A simple operational interpretation of the fidelity

Fisher–Kubo–Mori–Bogoliubov几何中经典保真度与路径长度的操作意义

Operational meaning of the classical fidelity and the path length in Fisher-Kubo-Mori-Bogoliubov geometry

本文揭示近可逆量子态输运的最小熵产生与Fisher-KMB路径长度的函数关系，赋予统计长度及经典Bhattacharyya保真度量化残余不可逆性的操作意义。

Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states

We introduce the resource quantifier of weight of resource for convex quantum resource theories of states with arbitrary resources. We show that it captures the advantage that a resourceful state offers over all possible free states, in the operational task of exclusion of subchannels. Furthermore, we introduce information-theoretic quantities related to exclusion and find a connection between the weight of resource of a state, and the exclusion-type information of ensembles it can generate. These results provide support to a recent conjecture made in the context of convex quantum resource the…

Lossless quantum data compression with exponential penalization: an operational interpretation of the quantum Rényi entropy

Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum Rényi entropies. In order to do this, we appeal to a very general quantum encoding scheme that satisfies a quantum version of the Kraft-McMillan inequality. Then, in the standard situation, where one is intended to minimize the usual average length of the quantum codewords, we recover the known results, namely that the von Neumann entropy of the source bounds the average length of the optimal codes. Otherwise, we show that by invoking an exponential averag…

复合量子假设检验中反向夹层Renyi散度的操作解释

Operational interpretation of the reverse sandwiched Renyi divergences in composite quantum hypothesis testing

研究复合量子假设检验的Hoeffding机制，建立结构假设下的量子Hoeffding界，发现反向夹层Renyi散度直接决定热平衡态与未知退相探测态区分的Hoeffding指数，提供其操作解释。

使用带误差界的迹距离操作形式测试量子网络中的链路保真度

Testing Link Fidelity in a Quantum Network using Operational Form of Trace Distance with Error Bounds

该研究针对量子网络评估的实际应用缺口，推导多节点网络的新型操作型迹距离，建立含误差界的迹距离-保真度基准，衔接量子操作与张量网络分析，为真实误差下的量子网络性能评估提供稳健框架。

Operational approach to the Uhlmann holonomy

We suggest a physical interpretation of the Uhlmann amplitude of a density operator. Given this interpretation we propose an operational approach to obtain the Uhlmann condition for parallelity. This allows us to realize parallel transport along a sequence of density operators by an iterative preparation procedure. At the final step the resulting Uhlmann holonomy can be determined via interferometric measurements.

量子信道演化的一种新保真度及其几何解释

A new fidelity of quantum channel evolution and its geometric interpretation

本文定义并研究了α-z-保真度，给出其在多种量子信道演化下的极值极限公式，推广了α-z-Rényi相对熵，并提供了度量量子态距离的几何解释。

Erasing Quantum Coherence: An Operational Approach

Despite being one of the hallmarks of quantum physics, there is a lack of operational interpretations of quantum coherence. Here we provide an operational interpretation of coherence of a quantum system, in terms of the amount of noise that is to be injected in order to fully decohere it. In particular, we show that in the asymptotic limit, the minimum amount of noise that is required to fully decohere a quantum system, is equal to the relative entropy of coherence. This quantifies the erasure cost of quantum coherence. We employ the entropy exchanged between system and environment during the …

Alignment of reference frames and an operational interpretation for the G-asymmetry

We determine the quantum states and measurements that optimize the accessible information in a reference frame alignment protocol associated with the groups U(1), corresponding to a phase reference, and $\mathbb{Z}_M$, the cyclic group of $M$ elements. Our result provides an operational interpretation for the $G$-asymmetry which is information-theoretic and which was thus far lacking. In particular, we show that in the limit of many copies of the bounded-size quantum reference frame, the accessible information approaches the Holevo bound. This implies that the rate of alignment of reference fr…

多路径干涉测量中可预测性与量子相干性之间的权衡及其操作解释

Trade-off between predictability and quantum coherence for multi-path interferometry and its operational interpretation

研究多路径设置下可预测性与量子相干性的互补关系，引入基于基的可预测性，推导二者权衡关系，该关系赋予相干性度量操作解释，为源独立量子随机数生成器的猜测概率提供最坏情况界限。

