Manik Banik, Subhadipa Das, A. S. Majumdar
Incompatible measurements in quantum theory always lead to Einstein-Podolsky-Rosen (EPR)-Schrödinger steering. Channel steering which is a generalized notion of EPR-Schrödinger steering, has been introduced recently. Here we establish a connection between lack of joint measureability and channel steering.
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Contextuality is a signature of operational nonclassicality in the outcome statistics of an experiment. This notion of nonclassicality applies to a breadth of physical phenomena. Here, we establish its relation to two fundamental nonclassical entities in quantum theory; measurement incompatibility and steering. We show that each is necessary and sufficient the failure of operational contextuality. We exploit the established connection to contextuality to provide a novel approach to problems in measurement incompatibility and steering.
We investigate the connection between steering and contextuality in general probabilistic theories. We show that for a class of bipartite states the steerability of the state by given set of measurements is equivalent to non-existence of preparation noncontextual hidden variable model for certain restricted theory constructed from the given state and measurements. The connection between steering and contextuality is provided by the concept of incompatibility in restricted theories, which we also investigate.
The certification of Bell nonlocality or quantum steering implies the use of incompatible measurements. Here we make this connection quantitative. We show how to strengthen robustness-based steering and nonlocality quantifiers in order that they give strong lower bounds to previously proposed incompatibility quantifiers. Our results can be seen from two perspectives. On the one hand, they can be used to estimate how much steering or nonlocality can be demonstrated with a given set of measurements. On the other hand, they gives one-sided device-independent and device-independent ways of estimat…
The term Einstein-Podolsky-Rosen steering refers to a quantum correlation intermediate between entanglement and Bell nonlocality, which has been connected to another fundamental quantum property: measurement incompatibility. In the finite-dimensional case, efficient computational methods to quantify steerability have been developed. In the infinite-dimensional case, however, less theoretical tools are available. Here, we approach the problem of steerability in the continuous variable case via a notion of state-channel correspondence, which generalizes the well-known Choi-Jamiołkowski correspon…
Faithful certification of steering- and incompatibility-breaking channels
本文提出利用已有方法忠实认证量子信道是否破坏导引性或测量不相容性，并给出实验判据，解决了无限测量组合下的验证难题。
Steering is one of the most counter intuitive non classical features of bipartite quantum system, first noticed by Schrödinger at the early days of quantum theory. On the other hand measurement incompatibility is another non classical feature of quantum theory, initially pointed out by N. Bohr. Recently the authors of Refs. [\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.160402}{Phys. Rev. Lett. {\bf 113}, 160402 (2014)}] and [\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.160403}{Phys. Rev. Lett. {\bf 113}, 160403 (2014)}] have investigated the relation…
Characterisation and fundamental limitations of irreversible stochastic steering distillation
本文研究了不可逆场景下的随机导引提纯问题，给出了完整表征，将最大相对熵解释为最优滤波成功概率，并证明测量不相容性为随机导引提纯设定了基本限制。
A typical bipartite quantum protocol, such as EPR-steering, relies on two quantum features, entanglement of states and incompatibility of measurements. Noise can delete both of these quantum features. In this work we study the behavior of incompatibility under noisy quantum channels. The starting point for our investigation is the observation that compatible measurements cannot become incompatible by the action of any channel. We focus our attention to channels which completely destroy the incompatibility of various relevant sets of measurements. We call such channels incompatibility breaking,…
Quantum steering is the central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another one via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables measurement assemblage (SEO), first proposed to connect the problem of steerability with measurement incompatibility. We provide an e…
A General Class of Functionals for Certifying Quantum Incompatibility
本文提出了一种通用的功能泛函框架，用于构建无需优化的非线性不相容性见证者，适用于量子引导、测量和仪器不相容性的证明，并通过两个操作相关的泛函验证了其有效性。
Exact Incompatibility-Breaking Criterion for Unital Qubit Channels
该研究推导了单位量子比特信道的精确不相容性破坏判据，通过操控-联合可测性对应关系得到两量子比特态的相关边界，还为非单位量子比特信道构造父POVM并给出充分条件。
We show that connections between a degree of incompatibility of pairs of observables and the strength of violations of Bell's inequality found in recent investigations can be extended to a general class of probabilistic physical models. It turns out that the property of universal uniform steering is sufficient for the saturation of a generalised Tsirelson bound, corresponding to maximal violations of Bell's inequality. It is also found that a limited form of steering is still available and sufficient for such saturation in some state spaces where universal uniform steering is not given. The te…
Can every set of incompatible measurements lead to genuine multipartite steering?
