George Jaroszkiewicz
We present a generalized POVM formalism for the calculation of quantum optics networks of arbitrary complexity and apply it in a detailed analysis of the Franson-Bell experiment. Our analysis suggests that when it comes to observations of quantum processes, laboratory apparatus cannot always be used according to classical principles.
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It is shown that the model introduced by Cabello et al. to criticize the Franson experiment suffers from the same weakness as the previous model introduced by Aerts et al. with the same purpose. It is also shown why we can assume with confidence that the Franson experiment does violate local realism.
Franson-type nonlocal correlation is a testing tool for Bell inequality violation using noninterfering interferometers, where coincidence measurements involve an interference fringe of g^((1)) correlation between noninterfering photon pairs. Like the Bell inequality, Franson correlation is also limited to a microscopic regime of entangled photon pairs. Here, randomness-based macroscopic Franson-type nonlocal correlation is presented using polarization-basis coherent superposition of laser light, where probabilistic randomness between bipartite orthonormal bases plays an important role for both…
There are many different definitions of what a Bell-Kochen-Specker proof with POVMs might be. Here we present and discuss the minimal proof on qubits for three of these definitions and show that they are indeed minimal.
A bipartite Bell inequality is derived which is maximally violated on the two-qubit state space if measurements describable by positive operator valued measure (POVM) elements are allowed rather than restricting the possible measurements to projective ones. In particular, the presented Bell inequality requires POVMs in order to be maximally violated by a maximally entangled two-qubit state. This answers a question raised by N. Gisin.
The two-photon interferometric experiment proposed by Franson [Phys. Rev. Lett. 62, 2205 (1989)] is often treated as a "Bell test of local realism". However, it has been suggested that this is incorrect due to the 50% postselection performed even in the ideal gedanken version of the experiment. Here we present a simple local hidden variable model of the experiment that successfully explains the results obtained in usual realizations of the experiment, even with perfect detectors. Furthermore, we also show that there is no such model if the switching of the local phase settings is done at a rat…
Recently, Vértesi and Bene [Phys. Rev. A. {\bf 82}, 062115 (2010)] derived a two-qubit Bell inequality, $I_{CH3}$, which they show to be maximally violated only when more general positive operator valued measures (POVMs) are used instead of the usual von Neumann measurements. Here we consider a general parametrization for the three-element-POVM involved in the Bell test and obtain a higher quantum bound for the $I_{CH3}$-inequality. With a higher quantum bound for $I_{CH3}$, we investigate if there is an experimental setup that can be used for observing that POVMs give higher violations in Bel…
We analyze some aspects of recently performed Franson-type experiments with entangled photon pairs aimed to test Bell's inequalities. We point out that quantum theory leads to the coincidence rate between detectors which includes in fact a dependence on the distance. We study this dependence and obtain that for large distances the correlation function vanishes. Therefore with taking into account the space parts of wave functions of photons for large distances quantum mechanical predictions are consistent with Bell's inequalities. We propose an experimental study of space dependence of correlat…
Coincidence detection is a key technique used in nonlocal quantum-correlation measurements to test Bell inequality violation between remotely separated local detectors. With individual uniform intensity of local measurements, the nonlocal correlation fringe is a mysterious quantum feature that cannot be achieved classically. Here, the coincidence detection is coherently investigated to understand the fundamental physics of the nonlocal correlation fringe via second-order quantum superposition between selected nonlocal measurement events. Because of the coherence feature of paired photons, the …
Franson's Bell experiment with energy-time entanglement [Phys. Rev. Lett. 62, 2205 (1989)] does not rule out all local hidden variable models. This defect can be exploited to compromise the security of Bell inequality-based quantum cryptography. We introduce a novel Bell experiment using genuine energy-time entanglement, based on a novel interferometer, which rules out all local hidden variable models. The scheme is feasible with actual technology.
A suitable generalized measurement described by a 4-element positive operator-valued measure (POVM) on each particle of a two-qubit system in the singlet state is, from the point of view of Einstein, Podolsky, and Rosen's (EPR's) criterion of elements of reality, equivalent to a random selection between two alternative projective measurements. It is shown that an EPR-experiment with a fixed POVM on each particle provides a violation of Bell's inequality without requiring local observers to choose between the alternatives. This approach could be useful for designing a loophole-free test of Bell…
We discuss the connection between the incompatibility of quantum measurements, as captured by the notion of joint measurability, and the violation of Bell inequalities. Specifically, we present explicitly a given a set of non jointly measurable POVMs $\mathcal{M}_A$ with the following property. Considering a bipartite Bell test where Alice uses $\mathcal{M}_A$, then for any possible shared entangled state $ρ$ and any set of (possibly infinitely many) POVMs $\mathcal{N}_B$ performed by Bob, the resulting statistics admits a local model, and can thus never violate any Bell inequality. This shows…
A Franson-type test of Bell inequalities by photons 10.9 km apart is presented. Energy-time entangled photon-pairs are measured using two-channel analyzers, leading to a violation of the inequalities by 16 standard deviations without subtracting accidental coincidences. Subtracting them, a 2-photon interference visibility of 95.5% is observed, demonstrating that distances up to 10 km have no significant effect on entanglement. This sets quantum cryptography with photon pairs as a practical competitor to the schemes based on weak pulses.
