Capacities of Quantum Channels and How to Find Them
P. W. Shor
本文综述了量子信道的信息传输能力，并提出了一种利用线性规划计算量子信道信息传输能力的方法。
We survey what is known about the information transmitting capacities of quantum channels, and give a proposal for how to calculate some of these capacities using linear programming.
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Entanglement-assisted capacities of time-correlated amplitude-damping channel
我们计算了一个时间相关的振幅阻尼信道的信息容量，假设发送者和接收者共享先验纠缠。我们的分析结果表明，零容量的噪声信道可以传输信息，如果它有有限的记忆。容量随着存储器的增加而增加，达到完美存储器通道的最大值。
Broadband channel capacities
我们研究了在不同噪声源存在下玻色宽带信道的通信能力。特别是，我们分析了存在白噪声和热浴的有损通道。在这种情况下，我们提供了一个数值解的纠缠辅助容量和上限和下限的经典和量子容量。
Classical information capacities of some single qubit quantum noisy channels
利用Holevo-Schumacher-Westmoreland（HSW）定理，通过直接求解量子噪声信道的态本征值，或借助Bloch球表象或Stokes参数化表象，研究了一些著名的量子噪声信道的经典信息容量.
Channel Capacities of an Exactly Solvable Spin-Star System
我们计算了一个精确可解的自旋星系统的纠缠辅助和无辅助通道容量，该系统模拟了量子退相通道。这种非马尔可夫模型的能力表现出强烈的依赖于浴自旋与系统的耦合强度，浴温度，浴自旋的数量。对于相等的耦合和浴频率，信道变得周期性无噪声。
Entanglement required in achieving entanglement-assisted channel capacities
量子通信信道两端之间共享的纠缠已被证明是增加这些信道的量子和经典容量的有用资源。假设每个通道使用无限量的共享纠缠，推导出纠缠辅助容量。在本文中，边界上的最小量的纠缠所需的每一个使用的通道，以渐近地实现的能力。这是通过引入一类纠缠辅助量子码来实现的。量子比特信道类的代码示出，以实现量子纠缠辅助的信道容量时，每个信道的共享纠缠量，E = 1 - Q_E，提供。它还表明，对于非常嘈杂的信道，作为容量变得很小，所需的纠缠量收敛的经典和量子容量。
We propose a method to detect lower bounds to quantum capacities of a noisy quantum communication channel by means of few measurements. The method is easily implementable and does not require any knowledge about the channel. We test its efficiency by studying its performance for most well known single qubit noisy channels and for the generalised Pauli channel in arbitrary finite dimension.
Capacities of Quantum Erasure Channels
经典擦除通道的量子模拟提供了一个简单的例子，可以精确地计算出在有和没有双向经典侧通道的帮助下，完整量子态忠实传输的渐近容量。我们推导出量子擦除信道和相关信道的量子和经典容量，并将它们与去极化信道进行比较，其中仅知道容量的上限和下限。
Extreme Capacities in Generalized Direct Sum Channels
本文构建了广义直和（GDS）信道框架，通过在Kraus算子中引入直和结构来研究量子信道容量，揭示了量子容量趋近零时无界超加性，以及私有与经典容量任意大导致的容量差距。
Classical capacity of unital qubit channels is well known, whereas that of nonunital qubit channels is not. We find lower and upper bounds on classical capacity of nonunital qubit channels by using a recently developed decomposition technique relating nonunital and unital positive qubit maps.