可操作性解释的稳定子熵

Operational interpretation of the Stabilizer Entropy

本文通过量子性质测试框架，提供稳定子熵的可操作性解释，证明其作为魔力单调量的鲁棒性，并揭示其在区分稳定子态与通用量子态中的作用。

Operational interpretation of coherence in quantum key distribution

Quantum coherence was recently formalized as a physical resource to measure the strength of superposition. Based on the resource theory, we present a systematic framework that connects a coherence measure to the security of quantum key distribution. By considering a generic entanglement-based key distribution protocol under the collective attack scenario, we show that the key rate can be quantified by the coherence of the shared bipartite states. This framework allows us to derive the key rate of the BB84 and six-state protocols. By utilizing fine-grained parameters, we also derive the improve…

Derivation of the Born Rule from Operational Assumptions

The Born rule is derived from operational assumptions, independent of the normalization of the state. Unlike Gleason's theorem, the argument applies even if probabilities are defined for only a single resolution of the identity, so it applies to all the major foundational approaches to quantum mechanics. There are important points of contact with Deutsch's program for deducing the probabilistic interpretation of quantum mechanics from decision thoery, as recently completed by Wallace. Decision theory can be used to supplement the present derivation, in application to the Everett interpretation…

通过k态排除实现Choi秩的操作诠释

Operational Interpretation of the Choi Rank Through k-State Exclusion

本研究通过纠缠辅助的k态排除操作任务诠释了量子信道Choi秩的物理意义，提出结论性k态排除的必要条件及强弱排除概念，证明Choi秩是该超密编码扩展任务成功概率的普适界。

Operational distance and fidelity for quantum channels

We define and study a fidelity criterion for quantum channels, which we term the minimax fidelity, through a noncommutative generalization of maximal Hellinger distance between two positive kernels in classical probability theory. Like other known fidelities for quantum channels, the minimax fidelity is well-defined for channels between finite-dimensional algebras, but it also applies to a certain class of channels between infinite-dimensional algebras (explicitly, those channels that possess an operator-valued Radon--Nikodym density with respect to the trace in the sense of Belavkin--Staszews…

相对量子资源理论及其在子信道判别中的操作性应用

Relative Quantum Resource Theory and Operational Applications in Subchannel Discrimination

本文提出相对量子资源理论，通过定义资源相对于特定凸集的相对优越性及状态不足的新框架，在子信道判别任务中量化相对优势与劣势，扩展了量子资源理论的操作解释。

The operational advantages provided by non-classical teleportation

The standard benchmark for teleportation is the average fidelity of teleportation and according to this benchmark not all states are useful for teleportation. It was recently shown however that all entangled states lead to non-classical teleportation, with there being no classical scheme able to reproduce the states teleported to Bob. Here we study the operational significance of this result. On the one hand we demonstrate that every entangled state is useful for teleportation if a generalization of the average fidelity of teleportation is considered which concerns teleporting quantum correlat…

Operational meaning of quantum measures of recovery

Several information measures have recently been defined which capture the notion of "recoverability." In particular, the fidelity of recovery quantifies how well one can recover a system $A$ of a tripartite quantum state, defined on systems $ABC$, by acting on system $C$ alone. The relative entropy of recovery is an associated measure in which the fidelity is replaced by relative entropy. In this paper, we provide concrete operational interpretations of the aforementioned recovery measures in terms of a computational decision problem and a hypothesis testing scenario. Specifically, we show tha…

自旋电子网络中对结构化不确定性敏感性的几何解释

Geometric Interpretation of Sensitivity to Structured Uncertainties in Spintronic Networks

本文提出一种几何模型描述自旋电子网络状态转移保真度误差的微分敏感性，证明在封闭系统中完美状态转移是实现最优鲁棒性的充要条件，且无需权衡保真度与敏感性。

Operationally Invariant Measure of the Distance between Quantum States by Complementary Measurements

We propose an operational measure of distance of two quantum states, which conversely tells us their closeness. This is defined as a sum of differences in partial knowledge over a complete set of mutually complementary measurements for the two states. It is shown that the measure is operationally invariant and it is equivalent to the Hilbert-Schmidt distance. The operational measure of distance provides a remarkable interpretation of the information distance between quantum states.

全同粒子的真空与过程矩阵的操作性解释

Operational interpretation of the vacuum and process matrices for identical particles

本文用过程矩阵形式体系分析 dSD 单粒子双向通信协议，指出真空相互作用应作为同等操作，并借助二次量子化将该形式体系推广至封顶 Fock 空间，以描述粒子数不确定的全同粒子协议。

What The Trace Distance Security Criterion in Quantum Key Distribution Does And Does Not Guarantee

Cryptographic security of quantum key distribution is currently based on a trace distance criterion. The widespread misinterpretation of the criterion as failure probability and also its actual scope have been discussed previously. Recently its distinguishability advantage interpretation is re-emphasized as an operational guarantee, and the failure probability misinterpretation is maintained with a further failure probability per bit interpretation. In this paper we explain the basic perpetuating error as a confusion on the correspondence between mathematics and reality. We note that the assig…

