We discuss coupling of violation of Bell's inequality and non-Kolmogorovness of statistical data in the EPR-Bohm experiment. We emphasize that nonlocalty and "death of realism" are only sufficient, but not necessary conditions of non-Kolmogorovness. There can be found other sufficient conditions of non-Kolmogorovness and, hence, violation of Bell's inequality. We find one important source of non-Kolmogorovness by analyzing axiomatics of quantum mechanics. We pay attention to the postulate (due to von Neumann and Dirac) on simultaneous measurement of quantum observables given by commuting operators. This postulate is criticized as nonphysical. We propose a new interpretation of the Born-von Neumann-Dirac rule for calculation of the joint probability distribution for such observables. It gets a natural physical interpretation by considering conditional measurement scheme. We use this argument (i.e., rejection of the postulate on simultaneous measurement to motivate non-Kolmogorovness of the probabilistic structure of the EPR-Bohm experiment.
This note is a part of my efforts for getting rid of nonlocality from quantum mechanics (QM). Quantum nonlocality is two faced Janus, one face is Lüders projection nonlocality, another face is Bell nonlocality. This paper is devoted to disillusion of the latter. The main casualty of Bell's model with hidden variables is that it straightforwardly contradicts to the Heinsenberg's uncertainty and generally Bohr's complementarity principles. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the mode…
The purpose of this comment is to show that a reinterpretation of the results from the Letter: "Physics and Metaphysics of Wigner's Friends: Even performed pre-measurements have no results" allows for reaching the conclusion "pre-measurements have no resul" [arXiv:2003.07464] based only on postulates of quantum mechanics without additional assumptions on irreversibility. Additionally, with supplementary reasoning based on Bell's theorem, one can show that unitary decoherence cannot be solely responsible for the quantum-to-classical transition, and an additional irreversibility model is require…
The present work is motivated by the question as to what aspect of correlation entailed by the two-qubit state serves as the appropriate quantitative resource for steering. To this end, considering Bell-diagonal states, suitable measures of simultaneous correlations in two and three complementary (mutually unbiased) bases are identified as the relevant resources for quantum steering. Quantitative relations between appropriate measures of quantum steering and the corresponding measures of simultaneous correlations in complementary bases are demonstrated which ensure that for two qubit steerable…
Several versions of quantum theory assume some form of localized collapse. If measurement outcomes are indeed defined by localized collapses, then a loophole-free demonstration of Bell non-locality needs to ensure space-like separated collapses associated with the measurements of the entangled systems. This collapse locality loophole remains largely untested, with one significant exception probing Diosi's and Penrose's gravitationally induced collapse hypotheses. I describe here techniques that allow much stronger experimental tests. These apply to all the well known types of collapse postulat…
The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell violation measurement is performed. From an observer in the laboratory frame, a Bell violation is observed due to entanglement swapping taking place, but in a moving frame the order of the measurements is reversed, and a Bell violation is observed even though no entanglement is present. Although the measurement results are identical, the wavefunctions for the two frames are different--- one is entangled and the other is not. Furthermore, for boosts in a p…
Trade-offs and experimental feasibility of nonlocal polygamy with two-outcome Bell inequalities
CRISP – Centre de Recerca Independent de sa Pobla（萨波拉独立研究中心）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文中心）；Center of Excellence in Artificial Intelligence, AGH University（AGH大学人工智能卓越中心）；Faculty of Physics, University of Warsaw（华沙大学物理学院）；Faculty of Physics and Applied Informatics, University of Lodz（罗兹大学物理与应用信息学院）
Comment on 'Improving the security of protocols of quantum key agreement solely using Bell states and Bell measurement'
设计一个量子密钥协商（QKA）协议一直是一个具有挑战性的任务，因为它必须同时考虑安全性和公平性。最近，Zhu等人（Quantum Inf Process 14（11）：4245-4254）指出，Shukla等人的QKA协议（Quantum Inf Process 13（11）：2391-2405）存在一些安全缺陷（导致参与者攻击）。此外，他们还提出了一项改进措施，以避免这些缺点。然而，该研究指出，改进的协议也遭受共谋攻击，即，协议中的两个不诚实的参与者可以合作来操纵最终密钥而不被发现。