Bounds on classical information capacities for a class of quantum memory channels
通过噪声量子信道的信息传输的最大速率主要是针对无记忆信道开发的，其中每个传输状态上的噪声被视为独立的。许多真实世界的通信信道经历噪声，其通过在单独的信道使用之间相关的误差来更好地建模。本文导出了一类量子存储通道的经典信息容量的上界。这类通道由不可分解的量子存储通道组成，是经典不可分解的有限态通道的推广。
Capacities of the covariant Pauli channel
本研究针对SO(2)协变的两参数Pauli信道，精确求解了经典与纠缠辅助容量，解析确定了量子容量为零区域，并利用标志扩展给出量子与私有容量的上下界，推进了完整Pauli信道容量的确定。
Channel Capacities versus Entanglement Measures in Multiparty Quantum States
对于两个子系统的量子态，纠缠度量与通信任务的能力有关--高纠缠态提供了更高的传输经典信息和量子信息的能力。然而，我们表明，这是没有更多的情况下，在一般情况下：量子容量的多访问信道，在量子网络中的通信的动机，没有任何关系，真正的多方纠缠措施。随着揭示多接入信道容量的结构丰富性，这给了我们一个工具来分类多方量子态从它在量子网络中的有用性的角度来看，这是不能可视化的已知多方纠缠措施。
Continuity of quantum channel capacities
我们证明了量子信道的大容量阵列是连续的。也就是说，相对于菱形规范接近的两个信道具有相应地类似的通信能力。我们首先表明，经典容量，量子容量，和私人经典容量是连续的，与参数的变化，除了由一个简单的函数的范围内，和通道的输出尺寸。我们的主要工具是一个上界的输出熵的变化的许多副本附近的两个通道给定相同的初始状态，该界是线性的副本的数量。我们的第二个证明是关于自由向后或双向公共经典通信存在下的量子容量。通过考虑相似信道之间的相互模拟，证明了这些容量在非零容量信道集合的内部是连续的。
We review in a unified way a recently proposed method to detect properties of unknown quantum channels and lower bounds to quantum capacities, without resorting to full quantum process tomography. The method is based on the preparation of a fixed bipartite entangled state at the channel input or, equivalently, an ensemble of an overcomplete set of single-system states, along with few local measurements at the channel output.
Nonadditivity effects in classical capacities of quantum multiple-access channels
我们研究了量子多址信道的经典容量，揭示了类Holevo容量的可加性的破坏。这种效应纯粹是量子的，因为正如有人指出的那样，任何经典的多路访问信道都有它们的区域加性。在这里呈现的量子版本中观察到的非可加性似乎是这种类型的第一个效应，没有涉及额外的资源，如侧经典或量子信息（或纠缠）。所涉及的量子信道的简单性类似于具有两个发射器和两个接收器的经典信道的情况下的蝴蝶效应。
We introduce potential capacities of quantum channels in an operational way and provide upper bounds for these quantities, which quantify the ultimate limit of usefulness of a channel for a given task in the best possible context. Unfortunately, except for a few isolated cases, potential capacities seem to be as hard to compute as their "plain" analogues. We thus study upper bounds on some potential capacities: For the classical capacity, we give an upper bound in terms of the entanglement of formation. To establish a bound for the quantum and private capacity, we first "lift" the channel to a…
We test a general method to detect lower bounds of the quantum channel capacity for two-qubit correlated channels. We consider in particular correlated dephasing, depolarising and amplitude damping channels. We show that the method is easily implementable, it does not require a priori knowledge about the channels, and it is very efficient, since it does not rely on full quantum process tomography.
A note on quantum entropy inequalities and channel capacities
研究了量子熵不等式。用几种方法得到了一些量子熵不等式。对于纠缠破坏信道，我们证明了纠缠辅助的经典容量是由$\log d$定义的上界。得到了纠缠辅助容量和单次无辅助容量之间的关系。这种关系表明，纠缠辅助信道容量的上限由$\log d$和一次性无辅助经典容量的总和。
General channel capacities from quantum channel-state duality
本研究基于量子信道-态对偶，证明了将Choi态作为信息源时的量子信道容量基本定理，丰富了信道容量集合，并为理解超加性现象与发现新量子纠错码提供了新机遇。
Reciprocal pairs of quantum channels are defined as completely positive transformations which admit a rigid, distance-preserving, yet not completely-positive transformation that allows to reproduce the outcome of one from the corresponding outcome of the other. From a classical perspective these transmission lines should exhibit the same communication efficiency. This is no longer the case in the quantum setting: explicit asymmetric behaviours are reported studying the classical communication capacities of reciprocal pairs of depolarizing and Weyl-covariant channels.