研究探讨了多粒子场景中不相容测量与真实多粒子引导之间的关系，证明在单个未表征方的场景中，不相容性是真实多粒子引导的必要且充分条件。
Witnessing Quantum Incompatibility Structures in High-Dimensional Multimeasurement Systems
针对高维多测量场景中复杂量子不相容结构难以见证的问题，提出改进的量子态判别协议，通过分解相容结构并利用噪声鲁棒性界定不相容性，推导出理论界限并实验验证了其在量子导引等领域的应用。
Equivalence between simulability of high-dimensional measurements and high-dimensional steering
本研究揭示了以维度量化的量子操控与测量不相容性之间的关联，证明高维测量可模拟性与高维操控等价，提出仅用共享随机性和低维纠缠即可复现部分高维纠缠态关联的方法，并推导了测量不相容性维度检验判据。
Chained correlation inequalities involving pairwise correlations of qubit observables in the equatorial plane are constructed based on the positivity of a sequence of moment matrices. When a jointly measurable set of fuzzy POVMs is employed in first measurement of every pair of sequential measurements, the chained pairwise correlations do not violate the classical bound imposed by the moment matrix positivity. We identify that incompatibility of measurements is only necessary, but not sufficient, in general, for the violation of the inequality. On the other hand, there exists a one-to-one equi…
Quantum steering refers to the possibility for Alice to remotely steer Bob's state by performing local measurements on her half of a bipartite system. Two necessary ingredients for steering are entanglement and incompatibility of Alice's measurements. In particular, it has been recently proven that for the case of pure states of maximal Schmidt rank the problem of steerability for Bob's assemblage is equivalent to the problem of joint measurability for Alice's observables. We show that such an equivalence holds in general, namely, the steerability of any assemblage can always be formulated as …
We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.
All star-incompatible measurements can certify steering-based randomness
本文证明了所有星不相容测量都能生成基于操控的随机性，建立了两个概念的等价性，并引入了星不相容性的度量。
A collection of quantum channels is called incompatible if they cannot be obtained as marginals from a single channel. No-cloning theorem is the most prominent instance of incompatibility of quantum channels. We show that every collection of incompatible channels can be more useful than compatible ones as preprocessings in a state discrimination task with multiple ensembles of states. This is done by showing that the robustness of channel incompatibility which is a measure for incompatibility of channels exactly quantifies the maximum advantage in the state discrimination. We also show that in…
Destroying and Preserving Measurement Incompatibility over a Quantum Channel
本研究通过zonotopes和zonoids框架刻画量子信道对测量不相容性的破坏与保持，给出量子比特单信道破坏不相容性的充要条件，证明两个破坏信道并行时的超激活现象，并证明匹配维度下保持不相容性等价于酉变换。
We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is incompatible, one considers the set of measurements obtained by projection onto any strict subspace of fixed dimension. We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility: measurements that become compatible in every subspace, (ii) fully compressible incompatibility: measurements that remain incompatible in every…
Necessary and Sufficient Condition for Randomness Certification from Incompatibility
本文以测量不相容性刻画非零可认证量子随机性的充要条件，并将操控情形推广至 Bell 情形，证明链式不等式违反可作为可靠随机性见证。
Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely non-classical phenomenon provides a necessary ingredient in many quantum information tasks such violating a Bell Inequality or nonlocally steering part of an entangled state. In this paper, we characterize incompatibility in terms of programmable measurement devices and the general notion of quantum programmability. This refers to the temporal freedom a user has in issuing programs to a quantum device. For devices with a classical control and clas…
Incompatibility and nonlocality are not only of foundational interest but also act as important resources for quantum information theory. In the Clauser-Horne-Shimony-Holt (CHSH) scenario, the incompatibility of a pair of observables is known to be equivalent to Bell nonlocality. Here, we investigate these notions in the context of qubit channels. The Bell-CHSH inequality has a greater perspective--compared to any genuine tripartite nonlocality scenario--while determining the interplay between nonlocality breaking qubit channels and incompatibility breaking qubit channels. In the Bell-CHSH sce…
We introduce the concept of assemblage moment matrices, i.e., a collection of matrices of expectation values, each associated with a conditional quantum state obtained in a steering experiment. We demonstrate how it can be used for quantum states and measurements characterization in a device-independent manner, i.e., without invoking any assumption about the measurement or the preparation device. Specifically, we show how the method can be used to lower bound the steerability of an underlying quantum state directly from the observed correlation between measurement outcomes. Combining such devi…
Measurement incompatibility and quantum steering via linear programming
提出一种线性规划层次方法，高效计算任意维度测量集的不相容鲁棒性上下界，并应用于量子导引的判定，在量子比特情形下可处理数百个测量。
Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and conjugation, and we show that all pairs of sufficiently noisy quantum channels are compatible. The complement relation of incompatibility can be seen as a unifying aspect for many quantum features. We demonstrate that several phenomena, such as impossibility of universal broadcasting and unavoidable measurement disturbance, appear naturally in this framework.
