In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of desirable properties: they agree with the standard quantum mechanical ones if the observables commute, they also depend continuously on the observables, and under unitary transformations they behave in a reasonable manner.
Twenty-five years after the invention of quantum teleportation, the concept of entanglement gained enormous popularity. This is especially nice to those who remember that entanglement was not even taught at universities until the 1990's. Today, entanglement is often presented as a resource, the resource of quantum information science and technology. However, entanglement is exploited twice in quantum teleportation. First, entanglement is the `quantum teleportation channel', i.e. entanglement between distant systems. Second, entanglement appears in the eigenvectors of the joint measurement that…
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 …
Classicality associated with joint measurability of operators manifests through a valid classical joint probability distribution on measurement outcomes. For qudits in dimension $n$, where $n$ is prime or power of prime, we present a method to construct unsharp versions of projective measurement operators which results in a geometric description of the set of quantum states for which the operators engender a classical joint probability distribution, and are jointly measurable. Specifically, within the setting of a generalised Bloch sphere in $n^2-1$ dimensions, we establish that the constructe…
A method for reconstructing joint photon-number distributions of twin beams from the experimental photocount histograms is suggested and experimentally implemented. Contrary to the standard reconstruction methods, it incorporates spatial noise reduction based on spatial pairing of photons. Superior performance of the method above the usual one for the maximum-likelihood approach is demonstrated.
We show an operational approach to bilocality with quasi-probability distributions and quasi-stochastic processes. This approach clearly demonstrates that negative probabilities are necessary to violate bilocality. It also highlights a subtle interplay between bilocal and local correlations and it can be easily extended to study N-locality.
Network Bell experiments give rise to a form of quantum nonlocality that conceptually goes beyond Bell's theorem. We investigate here the simplest network, known as the bilocality scenario. We depart from the typical use of the Bell State Measurement in the network central node and instead introduce a family of symmetric iso-entangled measurement bases that generalise the so-called Elegant Joint Measurement. This leads us to report noise-tolerant quantum correlations that elude bilocal variable models. Inspired by these quantum correlations, we introduce network Bell inequalities for the biloc…
Measurement-device-independent quantum key distribution (MDI-QKD) provides a method for secret communication whose security does not rely on trusted measurement devices. In all existing MDI-QKD protocols, the participant Charlie has to perform the Bell state measurement or other joint measurements. Here we propose an MDI-QKD protocol which requires individual measurements only. Meanwhile, all operations of the receiver Bob are classical, without the need for preparing and measuring quantum systems. Thus the implementation of the protocol has a lower technical requirement on Bob and Charlie.
We use hyper-entanglement to experimentally realize deterministic entanglement swapping based on quantum Elegant Joint Measurements. These are joint projections of two qubits onto highly symmetric, iso-entangled, bases. We report measurement fidelities no smaller than $97.4\%$. We showcase the applications of these measurements by using the entanglement swapping procedure to demonstrate quantum correlations in the form of proof-of-principle violations of both bilocal Bell inequalities and more stringent correlation criteria corresponding to full network nonlocality. Our results are a foray int…
When three pigeons are in two pigeonholes, at least two of them should be in the same pigeonhole, which is called pigeonhole principle. Recently Aharonov el al have shown that the principle can be violated in a pre-postselected quantum system. This violation sheds light on a new aspect of quantum correlations, as both of the pre and postselected states are separable states. To prove this kind of quantum correlations, a measurement apparatus must be arranged in entanglement to perform a joint measurement on the quantum system. In this paper we discuss how to design the state of entangled meters…
We analyze the validity of Bell and Kochen-Specker theorems under local (or noncontextual) realism but avoiding an assumption of the existence of a joint probability distribution for incompatible observables. We formulate a realist model which complies with this requirement. This is obtained by employing divergent sequences that nevertheless have marginals which are convergent. We find that under standard reasonable assumptions this possibility does not lead to a loophole of those theorems, by deriving a short of CHSH inequality valid for any finite size ensemble. Moreover, we analyze a Hardy'…
Heisenberg uncertainty relation in quantum mechanics sets the limit on the measurement precision of non-commuting observables, which prevents us from measuring them accurately at the same time. In some applications, however, the information are embedded in two or more non-commuting observables. On the other hand, quantum entanglement allows us to infer through Einstein-Podolsky-Rosen correlations two conjugate observables with precision better than what is allowed by Heisenberg uncertainty relation. With the help of the newly developed SU(1,1) interferometer, we implement a scheme to measure j…
In the standard quantum theory, one can measure precisely only a subset of the incompatible observables. It results in lack of a formal joint probability defining objective realism even if we accept nonlocal or certain faster-than-light interactions. We propose a construction of such realism extending the usual single-copy description to many copies, partially analogous to familiar many worlds. Failure of the standard single copy can be easily looked for experimentally. The copies should interact weakly at the macroscopic level, leading to effective collapse to a single identical pointer state…
Time-of-arrival distributions from position-momentum and energy-time joint measurements
从Arthurs和Kelly联合测量模型获得的位置-动量准分布被用于按照Kochaubrski和Wódkiewicz提出的量化程序间接获得“操作”到达时间（TOA）分布[Phys. Rev. A 60，2689（1999）]。该TOA分布不是时间协变的。通过使用其他相空间准分布的过程是广义的，并提供充分条件的时间协方差，限制可能的相空间准分布基本上维格纳函数，然而，提供了一个非正的TOA准分布。这些问题用另一方面不保证归一化的不同量化过程来补救。最后，Arthurs和Kelly测量模型的TOA和能量（有效的任意共轭变量时，其中一个变量是有界的从下面）的工作。这样得到的边际TOA分布是Kijowski分布的扭曲版本，是时间协变的、正的和归一化的。
We report successful joint operation of quantum and classical communications with shared hardware. Leveraging information learned from the classical DSP, low-noise quantum communications (0.009 SNU at 15 km) compatible with 15 Mbit/s QKD is demonstrated.