Classical and quantum capacities of a fully correlated amplitude damping channel
研究了作用于两个量子比特的完全相关振幅阻尼信道上的信息传输。我们推导出单次经典信道容量，并表明纠缠需要实现信道的最佳性能。我们讨论的降解性能的信道和评估的量子容量的任何值的噪声参数。最后计算了纠缠辅助的经典信道容量。
Energy-constrained two-way capacities of the pure-loss channel
该研究确定了平均输入光子数约束下纯损耗信道的双向量子与秘密密钥容量，给出了统一表达式，补充了纯损耗信道的容量公式，完善了玻色子量子通信的相关理论。
Capacities of lossy bosonic memory channels
我们介绍了一个有耗玻色记忆信道的一般模型，并计算了经典和量子容量，证明了相干态编码是最佳的。使用一组适当的集体场变量允许解开的内存，显示的n倍级联的内存通道是酉等价于n个单模有损玻色子通道的直接产品。
Quantum and private capacities of low-noise channels
本文解决了低噪声量子信道（如去极化信道）容量这一20余年开放问题，证明其量子容量与私密容量在首阶近似下均等于单字母相干信息，并表明超可加性、退化码和屏蔽在该区域收益可忽略。
Quantum Capacities of Bosonic Channels
研究了玻色量子信道传输量子信息的能力。通过证明每个信道都可以渐近模拟高斯信道，并由信道的二阶矩来表征信道的可测矩，从而确定可调速率。通过证明高斯编码是最优的，我们计算了一类高斯信道的量子容量，包括描述光子损耗光纤的信道。一路上，我们提供了一个完整的表征可降解的高斯信道和那些所产生的隐形传态协议。
We extend a recent method to detect lower bounds to the quantum capacity of quantum communication channels by considering realistic scenarios with general input probe states and arbitrary detection procedures at the output. Realistic certification relies on a new bound for the coherent information of a quantum channel that can be applied with arbitrary bipartite mixed input states and generalized output measurements.
We present upper bounds on the quantum and private capacity of single-mode, phase-insentitive Bosonic Gaussian Channels based on degradable extensions. Our findings are state-of-the-art in the following parameter regions: low temperature and high transmissivity for the thermal attenuator, low temperature for additive Gaussian noise, high temperature and intermediate amplification for the thermal amplifier.
Evaluating capacities of Bosonic Gaussian channels
我们将展示如何计算或至少估计各种容量相关的数量玻色子高斯信道。其中包括相干信息，纠缠辅助经典容量，一次性经典容量，和一个新的数量涉及转置操作，被证明是量子容量的一般上限，即使允许有限的错误。所有的界限明确评估的情况下，一个模式的信道与衰减/放大和经典噪声。
The capacity of noisy quantum channels characterizes the highest rate at which information can be reliably transmitted and it is therefore of practical as well as fundamental importance. Capacities of classical channels are computed using alternating optimization schemes, called Blahut-Arimoto algorithms. In this work, we generalize classical Blahut-Arimoto algorithms to the quantum setting. In particular, we give efficient iterative schemes to compute the capacity of channels with classical input and quantum output, the quantum capacity of less noisy channels, the thermodynamic capacity of qu…
Information capacity analysis of fully correlated multi-level amplitude damping channels
本文研究连续使用存在关联的三能级振幅阻尼信道，通过分析可退化性给出单次经典容量上界，并计算了普通及纠缠辅助场景下的量子与经典容量。
We present an effcient experimental procedure that certifies non vanishing quantum capacities for qubit noisy channels. Our method is based on the use of a fixed bipartite entangled state, where the system qubit is sent to the channel input. A particular set of local measurements is performed at the channel output and the ancilla qubit mode, obtaining lower bounds to the quantum capacities for any unknown channel with no need of a quantum process tomography. The entangled qubits have a Bell state configuration and are encoded in photon polarization. The lower bounds are found by estimating the…
Quantum Capacities of Channels with small Environment
我们研究了噪声量子信道的量子容量，它可以通过将系统耦合到一个有效的小环境来表示。容量公式推导出所有的情况下，系统和环境都是二维的-包括所有的极端量子位通道。类似地，对于作用于高维系统的通道，我们表明，如果通道产生于与量子位环境的足够小的耦合，则可以确定容量。扩展的情况下，具有较大的环境的通道，它示出了无约束环境的容量上的界限，可以从分解成小环境的通道。