We demonstrate how quantum optimal control can be used to enhance quantum resources for bipartite one-way protocols, specifically EPR-steering with qubit measurements. Steering is relevant for one-sided device-independent key distribution, the realistic implementations of which necessitate the study of noisy scenarios. So far mainly the case of imperfect detection efficiency has been considered; here we look at the effect of dynamical noise responsible for decoherence and dissipation. In order to set up the optimisation, we map the steering problem into the equivalent joint measurability probl…
Measurement incompatibility cannot be stochastically distilled
本文证明测量经滤波器处理无法增加不相容性，该结论适用于多种不相容性度量，还解决了EPR操控实验中局部滤波器最大操控性的显式计算问题，并推广到非物理映射。
We study incompatibility of measurements and its relation to steering and nonlocality in a class of finite dimensional general probabilistic theories (GPT).The basic idea is to represent finite collections of measurements as affine maps of a state space into a polysimplex and show that incompatibility is characterized by properties of these maps. We introduce the notion of an incompatibility witness and show its relation to incompatibility degree. We find the maximum incompatibility degree attainable by pairs of two-outcome quantum measurements and characterize state spaces for which incompati…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the incompatibility among three or more observables? Here we explore one possible route towards this goal through Heisenberg's uncertainty relations, which impose fundamental constraints on the measurement precisions for incompatible observables. Specifically, we quantify the incompatibility by the optimal state-independent bounds of additive variance-based uncertainty relat…
Quantum steering describes how local actions on a quantum system can affect another, space-like separated, quantum state. Lately, quantum steering has been formulated also for time-like scenarios and for quantum channels. We approach all the three scenarios as one using tools from Stinespring dilations of quantum channels. By applying our technique we link all three steering problems one-to-one with the incompatibility of quantum measurements, a result formerly known only for spatial steering. We exploit this connection by showing how measurement uncertainty relations can be used as tight stee…
In contrast with classical physics, in quantum physics some sets of measurements are incompatible in the sense that they can not be performed simultaneously. Among other applications, incompatibility allows for contextuality and Bell nonlocality. This makes of crucial importance developing tools for certifying whether a set of measurements posses a certain structure of incompatibility. Here we show that, for quantum or nonsignaling models, if the measurements employed in a Bell test satisfy a given type of compatibility, then the amount of violation of some specific Bell inequalities become li…
Preservability of Measurement Incompatibility: Purification, Activation, and a No-Go Theorem
本文在测量不相容性可保持性的资源理论中，引入基于鲁棒性的度量，证明预过滤无法从不兼容湮灭信道激活可保持性（不可行定理），但后过滤可随机激活，为量子信息处理提供实用框架。
Quantifying randomness with measurement incompatibility
研究制备与测量场景中测量不相容性与经典窃听者能力的权衡，利用广义鲁棒性通过半定规划限制窃听者策略，给出从不相容测量生成随机性协议，还推广到伊芙有量子记忆的场景，揭示导引性与随机性生成紧密联系。
Connection between the contextuality breaking and incompatibility breaking qubit channels
研究探讨了非局部性与测量不相容性在量子通道中的关联，通过非上下文性假设下的EBI违反揭示了上下文断裂与三重测量不相容性断裂的联系，证明了EBI上下文性断裂可导致CHSH非局域性断裂，但反之不成立。
Operational Coherent Measurements with Steering and Randomness
本文证明测量集合可用于半设备无关导引当且仅当其相干，并基于此提出一种无需纠缠认证且容忍任意低探测效率的量子随机数生成方案。
On compatibility of binary qubit measurements
本研究通过布尔超立方体函数及其傅里叶变换，完整几何表征任意有限无偏二元量子比特测量的联合可测量性，给出有偏情况必要条件，转化为紧导引不等式，提出二阶锥规划方法并证伪现有猜想。