Certification of quantum systems and operations is a central task in quantum information processing. Most current schemes rely on a tomography with fully characterised devices, while this may not be met in real experiments. Device characterisations can be removed with device-independent tests, it is technically challenging at the moment, though. In this letter, we investigate the problem of certifying entangled states and measurements via semi-quantum games, a type of non-local quantum games with well characterised quantum inputs, balancing practicality and device-independence. We first design…
We study scenarios which arise when two spatially-separated observers, Alice and Bob, are try to identify a quantum state sampled from several possibilities. In particular, we examine their strategies for maximizing both the probability of guessing their state correctly as well as their information gain about it. It is known that there are scenarios where allowing Alice and Bob to use LOCC offers an improvement over the case where they must make their measurements simultaneously. Similarly, Alice and Bob can sometimes improve their outcomes if they have access to a Bell pair. We show how LOCC …
Derivation and experimental violation of Bell-like inequalities involve the measurement of in-compatible observables. Simple complementarity forbids the existence of such joint probabilitydistribution. Moreover, the measurement of incompatible observables requires different experimen-tal procedures, which no necessarily must share a common joint statistics. In this work, we avoidthese difficulties by proposing a joint simultaneous measurement experiment. We can obtain theexact individual statistics of all the observables involved in the Bell inequalities after a suitable datainversion. A lack …
Composable simultaneous purification: when all communication scenarios reduce to spatial correlations
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；LIP6（LIP6实验室）；School of Informatics, University of Edinburgh（爱丁堡大学信息学院）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Grenoble INP（格勒诺布尔理工学院）；LIG（LIG实验室）
Bell's Inequality Violation (BIQV) with Non-Negative Wigner Function
一个贝尔不等式违反（BIQV）所允许的双模压缩态（TMSS），其维格纳函数是非负的，仅适用于动力学变量（DV）之间的相关性，不能通过本地隐变量（LHV）理论解释。对于Bell提出的EPR（Einstein，Podolsky and Rosen）态不允许BIQV与其Wigner代表态的非负性结合的观点，给出了明确的计算和解释.有人认为，贝尔定理不允许违反贝尔不等式内的一个本地隐藏变量理论取决于DV的有一个明确的价值-分配的LHV-即使当他们不能同时测量。分析使我们得出结论，BIQV是与赋予这些明确的价值观的DV的和{ \it不}与他们的地方属性。
Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. But the hypothesis from which Bell's inequalities are derived differ according to the probability space used to write them. The violation of Bell's inequalities can, alternatively, be explained assuming that the hidden variables do not exist at all, or that they exist but their values cannot be simultaneously assigned, or that the values can be assigned but joint probabilities cannot be properly defined, or that averages ta…
In 1862, George Boole derived an inequality for variables, now known as Boolean variables, that in his opinion represents a demarcation line between possible and impossible experience. This inequality forms an important milestone in the epistemology of probability theory and probability measures. In 1985 Leggett and Garg derived a physics related inequality, mathematically identical to Boole's, that according to them represents a demarcation between macroscopic realism and quantum mechanics. Their formalism, constructed for the magnetic flux of SQUIDS, includes general features and applies als…
Evaluating an expectation value of an arbitrary observable $A\in{\mathbb C}^{2^n\times 2^n}$ through naïve Pauli measurements requires a large number of terms to be evaluated. We approach this issue using a method based on Bell measurement, which we refer to as the extended Bell measurement method. This analytical method quickly assembles the $4^n$ matrix elements into at most $2^{n+1}$ groups for simultaneous measurements in $O(nd)$ time, where $d$ is the number of non-zero elements of $A$. The number of groups is particularly small when $A$ is a band matrix. When the bandwidth of $A$ is $k=O…
Exponentially decreasing critical detection efficiency for any Bell inequality
University of Gdansk（格但斯克大学）；Heinrich Heine University Düsseldorf（杜塞尔多夫海因里希·海涅大学）；Stockholm University（斯德哥尔摩大学）；International Centre for Theory of Quantum Technologies (ICTQT), University of Gdansk（格但斯克大学量子技术理论国际中心）；Universidad de Sevilla（塞维利亚大学）
Comment on "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometers"
在最近的一篇文章中，Hensen et al. [Nature 526，682（2015）]报道了一个复杂的贝尔实验，同时首次关闭了局部隐变量理论（HVT）的漏洞。作者声称，“地方现实主义”已被驳斥，在某些自然的假设。本评论的目的有两个。首先，它是敦促当地的HVTs，这是消除报告的实验类应指定比作者做的更详细。其次，有人认为，类的地方HVTs仍然生存是广泛和自然的。例如，描述“背景”字段的隐藏变量可以利用选择自由漏洞，这对于这种类型的隐藏变量来说是无法关闭的。这种基于背景的理论的动力学可以通过现有的系统来说明，例如来自流体力学。