Capacities of lossy bosonic channel with correlated noise
我们评估的相关噪声的有损玻色子信道的信息容量。该模型推广了最近在[Phys.Rev.A77，052324（2008）]中讨论的模型，其中记忆效应来自与相关环境的相互作用。环境的相关性量化的多模压缩参数，消失的记忆极限。我们表明，一个全球性的编码/解码方案，其中涉及不同的信道使用之间的输入纠缠态，总是优选的相对于一个本地的存在的内存。此外，在一定的参数范围内，我们给出了信道经典容量的解析表达式，表明全局编码/解码方案可以实现它，所有结果都可以应用于广泛的玻色高斯信道。
Methods for Estimating Capacities and Rates of Gaussian Quantum Channels
提出了一种估计一般高斯信道容量的优化方法。具体地，在有损玻色子信道的所有可能的高斯编码上追求经典容量作为Holevo信息的最大值的评估，但是扩展到其他容量和其他高斯信道似乎是可行的。无记忆和记忆通道的解决方案。它是第一次处理单用途（单模）信道的容量依赖于信道的参数进行了分析，提供了一个完整的分类可能的情况。然后，它是处理多用途（多模）信道的容量依赖于（多模）环境状态分析时，总的环境能量和环境纯度都是固定的。这允许在不同环境之间进行公平的比较，从而理解记忆的作用（模式间相关性）和容量的超加性等现象。所开发的方法也被用于推导传输速率与外差和零差测量在信道输出。经典的容量和传输速率在一个独特的框架内，速率可以被视为对数近似的能力。
Nonadditivity of quantum and classical capacities for entanglement breaking multiple-access channels and butterfly network
我们分析了量子网络的基元是纠缠打破。我们证明了量子多址信道和量子蝴蝶网络的量子和经典容量区域的超可加性。由于这种效应在高噪声下特别明显，因此他们认为量子信息效应在偶尔具有高噪声率的网络中可能特别有用。据我们所知，目前的影响提供了第一个定性的边界之间的超可加性的二部和多部系统。
Capacities of quantum channels and decoherence times both quantify the extent to which quantum information can withstand degradation by interactions with its environment. However, calculating capacities directly is known to be intractable in general. Much recent work has focused on upper bounding certain capacities in terms of more tractable quantities such as specific norms from operator theory. In the meantime, there has also been substantial recent progress on estimating decoherence times with techniques from analysis and geometry, even though many hard questions remain open. In this articl…
Quantum communication channels and quantum memories are the fundamental building blocks of large-scale quantum communication networks. Estimating their capacity to transmit and store quantum information is crucial in order to assess the performance of quantum communication systems, and to detect useful communication paths among the nodes of future quantum networks. However, the estimation of quantum capacities is a challenging task for continuous variable systems, such as the radiation field, for which a complete characterization via quantum tomography is practically unfeasible. Here we introd…
On Quantum Fidelities and Channel Capacities
我们证明了两种不同概念的量子信道容量的等价性：一种是使用纠缠保真度作为传输成功的标准，另一种是使用输入希尔伯特空间的子空间中纯态的最小保真度作为其标准。作为推论，任何熵率小于容量的源都可以以高纠缠保真度传输。我们还表明，一个限制类的编码是足以传输任何量子源，可以在一个给定的信道上传输。这使我们能够简化信道容量的已知上限。它还使我们能够表明，从编码器到解码器的辅助经典信道的可用性不会增加量子容量。
Strong Converses for Quantum Channel Capacities from Blowing-Up Lemmata
本文通过全量子放大引理和低次多项式近似，证明了任意有限维无记忆信道在速率超过量子容量时纠缠传输保真度指数衰减的强逆界。
Simultaneous classical-quantum capacities of quantum multiple access channels
描述了经典信息和量子信息在任意量子信道上从两个空间分离的接收端同时传输到单个接收端的速率。两个主要结果得到了详细的证明。第一个描述了一个发送者可以发送经典信息而另一个发送量子信息的速率区域。第二个描述了两个发射器都能发送量子信息的速率。对于这些情况中的每一个，给出了一个通道的例子，其中相关的区域承认一个单字母的描述。这是作者的博士学位。论文，2005年3月提交给斯坦福大学电气工程系。它代表了一个扩展版本的文件quant-ph/0501045，包含了一些教程的章节，可能是独立的兴趣，为那些学习量子香农理论。
We consider quantum key distribution (QKD) and entanglement distribution using a single-sender multiple-receiver pure-loss bosonic broadcast channel. We determine the unconstrained capacity region for the distillation of bipartite entanglement and secret key between the sender and each receiver, whenever they are allowed arbitrary public classical communication. A practical implication of our result is that the capacity region demonstrated drastically improves upon rates achievable using a naive time-sharing strategy, which has been employed in previously demonstrated network QKD systems. We s…