A quantum observable and a channel are considered compatible if they form parts of the same measurement device, otherwise they are incompatible. Constrains on compatibility between observables and channels can be quantified via relations highlighting the necessary trade-offs between noise and disturbance within quantum measurements. In this paper we shall discuss the general properties of these compatibility relations, and then fully characterize the compatibility conditions for an unbiased qubit observable and a Pauli channel. The implications of the characterization are demonstrated on some …
Measurement incompatibility under loss
本研究针对连续变量系统在纯损耗下的测量不相容性问题，推导了损耗使n个测量相容的透射率阈值，设计了抗极端损耗的不相容测量组并验证其可行性，证明损耗无法破坏所有测量不相容性，为损耗场景下量子导引的实现提供了理论支撑。
Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of $k$ MUB in dimension $d$, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of $k=d+1$ MUB (given $d$ is a prime power). On the way, we also derive a general upper bound on the …
We derive general conditions for the compatibility of channels in general probabilistic theory. We introduce formalism that allows us to easily formulate steering by channels and Bell nonlocality of channels as generalizations of the well-known concepts of steering by measurements and Bell nonlocality of measurements. The generalization does not follow the standard line of thinking stemming from the Einstein-Podolsky-Rosen paradox, but introduces steering and Bell nonlocality as entanglement-assisted incompatibility tests. We show that all of the proposed definitions are, in the special case o…
One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even higher order dynamics. In this manuscript, we show that two seemingly different aspects of quantum incompatibility: the quantum marginal problem of states and the incompatibility on the level of quantum channels are in many-to-one correspondence. Importantly, as incompatibility of measurements is a special case of the latter, it also forms an instance of the…
We study a recently proposed Einstein-Podolsky-Rosen steering inequality [arXiv- 1412.8178 (2014)]. Analogous to Clauser-Horne-Shimony-Holt (CHSH) inequality for Bell nonlocality, in the simplest scenario, i.e., 2 parties, 2 measurements per party and 2 outcomes per measurement, this newly proposed inequality has been proved to be necessary and sufficient for steering. In this article, using an equivalence between measurement incompatibility (non joint measurability) and steering, we find the optimal violation amount of this inequality in quantum theory. Interestingly, the optimal violation am…
Relating CP divisibility of dynamical maps with compatibility of channels
本文研究动力学映射 CP 可分性与信道相容性的关系，证明 CP 可分映射下不相容鲁棒性单调非增，并基于该鲁棒性提出 CP 不可分性度量。
Incompatibility of quantum instruments
本文研究了量子仪器的不相容性，推导了其对诱导POVMs和信道的影响，揭示了其与无干扰的关系，并证明了仪器相容性与互补仪器后处理的等价性。
Measurement incompatibility is a distinguishing property of quantum physics and an essential resource for many quantum information processing tasks. We introduce an approach to verify the joint measurability of measurements based on phase-space quasiprobability distributions. Our results therefore establish a connection between two notions of non-classicality, namely the negativity of quasiprobability distributions and measurement incompatibility. We show how our approach can be applied to the study of incompatibility-breaking channels and derive incompatibility-breaking sufficient conditions …
High-dimensional quantum entanglement can give rise to stronger forms of nonlocal correlations compared to qubit systems, offering significant advantages for quantum information processing. Certifying these stronger correlations, however, remains an important challenge, in particular in an experimental setting. Here we theoretically formalise and experimentally demonstrate a notion of genuine high-dimensional quantum steering. We show that high-dimensional entanglement, as quantified by the Schmidt number, can lead to a stronger form of steering, provably impossible to obtain via entanglement …
