相关论文: A new device-independent dimension witness and its…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional relationship between the dimension (say, $p$) and the sample size (say,…
Bell inequalities or Bell-like experiments are supposed to test hidden variable theories based on three intuitive assumptions: determinism, locality and measurement independence. If one of the assumptions of Bell inequality is properly…
We propose a single observable to witness the nonzero quantum discord of an unknown quantum state provided that we have four copies of the state. The expectation value of this observable provides a necessary and sufficient condition for…
We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities…
A recently proposed test of quantumness [R. Alicki and N. Van Ryn, J. Phys. A: Math. Theor. 41 062001 (2008)] is put into a broader mathematical and physical perspective. The notion of quantumness witness is introduced, in analogy to…
We analyze and compare the mathematical formulations of the criterion for separability for bipartite density matrices and the Bell inequalities. We show that a violation of a Bell inequality can formally be expressed as a witness for…
The violation of a Bell inequality is the paradigmatic example of device-independent quantum information: the nonclassicality of the data is certified without the knowledge of the functioning of devices. In practice, however, all Bell…
So far, various Bell type inequalities have been introduced to test the local realism in tripartite systems. In this article we consider a tripartite system with two measurements in each side and two outputs for each measurement. Then we…
Recently, a novel framework for semi-device-independent quantum prepare-and-measure protocols has been proposed, based on the assumption of a limited distinguishability between the prepared quantum states. Here, we discuss the problem of…
This paper introduces a new notion of dimensionality of probabilistic models from an information-theoretic view point. We call it the "descriptive dimension"(Ddim). We show that Ddim coincides with the number of independent parameters for…
The dimension is a key measure of complexity of partially ordered sets. Small dimension allows succinct encoding. Indeed if $P$ has dimension $d$, then to know whether $x \leq y$ in $P$ it is enough to check whether $x\leq y$ in each of the…
We present self-testing protocols to certify the presence of tensor products of Pauli measurements on maximally entangled states of local dimension $2^n$ for $n\in\mathbb{N}$. This provides self-tests of sets of informationally complete…
The concept of self-testing (or rigidity) refers to the fact that for certain Bell inequalities the maximal violation can be achieved in an essentially unique manner. In this work we present a family of Bell inequalities which are maximally…
We consider a non-contextual inequality in the sequential measurement scenario and derive the optimal quantum violation of it without assuming the dimension of the system. Since the measurement is dichotomic and the dimension of the quantum…
We explore quantum nonlocality in one of the simplest bipartite scenarios. Several new facet-defining Bell inequalities for the {[3 3 3] [3 3 3]} scenario are obtained with their quantum violations analyzed in details. Surprisingly, all…
Quantum communication devices, such as quantum repeaters, quantum memories, or quantum channels, are unavoidably exposed to imperfections. However, the presence of imperfections can be tolerated, as long as we can verify such devices retain…
Violation of Bell inequalities is an essential requirement for many quantum information and communication protocols. In high-dimensional systems, Bell inequality tests face the challenge of implementing genuinely multi-outcome measurements,…
We show how to detect entangled, bound entangled, and separable bipartite quantum states of arbitrary dimension and mixedness using geometric entanglement witnesses. These witnesses are constructed using properties of the Hilbert-Schmidt…
For testing the independence of two vectors with respective dimensions $p_1$ and $p_2$, the existing literature in high-dimensional statistics all assume that both dimensions $p_1$ and $p_2$ grow to infinity with the sample size. However,…
We prove that as conjectured by Ac\'{\i}n et al. [Phys. Rev. A 93, 040102(R) (2016)], two bits of randomness can be certified in a device-independent way from one bit of entanglement using the maximal quantum violation of Gisin's elegant…