The violation of Bell's inequality requires a well-designed experiment to validate the result. In experiments using energy-time and time-bin entanglement, initially proposed by Franson in 1989, there is an intrinsic loophole due to the high postselection. To obtain a violation in this type of experiment, a chained Bell inequality must be used. However, the local realism bound requires a high visibility in excess of 94.63 percent in the time-bin entangled state. In this work, we show how such a high visibility can be reached in order to violate a chained Bell inequality with 6, 8 and 10 terms.
It is the purpose of the present contribution to demonstrate that the generalization of the concept of a quantum mechanical observable from the Hermitian operator of standard quantum mechanics to a positive operator-valued measure is not a peripheral issue, allegedly to be understood in terms of a trivial nonideality of practical measurement procedures, but that this generalization touches the very core of quantum mechanics, viz. complementarity and violation of the Bell inequalities.
Cabello has recently (in quant-ph/0210081) observed that ``...an EPR-experiment with a fixed POVM on each particle provides a violation of Bell's inequality without requiring local observers to choose between the alternatives.'' In this note I discuss the implications of this observation for tests of locality.
Here we propose an implementation of all possible Positive Operator Value Measures (POVMs) of two-photon polarization states. POVMs are the most general class of quantum measurements. Our setup requires linear optics, Bell State measurements and an entangled three-photon ancilla state, which can be prepared separately and in advance (or 'off-line'). As an example we give the detailed settings for a simultaneous measurement of all four Bell States for an arbitrary two-photon polarization state, which is impossible with linear optics alone.
The technological refinement of experimental techniques has recently allowed the generation of two-photon polarization-entangled states at low Earth orbit, which has been subsequently applied to quantum communications. This achievement paves the way to study the interplay between General Relativity and Quantum Mechanics in new setups. Here, we study the generation of two-photon energy-time entangled states via large scale Franson and Hugged interferometric arrays in the presence of a weak gravitational field. We show that for certain configurations of the arrays, an entangled state emerges as …
Bell Test of Photons from Electron-Positron Annihilation via POVM-based Compton Polarimetry
本文提出利用康普顿偏振度量和POVM框架研究高能光子偏振纠缠，通过多次交互逐步逼近理想投影测量，实现对CHSH不等式的实验违反。
In the derivation of local bound of a Bell's inequality, the response functions corresponding to the different outcomes of measurements are fixed by the relevant hidden variables irrespective of the fact if the measurement is unsharp. In the context of a recent result by Spekkens that tells even in an ontological model the unsharp observable cannot be assigned a deterministic response function, we derive a modified local bound of CHSH inequality in unsharp measurement scenario. We consider response function for a given POVM which is determined by the response functions of the relevant projecto…
We study how different types of quantum correlations can be established as the consequence of a generalized entanglement swapping protocol where starting from two Bell pairs (1, 2) and (3, 4), a general quantum measurement (denoted by a positive operator-valued measure or POVM) is performed on the pair (2, 3), which results in creating quantum correlation in (1, 4) shared between two spatially separated observers. Contingent upon using different kinds of POVMs, we show generation or destruction of different quantum correlations in the pairs (1, 4), (1, 2) and (3, 4). This thus reflects non-tri…
Secure and Efficient n-Qubit Entangled State Teleportation Using Partially Entangled GHZ Channels and Optimal POVM
针对特定n量子比特纠缠态，提出基于部分纠缠GHZ信道和最优POVM的量子隐形传态协议，实现无歧义态区分，降低经典通信成本，可集成传统协议并增强量子逐跳通信安全性。
Bell Inequality Violation with Vacuum-One-Photon Number Superposition States
本研究提出一种基于单量子点共振荧光的纠缠生成新方案，利用真空-单光子数叠加态经分束器退局域化实现时间箱纠缠，观测到贝尔不等式违反，简化了实验要求并为固态纠缠光子源提供可扩展路径。
The Franson interferometer, proposed in 1989 [J. D. Franson, Phys. Rev. Lett. 62:2205-2208 (1989)], beautifully shows the counter-intuitive nature of light. The quantum description predicts sinusoidal interference for specific outcomes of the experiment, and these predictions can be verified in experiment. In the spirit of Einstein, Podolsky, and Rosen it is possible to ask if the quantum-mechanical description (of this setup) can be considered complete. This question will be answered in detail in this paper, by delineating the quite complicated relation between energy-time entanglement experi…
Energy-time entanglement from a resonantly driven quantum dot three-level system
本文研究共振驱动量子点三能级系统的双激子级联发射，通过 Franson 干涉获得超过 Bell 界限的能量-时间纠缠可见度，并分析驱动强度、退相干和级联发射偏离的影响。
Analytic Qubit Separation between POVMs and Projective Measurements
该研究构造有理系数贝尔泛函，实现局域维度2下量子比特POVM与投影测量的解析分离，得到大于1/1000的认证间隙，还证明对应策略达到量子最优值。
Quantum bounds and device-independent security with rank-one qubit measurements
研究秩一量子比特POVM在设备无关协议中的作用，证明其能饱和Tsirelson不等式，从而计算猜测概率和条件熵，并通过实验验证了随机性认证方法。
I give a first characterization of the class of generalized measurements that can be exactly realized on a pair of qudits encoded in indistinguishable particles, by using only linear elements and particle detectors. Two immediate results follow from this characterization. (i) The Schmidt number of each POVM element cannot exceed the number of initial particles. This rules out any possibility of performing perfect Bell-measurements for qudits. (ii) The maximum probability of performing a generalized incomplete Bell-measurement is 1/2.