Incompatibility of quantum measurements is of fundamental importance in quantum mechanics. It is closely related to many nonclassical phenomena such as Bell nonlocality, quantum uncertainty relations, and quantum steering. We study the necessary and sufficient conditions of quantum compatibility for a given collection of $n$ measurements in $d$-dimensional space. From the compatibility criterion for two-qubit measurements, we compute the incompatibility probability of a pair of independent random measurements. For a pair of unbiased random qubit measurements, we derive that the incompatibility…
Quantum steering can be detected via the violation of steering inequalities, which provide sufficient conditions for the steerability of quantum states. Here we discuss the converse problem, namely ensuring that a state is unsteerable, and hence Bell local. We present a simple criterion, applicable to any two-qubit state, which guarantees that the state admits a local hidden state model for arbitrary projective measurements. We find new classes of unsteerable entangled states, which can thus not violate any steering or Bell inequality. In turn, this leads to sufficient conditions for a state t…
Incompatibility as a resource for programmable quantum instruments
该研究从资源理论角度研究可编程量子仪器设备，明确无需量子存储器的自由PID对应不可操控信道集合，证明测量不相容性是资源，提出PID间的不相容性预序及转化充要条件，给出不相容性的操作表征与半设备无关测试。
Incompatibility of quantum devices is one of the cornerstones of quantum theory, and the incompatibility of quantum measurements and channels has been linked to quantum advantage in certain information theoretic tasks. In this work, we focus on the less well-explored question of the incompatibility of quantum instruments, that is, devices that describe the measurement process in its entirety, accounting for both the classical measurement outcome and the quantum post-measurement state. In particular, we focus on the recently introduced notion of parallel compatibility of instruments, which has …
We introduce a new incompatibility criterion for quantum channels, based on the notion of (quantum) Fisher information. Our construction is based on a similar criterion for quantum measurements put forward by H.~Zhu. We then study the power of the incompatibility criterion in different scenarios. Firstly, we prove the first analytical conditions for the incompatibility of two Schur channels. Then, we study the incompatibility structure of a tuple of depolarizing channels, comparing the newly introduced criterion with the known results from asymmetric quantum cloning.
Einstein-Podolsky-Rosen steering paradox "2=1'' for $N$ qubits
本文提出EPR导引悖论“2=1”，证明在纯态和测量条件满足时，该矛盾对任意$N$量子比特态成立，并给出实例分析。
We introduce the notion of incompatibility witness for quantum channels, defined as an affine functional that is non-negative on all pairs of compatible channels and strictly negative on some incompatible pair. This notion extends the recent definition of incompatibility witnesses for quantum measurements. We utilize the general framework of channels acting on arbitrary finite dimensional von Neumann algebras, thus allowing us to investigate incompatibility witnesses on measurement-measurement, measurement-channel and channel-channel pairs. We prove that any incompatibility witness can be impl…
The incompatibility of quantum channels in general probabilistic theories
本文针对一般概率理论中复合系统定义不唯一的问题，引入最小张量相容性与近量子相容信道对概念，通过量子比特含噪恒等信道实验，证明三者相容集合存在严格包含关系。
Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
本文研究了量子测量不相容性与非定域性的关系，证明了任何不相容测量集合均可演示EPR导向，表明两者等价；同时通过展示不违反Bell不等式的不相容测量集合，证明了Bell非定域性与联合可测性不等价。
Spatial Incompatibility Witnesses for Quantum Temporal Correlations
本文基于伪密度矩阵形式提出空间不相容见证框架，用于认证量子时间关联，证明测量扰动可增强时间关联认证效果。
Some quantum measurements can not be performed simultaneously, i.e. they are incompatible. Here we show that every set of incompatible measurements provides an advantage over compatible ones in a suitably chosen quantum state discrimination task. This is proven by showing that the Robustness of Incompatibility, a quantifier of how much noise a set of measurements tolerates before becoming compatible, has an operational interpretation as the advantage in an optimally chosen discrimination task. We also show that if we take a resource-theory perspective of measurement incompatibility, then the g…
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