Logarithmic coherence: Operational interpretation of $\ell_1$-norm coherence

We show that the distillable coherence---which is equal to the relative entropy of coherence---is, up to a constant factor, always bounded by the $\ell_1$-norm measure of coherence (defined as the sum of absolute values of off diagonals). Thus the latter plays a similar role as logarithmic negativity plays in entanglement theory and this is the best operational interpretation from a resource-theoretic viewpoint. Consequently the two measures are intimately connected to another operational measure, the robustness of coherence. We find also relationships between these measures, which are tight f…

Correlation Detection and an Operational Interpretation of the Renyi Mutual Information

A variety of new measures of quantum Renyi mutual information and quantum Renyi conditional entropy have recently been proposed, and some of their mathematical properties explored. Here, we show that the Renyi mutual information attains operational meaning in the context of composite hypothesis testing, when the null hypothesis is a fixed bipartite state and the alternate hypothesis consists of all product states that share one marginal with the null hypothesis. This hypothesis testing problem occurs naturally in channel coding, where it corresponds to testing whether a state is the output of …

最大量子泄漏：操作解释与量子信道分析

Maximal quantum leakage: operational interpretation and quantum channel analysis

研究最大量子泄漏，证明其计算等同于特定量子态判别，给出操作解释。分析集体测量影响，明确渐近极限下最大泄漏。扩展到量子信道，开发迭代算法并通过数值示例验证，解决计算难题并刻画最大泄漏特性。

Some geometric interpretations of quantum fidelity

We consider quantum fidelity between two states $ρ$ and $σ$, where we fix $ρ$ and allow $σ$ to be sent through a quantum channel. We determine the minimal fidelity where one minimizes over (a) all unital channels, (b) all mixed unitary channels, and (c) arbitrary channels. We derive results involving the minimal eigenvalue of $ρ$, which we can interpret as a convex combination coefficient. As a consequence, we give a new geometric interpretation of the minimal fidelity with respect to the closed, convex set of density matrices and with respect to the closed, convex set of quantum channels. We …

Fidelity of quantum strategies with applications to cryptography

We introduce a definition of the fidelity function for multi-round quantum strategies, which we call the strategy fidelity, that is a generalization of the fidelity function for quantum states. We provide many properties of the strategy fidelity including a Fuchs-van de Graaf relationship with the strategy norm. We also provide a general monotinicity result for both the strategy fidelity and strategy norm under the actions of strategy-to-strategy linear maps. We illustrate an operational interpretation of the strategy fidelity in the spirit of Uhlmann's Theorem and discuss its application to t…

Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies

We show that the new quantum extension of Renyi's α-relative entropies, introduced recently by Muller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J. Math. Phys. 54, 122203, (2013), and Wilde, Winter, Yang, Commun. Math. Phys. 331, (2014), have an operational interpretation in the strong converse problem of quantum hypothesis testing. Together with related results for the direct part of quantum hypothesis testing, known as the quantum Hoeffding bound, our result suggests that the operationally relevant definition of the quantum Renyi relative entropies depends on the parameter α: for α<1, the …

基于弱值测量的量子迹范数不对称性的操作诠释与估计及若干界

Operational interpretation and estimation of quantum trace-norm asymmetry based on weak value measurement and some bounds

该研究给出量子迹范数不对称性的操作诠释，证明其等于希尔伯特空间正交基优化下平移群生成元弱值的平均绝对虚部，可通过弱值测量结合变分优化估计，并推导其与量子Fisher信息的类不确定性权衡关系。

Axiomatic and operational connections between the $l_1$-norm of coherence and negativity

Quantum coherence plays a central role in various research areas. The $l_1$-norm of coherence is one of the most important coherence measures that are easily computable, but it is not easy to find a simple interpretation. We show that the $l_1$-norm of coherence is uniquely characterized by a few simple axioms, which demonstrates in a precise sense that it is the analog of negativity in entanglement theory and sum negativity in the resource theory of magic-state quantum computation. We also provide an operational interpretation of the $l_1$-norm of coherence as the maximum entanglement, measur…

Sub-fidelity as a measure of irreversibility of decoherence

Quantum correlations between two systems can be impaired by the presence of an environment, as it can make systems decohere. We wish to evaluate how much coherence has been irreversibly lost. To do so, we study two qubits which leak correlations into an arbitrarily large environment and we find that our ability to steer one of them to the most coherent set of states possible by acting on the other is given by the sub-fidelity of two conditional states of the environment. Sub-fidelity is a quantity that was already known, but that until now lacked an operational interpretation. Furthermore, we …

Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics

In the framework of quantum thermodynamics preparing a quantum system in a general state requires the consumption of two distinct resources, namely, work and coherence. It has been shown that the work cost of preparing a quantum state is determined by its free energy. Considering a similar setting, here we determine the coherence cost of preparing a general state when there are no restrictions on work consumption. More precisely, the coherence cost is defined as the minimum rate of consumption of systems in a pure coherent state, that is needed to prepare copies of the desired system. We show …

Operational Interpretation of Renyi Information Measures via Composite Hypothesis Testing Against Product and Markov Distributions

We revisit the problem of asymmetric binary hypothesis testing against a composite alternative hypothesis. We introduce a general framework to treat such problems when the alternative hypothesis adheres to certain axioms. In this case we find the threshold rate, the optimal error and strong converse exponents (at large deviations from the threshold) and the second order asymptotics (at small deviations from the threshold). We apply our results to find operational interpretations of various Renyi information measures. In case the alternative hypothesis is comprised of bipartite product distribu…

双重最小化Petz和sandwiched Renyi互信息：从二元量子态鉴别获得的操作解释

Doubly minimized Petz and sandwiched Renyi mutual information: Operational interpretation from binary quantum state discrimination

本文研究了二元量子态鉴别问题，证明了双重最小化Petz Renyi互信息决定直接指数，而sandwiched Renyi互信息决定强反向指数，扩展了经典分布结果到量子领域。

夹心Rényi散度在阶数1/2到1之间的运算解释：作为强逆指数的精确表征

Operational Interpretation of the Sandwiched Rényi Divergence of Order 1/2 to 1 as Strong Converse Exponents

本研究为阶数在1/2到1之间的夹心Rényi散度提供了运算解释，将其与量子任务的精确强逆指数相关联，涵盖平滑化、隐私放大和解耦，首次给出了该参数区间散度的精确运算意义。

源自Kirkwood-Dirac非经典性的量子相干性、若干界及其操作诠释

Quantum coherence from Kirkwood-Dirac nonclassicality, some bounds, and operational interpretation

本研究基于KD准概率的非实性与负性构建量子相干性量化指标，推导其上下界、纯态闭式表达式及非对易基下的权衡关系，提出基于弱值测量的估计方案并探讨与量子互文性的关联。

Operational formulation of weak values without probe systems

Weak values are the fundamental values for observables in a pre- and post-selected system. Weak values are typically measured by weak measurement, in which weak values appear in the change of not the pre- and post-selected system but the probe system. This indirect characteristic of weak measurement obscures the meaning of weak values for the pre- and post-selected system, in contrast to conventional physical quantities, which have a clear operational meaning. In this study, we operationally formulate weak values as the sensitivity of post-selection probability amplitude to small transformatio…

Convexity and Operational Interpretation of the Quantum Information Bottleneck Function

In classical information theory, the information bottleneck method (IBM) can be regarded as a method of lossy data compression which focusses on preserving meaningful (or relevant) information. As such it has recently gained a lot of attention, primarily for its applications in machine learning and neural networks. A quantum analogue of the IBM has recently been defined, and an attempt at providing an operational interpretation of the so-called quantum IB function as an optimal rate of an information-theoretic task, has recently been made by Salek et al. However, the interpretation given in th…

Family of coherence measures and duality between quantum coherence and path distinguishability

Coherence measures and their operational interpretations lay the cornerstone of coherence theory. In this paper, we introduce a class of coherence measures with $α$-affinity, say $α$-affinity of coherence for $α\in (0, 1)$. Furthermore, we obtain the analytic formulae for these coherence measures and study their corresponding convex roof extension. We provide an operational interpretation for $1/2$-affinity of coherence by showing that it is equal to the error probability to discrimination a set of pure states with the least square measurement. Employing this relationship we regain the optimal…

A fidelity measure for quantum states based on the matrix geometric mean

Uhlmann's fidelity function is one of the most widely used similarity measures in quantum theory. One definition of this function is that it is the minimum classical fidelity associated with a quantum-to-classical measurement procedure of two quantum states. In 2010, Matsumoto introduced another fidelity function which is dual to Uhlmann's in the sense that it is the maximimum classical fidelity associated with a classical-to-quantum preparation procedure for two quantum states. Matsumoto's fidelity can also be defined using the well-established notion definition of the matrix geometric mean. …

Interpreting quantum discord through quantum state merging

We present an operational interpretation of quantum discord based on the quantum state merging protocol. Quantum discord is the markup in the cost of quantum communication in the process of quantum state merging, if one discards relevant prior information. Our interpretation has an intuitive explanation based on the strong subadditivity of von Neumann entropy. We use our result to provide operational interpretations of other quantities like the local purity and quantum deficit. Finally, we discuss in brief some instances where our interpretation is valid in the single copy scenario.

