Igor Devetak, Andreas Winter
We describe how to achieve optimal entanglement generation and one-way entanglement distillation rates by coherent implementation of a class of secret key generation and secret key distillation protocols, respectively. This short paper is a high-level descrioption of our detailed papers [8] and [10].
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Quantum coherence as an important quantum resource plays a key role in quantum theory. In this paper, using entropy-based measures, we investigate the relations between quantum correlated coherence, which is the coherence between subsystems [K. C. Tan, H. Kwon, C. Y. Park, and H. Jeong, Phys. Rev. A 94, 022329 (2016)], and two main kinds of quantum correlations as defined by quantum discord as well as quantum entanglement. In particular, we show that quantum discord and quantum entanglement can be well characterized by quantum correlated coherence. Moreover, we prove that the entanglement meas…
Relating the Glauber-Sudarshan, Wigner and Husimi quasiprobability distributions operationally through the quantum limited amplifier and attenuator channels
本文证明有限强度量子受限放大器和衰减器信道的单次组合可将Glauber-Sudarshan分布转化为Wigner分布，进而转化为Husimi分布，揭示了准概率分布间的操作联系及量子到经典的转变。
Quantum coherence and quantum entanglement represent two fundamental features of non-classical systems that can each be characterized within an operational resource theory. In this paper, we unify the resource theories of entanglement and coherence by studying their combined behavior in the operational setting of local incoherent operations and classical communication (LIOCC). Specifically we analyze the coherence and entanglement trade-offs in the tasks of state formation and resource distillation. For pure states we identify the minimum coherence-entanglement resources needed to generate a g…
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 …
We establish a general operational one-to-one mapping between coherence measures and entanglement measures: Any entanglement measure of bipartite pure states is the minimum of a suitable coherence measure over product bases. Any coherence measure of pure states, with extension to mixed states by convex roof, is the maximum entanglement generated by incoherent operations acting on the system and an incoherent ancilla. Remarkably, the generalized CNOT gate is the universal optimal incoherent operation. In this way, all convex-roof coherence measures, including the coherence of formation, are end…
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 …
Quantum coherence is a crucial resource for quantum information processing. By employing the language of coherence orders largely applied in NMR systems, quantum coherence has been currently addressed in terms of multiple quantum coherences (MQCs). Here we investigate the $α$-MQCs, a novel class of multiple quantum coherences which is based on $α$-relative purity, an information-theoretic quantifier analogous to quantum fidelity and closely related to Rényi relative entropy of order $α$. Our framework enables linking $α$-MQCs to Wigner-Yanase-Dyson skew information (WYDSI), an asymmetry monoto…
We establish a set of resource conversion relationships between quantum coherence and multipartite entanglement in many-body systems, where the operational measures of resource cost and distillation are focused. Under the multipartite incoherent operation, the initial coherence of single-party system bounds the maximal amounts of corresponding operational entanglement in an arbitrary bipartite partition as well as the genuine multipartite entanglement in many-body systems. Furthermore, the converted multipartite entanglement can be transferred to its subsystems and restored to coherence of a s…
Out-of-time-order correlations (OTOCs) characterize the scrambling, or delocalization, of quantum information over all the degrees of freedom of a system and thus have been proposed as a proxy for chaos in quantum systems. Recent experimental progress in measuring OTOCs calls for a more thorough understanding of how these quantities characterize complex quantum systems, most importantly in terms of the buildup of entanglement. Although a connection between OTOCs and entanglement entropy has been derived, the latter only quantifies entanglement in pure systems and is hard to access experimental…
Coherence-based operational nonclassicality criteria
本文提出仅依赖实验可测数据的可操作判据，用于检测单个量子相干性的非经典性，并分析其在损耗与噪声信道下的鲁棒性，可广泛应用于多类量子实验。
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…
Imaginarity as a Resource within Quantum Coherence: Geometric Decomposition and Operational Conversion
研究将虚部性作为量子相干基本资源，通过几何分解划分相干性，给出两体系统相关界限，设计操作协议实现资源转换，对角哈密顿量下动力学演化有互补振荡，为分布式量子技术资源管理提供见解。
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…
We demonstrate the simple and deep equivalence between quantum coherence and nonclassicality and the definite way in which they determine metrological resolution. Moreover, we define a coherence observable consistent with a classical intuition relating coherence with phase statistics.
