established. Due to the complex nature of quantum networks and high cost of establishment, a physical implementation of the same is not feasible. Hence a simulation has been implemented via the use of NS-3 (Network Simulator Version 3) which has QKDNetSim module built into it. Finally, our simulation indicates the presence of an intruder by virtue of various network implementations within the quantum channel.     

Bidirectional controlled quantum teleportation and secure direct communication using five-qubit entangled state

A scheme is presented to implement bidirectional controlled quantum teleportation (QT) by using a five-qubit entangled state as a quantum channel, where Alice may transmit an arbitrary single qubit state called qubit A to Bob and at the same time, Bob may also transmit an arbitrary single qubit state called qubit B to Alice via the control of the supervisor Charlie. Based on our channel, we explicitly show how the bidirectional controlled QT protocol works. By using this bidirectional controlled teleportation, espcially, a bidirectional controlled quantum secure direct communication (QSDC) protocol, i.e., the so-called controlled quantum dialogue, is further investigated. Under the situation of insuring the security of the quantum channel, Alice (Bob) encodes a secret message directly on a sequence of qubit states and transmits them to Bob (Alice) supervised by Charlie. Especially, the qubits carrying the secret message do not need to be transmitted in quantum channel. At last, we show this QSDC scheme may be determinate and secure.     

Deterministic controlled bidirectional remote state preparation via a six-qubit entangled state

In this paper, we presented a controlled bidirectional remote state preparation scheme which used the six-qubit entangled state as quantum channel. In our scheme, Alice and Bob can prepare simultaneously an arbitrary single-qubit state in each other’s place with the control of the supervisor Charlie. The success probability for our scheme reaches unit. Furthermore, we analyze the expression of quantum channel for controlled bidirectional remote state preparation. Finally, we discuss the security of our scheme, the detailed security analysis shows that the supervisor Charlie’s control can greatly improve the security of our scheme.

     

How to re-use a one-time pad safely and almost optimally even if P = NP

Assuming an insecure quantum channel, a quantum computer, and an authenticated classical channel, we propose an unconditionally secure scheme for encrypting classical messages under a shared key, where attempts to eavesdrop the ciphertext can be detected. If no eavesdropping is detected, we can securely re-use the entire key for encrypting new messages. If eavesdropping is detected, we must discard a number of key bits corresponding to the length of the message, but can re-use almost all of the rest. We show this is essentially optimal. Thus, provided the adversary does not interfere (too much) with the quantum channel, we can securely send an arbitrary number of message bits, independently of the length of the initial key. Moreover, the key-recycling mechanism only requires one-bit feedback. While ordinary quantum key distribution with a classical one time pad could be used instead to obtain a similar functionality, this would need more rounds of interaction and more communication.     

Quantum key agreement with EPR pairs and single-particle measurements

In this paper, we present a QKA protocol with the block transmission of EPR pairs. There are several advantages in this protocol. First, this protocol can guarantee both the fairness and security of the shared key. Second, this protocol has a high qubit efficiency since there is no need to consume any quantum state except the ones used for establishing the shared key and detecting eavesdropping. In addition, this protocol uses EPR pairs as the quantum information carriers and further utilizes single-particle measurements as the main operations. Therefore, it is more feasible than the protocols that need to perform Bell measurements. Especially, we also introduce a method for sharing EPR pairs between two participants over collective-dephasing channel and collective-rotation channel, respectively. This method is meaningful since sharing EPR pairs between two participants is an important work in many quantum cryptographic protocols, especially in the protocols over non-ideal channels. By utilizing this method, the QKA protocols, which are based on EPR pairs, can be immune to these kinds of collective noise.     

Dynamics of quantum entanglement in quantum channels

Based on the von Neumann entropy, we give a computational formalism of the quantum entanglement dynamics in quantum channels, which can be applied to a general finite systems coupled with their environments in quantum channels. The quantum entanglement is invariant in the decoupled local unitary quantum channel, but it is variant in the non-local coupled unitary quantum channel. The numerical investigation for two examples, two-qubit and two-qutrit models, indicates that the quantum entanglement evolution in the quantum non-local coupling channel oscillates with the coupling strength and time, and depends on the quantum entanglement of the initial state. It implies that quantum information loses or gains when the state of systems evolves in the quantum non-local coupling channel.     

“乒乓”量子通信协议的不安全性

"乒乓"量子通信协议的量子直接通信已引起了许多学者们的关注,然而,由于双向量子信道的对称性,该协议存在安全性缺陷.基于量子纠错码(QECC)编码原理和构造技术提出了一种新的攻击策略.基于该攻击策略分别对纠缠态和非正交态的"乒乓"协议进行了论证,并从信息论角度对Eve可以获得的信息量和可能被检测到的概率进行了分析.分析结果表明,以前提出的"乒乓"量子通信协议都是不安全的,即攻击者可以在不被检测到的情况下获得传输的信息.     

Authenticated semiquantum dialogue with secure delegated quantum computation over a collective noise channel

Semiquantum communication permits a communication party with only limited quantum ability (i.e., “classical” ability) to communicate securely with a powerful quantum counterpart and will obtain a significant advantage in practice when the completely quantum world has not been built up. At present, various semiquantum schemes for key distribution, secret sharing and secure communication have been proposed. In a quantum dialogue (QD) scenario, two communicants mutually transmit their respective secret messages and may have equal power (such as two classical parties). Based on delegated quantum computation model, this work extends the original semiquantum model to the authenticated semiquantum dialogue (ASQD) protocols, where two “classical” participants can mutually transmit secret messages without any information leakage and quantum operations are securely delegated to a quantum server. To make the proposed ASQD protocols more practical, we assume that the quantum channel is a collective noise channel and the quantum server is untrusted. The security analysis shows that the proposed protocols are robust even when the delegated quantum server is a powerful adversary.     

Quantum privacy and quantum wiretap channels

Following Schumacher and Westmoreland, we address the problem of the capacity of a quantum wiretap channel. We first argue that, in the definition of the so-called quantum privacy, Holevo quantities should be used instead of classical mutual informations. The argument actually shows that the security condition in the definition of a code should limit the wiretappers Holevo quantity. Then we show that this modified quantum privacy is the optimum achievable rate of secure transmission.Translated from Problemy Peredachi Informatsii, No. 4, 2004, pp. 26–47. Original Russian Text Copyright © 2004 by Cai, Winter, Yeung.