物理量测量程序的统计解释

Statistical Interpretation of the Procedures Measurement of Physical Quantities

本文通过重新组织和综合现有模型，提出量子物理基础的框架，强调实验可行程序和实验室实践的统计模型，为量子力学的公理化重述提供基础。

量子网络中广播真正多方纠缠的限制

Limits on Broadcasting Genuine Multipartite Entanglement in Quantum Networks

研究量子网络中真正多方纠缠广播限制，通过分布式协议推导出特定态广播保真度表达式，证明同时认证GME不可行，揭示多方纠缠广播性与可认证性权衡及纠缠分布内在限制。

Watching the Clocks: Interpreting the Page-Wootters Formalism and the Internal Quantum Reference Frame Programme

We discuss some difficulties that arise in attempting to interpret the Page-Wootters and Internal Quantum Reference Frames formalisms, then use a 'final measurement' approach to demonstrate that there is a workable single-world realist interpretation for these formalisms. We note that it is necessary to adopt some interpretation before we can determine if the 'reference frames' invoked in these approaches are operationally meaningful, and we argue that without a clear operational interpretation, such reference frames might not be suitable to define an equivalence principle. We argue that the n…

响应寄存器量子预言机中最优值读出的信息论表征

An Information-Theoretic Characterization of Optimal Value-Readout in Response-Register Quantum Oracles

研究响应寄存器量子预言机中值读出与相位反冲的定量关系，证明有限阿贝尔响应群中最优单查询值读出概率是响应状态的归一化Rényi - ½有效傅里叶支撑，给出其信息论表征、操作解释及相关定理。

A gambling interpretation of some quantum information-theoretic quantities

It is known that repeated gambling over the outcomes of independent and identically distributed (i.i.d.) random variables gives rise to alternate operational meaning of entropies in the classical case in terms of the doubling rates. We give a quantum extension of this approach for gambling over the measurement outcomes of tensor product states. Under certain parameters of the gambling setup, one can give operational meaning of von Neumann entropies. We discuss two variants of gambling when a helper is available and it is shown that the difference in their doubling rates is the quantum discord.…

Operational Resource Theory of Coherence

We establish an operational theory of coherence (or of superposition) in quantum systems, by focusing on the optimal rate of performance of certain tasks. Namely, we introduce the two basic concepts - "coherence distillation" and "coherence cost" in the processing quantum states under so-called incoherent operations [Baumgratz/Cramer/Plenio, Phys. Rev. Lett. 113:140401 (2014)]. We then show that in the asymptotic limit of many copies of a state, both are given by simple single-letter formulas: the distillable coherence is given by the relative entropy of coherence (in other words, we give the …

理解量子理论：一种操作重建方法

Understanding Quantum Theory: An Operational Reconstructive Approach

本文提出通过操作重建方法重新审视量子理论，强调数学结构与实验实践的结合，以避免传统解释方法的局限。

Von Neumann's information engine without the spectral theorem

Von Neumann obtained the formula for the entropy of a quantum state by assuming the validity of the second law of thermodynamics in a thought experiment involving semipermeable membranes and an ideal gas of quantum-labeled particles. Despite being operational in the most part, von Neumann's argument crucially departs from an operational narrative in its use of the spectral theorem. In this work we show that the role of the spectral theorem in von Neumann's argument can be taken over by the operational assumptions of repeatability and reversibility, and using these we are able to explore the co…

广义对称性下量子态可区分性的操作管-扇区理论

Operational Tube-Sector Theory of Quantum State Distinguishability Under Generalized Symmetries

建立多体系统中量子态可区分性的变分原理，涵盖融合范畴描述的非可逆对称性，通过边界管代数定义最优测量结构，给出管扇区概率和管POVM，实现对称约束下的最优一次性假设检验可区分性。

Quantum cloning and teleportation fidelity in the noncommutative phase-space

The formulation of the no-cloning theorem in the framework of phase-space noncommutative (NC) quantum mechanics (QM) is examined, and its implications for the computation of quantum cloning probabilities and teleportation fidelity are investigated through the Weyl-Wigner formulation of QM. The principles of QM re-edited in terms of a deformed Heisenberg-Weyl algebra are shown to provide a covariant formulation for the quantum fidelity, through which the results from the no-cloning theorem for the ordinary QM can be reproduced. Besides exhibiting an explicit correspondence between standard and …