The quantum nature of the state of a bosonic quantum field manifests itself in its entanglement, coherence, or optical nonclassicality which are each known to be resources for quantum computing or metrology. We provide quantitative and computable bounds relating entanglement measures with optical nonclassicality measures. These bounds imply that strongly entangled states must necessarily be strongly optically nonclassical. As an application, we infer strong bounds on the entanglement that can be produced with an optically nonclassical state impinging on a beam splitter. For Gaussian states, we…
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。
We characterize the operational capabilities of quantum channels which can neither create nor detect quantum coherence vis-à-vis efficiently manipulating coherence as a resource. We study the class of dephasing-covariant operations (DIO), unable to detect the coherence of any input state, as well as introduce an operationally-motivated class of channels $ρ$-DIO which is tailored to a specific input state. We first show that pure-state transformations under DIO are completely governed by majorization, establishing necessary and sufficient conditions for such transformations and adding to the li…
Based on the resource theory for quantifying the coherence of quantum channels, we introduce a new coherence quantifier for quantum channels via maximum relative entropy. We prove that the maximum relative entropy for coherence of quantum channels is directly related to the maximally coherent channels under a particular class of superoperations, which results in an operational interpretation of the maximum relative entropy for coherence of quantum channels. We also introduce the conception of sub-superchannels and sub-superchannel discrimination. For any quantum channels, we show that the adva…
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…
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…
As the precious resource for quantum information processing, quantum coherence can be created remotely if the involved two sites are quantum correlated. It can be expected that the amount of coherence created should depend on the quantity of the shared quantum correlation, which is also a resource. Here, we establish an operational connection between coherence induced by steering and the quantum correlation. We find that the steering-induced coherence quantified by such as relative entropy of coherence and trace-norm of coherence is bounded from above by a known quantum correlation measure def…
We introduce and study the l1 norm of coherence of assistance both theoretically and operationally. We first provide an upper bound for the l1 norm of coherence of assistance and show a necessary and sufficient condition for the saturation of the upper bound. For two and three dimensional quantum states, the analytical expression of the l1 norm of coherence of assistance is given. Operationally, the mixed quantum coherence can always be increased with the help of another party' s local measurement and one way classical communication since the l1 norm of coherence of assistance, as well as the …
Quantum coherence plays a fundamental and operational role in different areas of physics. A resource theory has been developed to characterize the coherence of distinguishable particles systems. Here we show that indistinguishability of identical particles is a source of coherence, even when they are independently prepared. In particular, under spatially local operations, states that are incoherent for distinguishable particles, can be coherent for indistinguishable particles under the same procedure. We present a phase discrimination protocol, in which we demonstrate the operational advantage…
Quantum resource theories have been widely studied to systematically characterize the non-classicality of quantum systems. Most resource theories focus on quantum states and study their interconversions. Although quantum channels are generally used as the tool for state manipulation, such a manipulation capability can be naturally regarded as a generalized quantum resource, leading to an open research direction in the resource theories of quantum channels. Various resource-theoretic properties of channels have been investigated, however, without treating channels themselves as operational reso…
Catalytic Transformations in Coherence Theory
本文利用催化剂概念，在单拷贝情形下为相干相对熵、形成相干和量子非相干相对熵赋予操作性意义，并证明了渐近与催化态变换之间的对应关系。
The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of coherence is directly related to the maximum overlap with maximally coherent states under a particular class of operations, which provides an operational interpretation of max-relative entropy of coherence. Moreover, we show that, for any coherent state, there are examples of subchannel discrimination problems such that this coherent state allows for a higher pro…
The operational meaning of coherence measure lies at very heart of the coherence theory. In this paper, we provide an operational interpretation for geometric coherence, by proving that the geometric coherence of a quantum state is equal to the minimum error probability to discriminate a set of pure states with von Neumann measurement. On the other hand, we also show that a task to ambiguously discriminate a set of linearly independent pure states can be also regards as a problem of calculating geometric coherence. That is, we reveal an equivalence relation between ambiguous quantum state disc…
Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of quantum coherence. The measure is shown to be observable, as it can be recast as the expectation value of a coherence witness operator for any quantum state. The robustness of coherence is evaluated analytically on relevant classes of states, and an efficient semidefinite program that computes it on general states is given. An operational interpretation is fina…
We establish two complementarity relations for the relative entropy of coherence in quantum information processing, i.e., quantum dense coding and teleportation. We first give an uncertaintylike expression relating local quantum coherence to the capacity of optimal dense coding for bipartite system. The relation can also be applied to the case of dense coding by using unital memoryless noisy quantum channels. Further, the relation between local quantum coherence and teleportation fidelity for two-qubit system is given.