The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions. In recent years, the sharing ability of the Bell nonlocality has been extensively studied. The nonlocality of quantum network states is more complex. We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements, and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability, but different under …
Quantum discord is a measure based on local projective measurements which captures quantum correlations that may not be fully captured by entanglement. A change in the measurement process, achieved by replacing rank-one projectors with a weak positive operator-valued measure (POVM), allows one to define weak variants of quantum discord. In this work, we experimentally simulate the effect of a weak POVM on a nuclear magnetic resonance quantum information processor. The two-qubit system under investigation is part of a three-qubit system, where one of the qubits is used as an ancillary to implem…
The existence of incompatible measurements is a fundamental phenomenon having no explanation in classical physics. Intuitively, one considers given measurements to be incompatible within a framework of a physical theory, if their simultaneous implementation on a single physical device is prohibited by the theory itself. In the mathematical language of quantum theory, measurements are described by POVMs (positive operator valued measures), and given POVMs are by definition incompatible if they cannot be obtained via coarse-graining from a single common POVM; this notion generalizes noncommutati…
We study the distinguishability of bipartite quantum states by Positive Operator-Valued Measures with positive partial transpose (PPT POVMs). The contributions of this paper include: (1). We give a negative answer to an open problem of [M. Horodecki $et. al$, Phys. Rev. Lett. 90, 047902(2003)] showing a limitation of their method for detecting nondistinguishability. (2). We show that a maximally entangled state and its orthogonal complement, no matter how many copies are supplied, can not be distinguished by PPT POVMs, even unambiguously. This result is much stronger than the previous known on…
Entanglement cost of discriminating quantum states under locality constraints
本文研究局部约束下区分量子态的纠缠代价，引入谱PPT距离量化测量局域性并给出下界，同时建立上界，证明单个Bell态可辅助纯态最优区分任意其他态。
In 1960, the mathematician Ernst Specker described a simple example of nonclassical correlations which he dramatized using a parable about a seer who sets an impossible prediction task to his daughter's suitors. We revisit this example here, using it as an entree to three central concepts in quantum foundations: contextuality, Bell-nonlocality, and complementarity. Specifically, we show that Specker's parable offers a narrative thread that weaves together a large number of results, including: the impossibility of measurement-noncontextual and outcome-deterministic ontological models of quantum…
The nonlocality of certain quantum states can be revealed by using local filters before performing a standard Bell test. This phenomenon, known as hidden nonlocality, has been so far demonstrated only for a restricted class of measurements, namely projective measurements. Here we prove the existence of genuine hidden nonlocality. Specifically, we present a class of two-qubit entangled states, for which we construct a local model for the most general local measurements (POVMs), and show that the states violate a Bell inequality after local filtering. Hence there exist entangled states, the nonl…
Quantum theory violates Bell's inequality, but not to the maximum extent that is logically possible. We derive inequalities (generalizations of Cirel'son's inequality) that quantify the upper bound of the violation, both for the standard formalism and the formalism of generalized observables (POVMs). These inequalities are quantum analogues of Bell inequalities, and they can be used to test the quantum version of locality. We discuss the nature of this kind of locality. We also go into the relation of our results to an argument by Popescu and Rohrlich (Found. Phys. 24, 379 (1994)) that there i…
Compatibility of Generalized Noisy Qubit Measurements
本文研究了噪声对量子比特测量兼容性的影响，确定了使所有POVM兼容的临界可见度，并改进了两量子比特韦纳态的局部隐变量模型。
Entanglement Detection with Rotationally Covariant Measurements -- From Compton Scattering to Lemonade
本文提出了一种基于旋转协变测量的纠缠检测方法，通过推导POVMs并结合SDP技术，展示了极化光子纠缠检测的可行性，并通过柠檬水实验验证了其应用潜力。
Quantum teleportation provides a `bodiless' way of transmitting the quantum state from one object to another, at a distant location, using a classical communication channel and a previously shared entangled state. In this paper, we present a tripartite scheme for probabilistic teleportation of an arbitrary single qubit state, without losing the information of the state being teleported, via a four-qubit cluster state of the form $\left.|ϕ\right\rangle_{1234}=\left.α|0000\right\rangle+\left.β|1010\right\rangle+\left.γ|0101\right\rangle-η\left.|1111\right\rangle$, as the quantum channel, where t…
Anubuddhi: A Multi-Agent AI System for Designing and Simulating Quantum Optics Experiments
Anubuddhi通过多智能体系统实现自然语言提示下的量子光学实验设计与模拟，支持灵活数学表示，提升实验设计民主化。
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