Quantum channel capacities - multiparty communication
我们分析了量子无记忆信道上多方通信的不同方面，并将一些已知的关键结果从二分信道推广到多方情形。特别是，我们引入多方版本的最小子空间传输保真度和纠缠传输保真度。我们还提供了替代的，本地的，版本的并行性，并显示其等效的全球范围内的能力区域定义。证明了两种不同容量概念对两种不同容量概念的等价性。类比于二分情况，通过等距编码定理的充分性，证明了附加的经典前向侧信道不增加任何具有$k$接收器和$m$接收器的量子信道的容量区域，它代表了一般量子网络理论的紧凑单元.结果表明，多址信道的最近提供容量域（[M. Horodecki等人，Nature { \bf 436} 673（2005）]，[J.Yard等人，quant-ph/0501045]）在前向经典通信的附加支持的情况下也是最佳的。
The Adaptive Classical Capacity of a Quantum Channel, or Information Capacities of Three Symmetric Pure States in Three Dimensions
我们研究了三个实维中三个对称的量子态承载经典信息的能力。根据发送和接收协议中允许的操作，已经定义了几种这样的能力。这些包括C_{1,1}容量和C_{1,infinity}容量，C_{1,1}容量是如果必须对每个接收到的状态使用单独的测量则可实现的容量，C_{1,infinity}容量是如果允许对所有接收到的状态的张量积进行联合测量则可实现的容量。我们发现了量子信道的一种新的经典信息容量--自适应容量C_{1,A}，它严格地介于C_{1,1}和C_{1,infinity}容量之间.自适应能力要求每个信号由单独的装置测量，但是允许分阶段测量这些信号的量子态，其中第一阶段部分地减少它们的量子态，并且其中进一步减少量子态的后续阶段中的测量可以取决于将第一轮测量的结果作为输入的经典计算的结果。
Capacities of classical compound quantum wiretap and classical quantum compound wiretap channels
我们确定了经典的复合量子窃听信道的容量与信道状态信息在发送端。此外，我们推导出一个下界的容量，这种信道没有信道状态信息和确定的容量的经典量子复合窃听信道的信道状态信息在发送端。
We study quantum channels that vary on time in a deterministic way, that is, they change in an independent but not identical way from one to another use. We derive coding theorems for the classical entanglement assisted and unassisted capacities. We then specialize the theory to lossy bosonic quantum channels and show the existence of contrasting examples where capacities can or cannot be drawn from the limiting behavior of the lossy parameter.
Inequalities and separations among assisted capacities of quantum channels
我们展示了离散无记忆量子信道，其量子容量由双向经典通信$Q_2$辅助，超过其无辅助的单次Holevo容量$C_H$。这些通道可以被认为具有数据输入和输出，以及部分影响的控制输入和部分揭示数据在从输入到输出的途中经历的一组酉演变中的哪一个的控制输出。信道被设计为使得数据的演变可以通过1）控制输出和2）与控制输入纠缠的参考系的经典协调处理来精确地推断，而不是单独从这些资源中的任一个来推断。因此，双向经典侧信道允许校正数据的噪声演化，从而大大增加容量。同一信道族提供了由经典反馈辅助的经典容量$C_B$和由经典反馈辅助的量子容量$Q_B$都超过$C_H$的示例。一个相关信道，其数据输入在与控制输入交互之前经历去相位，具有严格小于其$C_2$的经典容量$C=C_H$，该经典容量由独立经典通信辅助。
Finite-energy two-way assisted capacities: Exact formulas for multimode loss and fading
该研究推导了多模损耗与衰落信道在局域量子操作和双向经典通信辅助下的有限能量双向量子与密钥容量精确公式，为能量受限的光量子通信提供了能量分配指导与性能基准。
Capacities of a two-parameter family of noisy Werner-Holevo channels
本文将Landau-Streater信道推广到任意维度并构造含噪双参数信道族，分析其协变性、谱、Holevo量及各类容量性质。
Following initial work by Gregoratti and Werner [J. Mod. Optics 50, 913-933, 2003 and quant-ph/0403092] and Hayden and King [quant-ph/0409026], we study the problem of the capacity of a quantum channel assisted by a "friendly (channel) environment" that can locally measure and communicate classical messages to the receiver. Previous work [quant-ph/0505038] has yielded a capacity formula for the quantum capacity under this kind of help from the environment. Here we study the problem of the environment-assisted classical capacity, which exhibits a somewhat richer structure (at least, it seems to…
We consider classical message transmission under entanglement assistance for compound memoryless and arbitrarily varying quantum channels. In both cases, we prove general coding theorems together with corresponding weak converse bounds. In this way, we obtain single-letter characterizations of the entanglement-assisted classical capacities for both channel models. Moreover, we show that the entanglement-assisted classical capacity does exhibit no strong converse property for some compound quantum channels for the average as well as the maximal error criterion. A strong converse to the entangle…