Quantum partial coherence measures constructed from Fisher information
本文通过后选择非幺正参数化过程，引入基于量子Fisher信息的部分相干性度量，将其与参数估计精度直接关联，并探讨了其在幺正参数化下与量子Fisher信息的区别及在量子态判别中的操作意义。
Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated and quantified. Operationally, considering the projective measurement of the state in the computational basis, coherence quantifies the intrinsic randomness of the measurement outcome conditioned on all the other quantum systems. However, such a relation is only proven when randomness is characterized by the Von-Neumann entropy. In this work, we consider seve…
Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantum system. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem.
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 bounds and diagnostics for coherence in energy transfer
本文提出了一种资源理论方法，用于量化初始相干对能量传输的影响，并通过两个模型分析相干敏感性及传输性能的界限。
A coherence quantifier based on the quantum optimal transport cost
本文提出一种基于量子最优输运成本的相干性度量，采用凸包扩展方法，给出纯态解析解，并提供操作性诠释。
Operational Relation Between One-Time and Two-Time Work Protocols and Measurement-Resolution-Induced Transitions in Quantum Work Statistics
该研究建立量子功统计中OTM与TTM协议的操作联系，通过经典后处理从TTM数据重建OTM功值，揭示相干信息潜藏其中。在驱动二能级系统中发现分辨率驱动的统计转变，可进行相干量化，并在氮空位中心平台展示了实验可及性。
From an operational perspective, quantumness characterizes the exotic behavior in a physical process which cannot be explained with Newtonian physics. There are several widely used measures of quantumness, including coherence, discord, and entanglement, each proven to be essential resources in particular situations. There exists evidence of fundamental connections amongst the three measures. However, those quantumnesses are still regarded differently and such connections are yet to be elucidated. Here, we introduce a general framework of defining a unified quantumness with an operational motiv…
Quantum coherence as randomness under classical control
针对经典控制隐藏的量子设备，提出基于半定规划层次结构的完整且高效的相干性认证方法，并应用于量子信道相干性保持能力的判定。
Operational Quasiprobability in Quantum Thermodynamics: Work Extraction by Coherence and Non-joint Measurability
本研究将操作准概率（OQ）用作功分布，证明相干性与非联合可测性可提升量子系统的可提取功，还发现准概率负性大小并非非经典功的可靠指标。
One-shot manipulation of coherence in dynamic quantum resource theory
该研究基于超信道理论构建量子相干性动态资源理论，定义相关自由超信道与资源单位，建立动态相干代价与蒸馏的单次理论，引入δ-MISC超信道并给出单次催化动态相干代价的上下界。
Deviations from classical physics when distant quantum systems become correlated are interesting both fundamentally and operationally. There exist situations where the correlations enable collaborative tasks that are impossible within the classical formalism. Here, we consider the efficiency of quantum computation protocols compared to classical ones as a benchmark for separating quantum and classical resources and argue that the computational advantage of collaborative quantum protocols in the discrete variable domain implies the nonclassicality of correlations. By analysing a toy model, it t…
The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can however be lifted when considering sets of quantum states. Here we introduce the concept of set coherence for characterising the coherence of a set of quantum systems in a basis-independent way. We construct measures for quantifying set coherence of sets of quantum states as well as quantum measurements. These measures feature an operational meaning in terms of discrimination games and capture precisely the advantage offered by a given set over incoherent …
All coherent measurements provide observational ergotropic advantage
本文建立测量相干性与功提取优势的定量联系，证明相干性是正优势的充要条件，并给出上下界，从资源理论角度表征其热力学价值。
Delayed Choice Quantum Eraser Experiment Revisited: Causality and Informational Coherence
本文通过延迟选择量子擦除实验，利用单光子干涉检测区分因果性和信息一致性假说，无需后选择。
Quantum coherence with respect to orthonormal bases has been studied extensively in the past few years. Recently, Bischof, et al. [Phys. Rev. Lett. 123, 110402 (2019)] generalized it to the case of general positive operator-valued measure (POVM) measurements. Such POVM-based coherence, including the block coherence as a special case, have significant operational interpretations in quantifying the advantage of quantum states in quantum information processing. In this work we first establish an alternative framework for quantifying the block coherence and provide several block coherence measures…
Considerable work has recently been directed toward developing resource theories of quantum coherence. In most approaches, a state is said to possess quantum coherence if it is not diagonal in some specified basis. In this letter we establish a criterion of physical consistency for any resource theory in terms of physical implementation of the free operations, and we show that all currently proposed basis-dependent theories of coherence fail to satisfy this criterion. We further characterize the physically consistent resource theory of coherence and find its operational power to be quite limit…
Geometric and Operational Characterization of Two-Qutrit Entanglement
本文提出通过几何和操作视角研究两量子三能级纠缠，利用行列式定义不变量并建立与光学干涉仪的对应关系，揭示纠缠态的几何特征和操作属性。
In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define a coherence monotone of measurement. For instance, the relative entropy fulfills all the required properties as a proper monotone. We specifically introduce a coherence monotone of measurement in terms of off-diagonal elements of Positive-Operator-Valued Measure (POVM) components. This quantification provides a lower bound on the robustness of measurement-co…
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…
Based on the theory of quantum mechanics, intrinsic randomness in measurement distinguishes quantum effects from classical ones. From the perspective of states, this quantum feature can be summarized as coherence or superposition in a specific (classical) computational basis. Recently, by regarding coherence as a physical resource, Baumgratz et al.~present a comprehensive framework for coherence measures. Here, we propose a quantum coherence measure essentially using the intrinsic randomness of measurement. The proposed coherence measure provides an answer to the open question in completing th…
Quantifying coherence is a key task in both quantum mechanical theory and practical applications. Here, a reliable quantum coherence measure is presented by utilizing the quantum skew information of the state of interest subject to a certain broken observable. This coherence measure is proven to fulfill all the criteria (especially the strong monotonicity) recently introduced in the resource theories of quantum coherence. The coherence measure has an analytic expression and an obvious operational meaning related to quantum metrology. In terms of this coherence measure, the distribution of the …
In this paper we study an error correcting protocol that specifically derives its error correcting properties from elementary units of coherence. The entire protocol from beginning to end is performed using non-coherence increasing operations, resulting in the consumption of the input coherence, thus necessitating further quantum resources if one wishes to perform the protocol again. We show that even when the input quantum resource is just 1 coherent qubit, one may acquire partial protection from phase flip errors, and that this can be scaled up to protect against arbitrary qubit errors with …
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 …
Quantum coherence is a fundamental manifestation of the quantum superposition principle. Recently, Baumgratz \emph{et al}. [Phys. Rev. Lett. \textbf{113}, 140401 (2014)] presented a rigorous framework to quantify coherence from the view of theory of physical resource. Here we propose a new valid quantum coherence measure which is a convex roof measure, for a quantum system of arbitrary dimension, essentially using the generalized Gell-Mann matrices. Rigorous proof shows that the proposed coherence measure fulfills all the requirements dictated by the resource theory of quantum coherence measur…
Unlocking thermodynamic multitasking: Exploring the functioning of two-qubit engines through coherence and entanglement
本文研究双量子比特热机在双热浴和耗散环境下的运行，揭示纠缠与相干性对运行模式、信息流和效率的影响，并确定热机与制冷机模式的最优参数区域。
Coherence and correlation are key features of the quantum system. Quantifying these quantities are astounding task in the framework of resource theory of quantum information processing. In this article, we identify an affinity-based metric to quantify closeness between two states. Using this metric, we introduce a valid quantum coherence measure. It is shown that the affinity based coherence measure is bounded by that based on fidelity and trace distance. Further, we propose a bipartite quantum correlation measure based on the affinity metric. The connection between the quantum correlation of …
Coherence is a cornerstone of quantum theory and a prerequisite for the advantage of quantum technologies. In recent work, the notion of coherence with respect to a general quantum measurement (POVM) was introduced and embedded into a resource-theoretic framework that generalizes the standard resource theory of coherence. In particular, POVM-incoherent (free) states and operations were established. In this work, we explore features of this framework which arise due to the rich structure of POVMs compared to projective measurements. Moreover, we introduce a rigorous, probabilisitic framework fo…
In this paper we consider quantum resources required to maximize the mean values of any nontrivial quantum observable. We show that the task of maximizing the mean value of an observable is equivalent to maximizing some form of coherence, up to the application of an incoherent operation. As such, for any nontrivial observable, there exists a set of preferred basis states where the superposition between such states is always useful for optimizing a quantum observable. The usefulness of such states is expressed in terms of an infinitely large family of valid coherence measures which is then show…
Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
本文证明在渐近与催化变换两种操作设定下，任意低相干态均可任意好地转换为任意高相干态，且催化剂可将相干蒸馏速率从零提升至无限，揭示了相干资源理论区别于纠缠与量子热力学的独特性质。
Trade-off relations of geometric coherence
本文研究量子比特系统中几何相干性的权衡关系，通过量子态纯度导出其上限并建立相干性与混合度的互补关系，同时导出多测量基下的量子不确定性关系及纯态系综鉴别错误概率的互补关系。
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