On n-partite superactivation of quantum channel capacities
将量子信道容量的超激活推广到n>2信道的情形。对于n=3，构造了一次量子零误差容量的这种超激活的一个明确的例子。这个例子和它的重新制定的量子测量方面的一些影响进行了说明。
Quantum Channel Capacities
量子通信信道可以有很多用途：它可以传输经典信息，私人经典信息或量子信息。它可以单独使用，共享纠缠，或与其他通道一起使用。对于这些设置中的每一个，都有一个容量来量化信道的通信潜力。在这篇简短的评论中，我总结了量子通道的各种容量，包括相关的可加性问题的讨论。我也给出了一些潜在的有趣的方向，为未来的研究指示。
Fast convergence of Dynamic Capacities of GNS-Symmetric Quantum Channels
研究GNS对称量子信道的信息容量随时间演化，推导出经典和量子容量的指数收敛界，基于熵性质，并探讨其对主动与被动纠错方案性能的量化作用。
In this article we consider flagged extensions of convex combination of quantum channels, and find general sufficient conditions for the degradability of the flagged extension. An immediate application is a bound on the quantum $Q$ and private $P$ capacities of any channel being a mixture of a unitary map and another channel, with the probability associated to the unitary component being larger than $1/2$. We then specialize our sufficient conditions to flagged Pauli channels, obtaining a family of upper bounds on quantum and private capacities of Pauli channels. In particular, we establish ne…
Capacities of linear quantum optical systems
各种各样的通信信道使用量化的电磁场来传递信息。它们的通信能力关键取决于与信道的空间特性（例如衍射和天线设计）相关联的损耗。在这里，我们专注于通信通过一个有限的瞳孔，衍射被正式描述为一个记忆通道。通过利用这种等价性，我们然后计算的光学重聚焦系统的通信容量，建模为一个会聚透镜。即使损失的信息源于有限的瞳孔的镜头，我们表明，存在的重新聚焦系统可以大大提高通信能力。我们主要集中在经典信息的通信，扩展到量子信息是直接的。
Quantum amplifier channels are at the core of several physical processes. Not only do they model the optical process of spontaneous parametric down-conversion, but the transformation corresponding to an amplifier channel also describes the physics of the dynamical Casimir effect in superconducting circuits, the Unruh effect, and Hawking radiation. Here we study the communication capabilities of quantum amplifier channels. Invoking a recently established minimum output-entropy theorem for single-mode phase-insensitive Gaussian channels, we determine capacities of quantum-limited amplifier chann…
Quantum communication is an important branch of quantum information science, promising unconditional security to classical communication and providing the building block of a future large-scale quantum network. Noise in realistic quantum communication channels imposes fundamental limits on the communication rates of various quantum communication tasks. It is therefore crucial to identify or bound the quantum capacities of a quantum channel. Here, we consider Gaussian channels that model energy loss and thermal noise errors in realistic optical and microwave communication channels and study the…
The set of Multi-level Amplitude Damping (MAD) quantum channels is introduced as a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension $d$. In the special case of $d=3$, by exploiting degradability, data-processing inequalities, and channel isomorphism, we compute the associated quantum and private classical capacities for a rather wide class of maps, extending the set of solvable models known so far. We proceed then to the evaluation of the entanglement assisted, quantum and classical, capacities.
Classical capacities under physical constraints: More capacity with less entanglement
本文研究了在能量约束下量子通道的经典容量，提出了一种能量受限的密集编码协议，并证明了在两qubit情况下该协议最优，同时展示了纠缠辅助在特定条件下提升容量的现象。
An additive refinement of quantum channel capacities
针对现有量子信道容量度量不满足加性、需渐近正则化导致研究困难的问题，研究通过微调量子通信物理设置，得到可用于量子香农定理的加性容量量，验证了冯·诺依曼熵的核心地位。
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