Related papers: Maximal randomness expansion from steering inequal…

The ultimate random number generators are those certified to be unpredictable -- including to an adversary. The use of simple quantum processes promises to provide numbers that no physical observer could predict but, in practice, unwanted…

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…

The verification of quantum devices is an important aspect of quantum information, especially with the emergence of more advanced experimental implementations of computation and secure communication. Within this, the theory of…

Einstein-Podolsky-Rosen (EPR) steering is a quantum mechanical phenomenon that allows one party to steer the state of a distant party by exploiting their shared entanglement. It has potential applications in secure quantum communication. In…

We study a class of ergodic BSDEs related to PDEs with Neumann boundary conditions. The randomness of the drift is given by a forward process under weakly dissipative assumptions with an invertible and bounded diffusion matrix. Furthermore,…

A recent sequence of works, initially motivated by the study of the nonlocal properties of entanglement, demonstrate that a source of information-theoretically certified randomness can be constructed based only on two simple assumptions:…

EPR steering is an asymmetric form of correlations which is intermediate between quantum entanglement and Bell nonlocality, and can be exploited for quantum communication with one untrusted party. In particular, steering of continuous…

We analyse notion of independence in the EPR-Bohm framework by using comparative analysis of independence in conventional and frequency probability theories. Such an analysis is important to demonstrate that Bell's inequality was obtained…

We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…

Einstein-Podolsky-Rosen steering is a form of quantum nonlocality intermediate between entanglement and Bell nonlocality. Although Schr\"odinger already mooted the idea in 1935, steering still defies a complete understanding. In analogy to…

This document expands upon the relationship between discrete and continuous entropy given in (Phys. Rev. Lett. 110 130407), \Violating Continuous Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements". We provide a detailed…

We study a Markov process with two components: the first component evolves according to one of finitely many underlying Markovian dynamics, with a choice of dynamics that changes at the jump times of the second component. The second…

A large number of inequalities have been proposed for the detection of bipartite continuous variable entanglement and Einstein-Podolsky-Rosen steering. Many of these are based on either measured or inferred variances and are relatively…

In this paper we develop a method for investigating semi-device-independent randomness expansion protocols that was introduced in [Li et al., Phys. Rev. A $\mathbf{87}$, 020302(R) (2013)]. This method allows to lower-bound, with…

The generation of series of random numbers is an important and difficult problem. Appropriate measurements on entangled states have been proposed as the definitive solution, based on the impossibility of exploiting quantum non locality to…

Schr\"odinger held that a local quantum system has some objectively real quantum state and no other (hidden) properties. He therefore took the Einstein-Podolsky-Rosen (EPR) phenomenon, which he generalized and called `steering', to require…

Empirical divergence maximization (EDM) refers to a recently proposed strategy for estimating f-divergences and likelihood ratio functions. This paper extends the idea to empirical vector quantization where one seeks to empirically derive…

We study optimal control of PDEs under uncertainty with the state variable subject to joint chance constraints. The controls are deterministic, but the states are probabilistic due to random variables in the governing equation. Joint chance…

We derive two types of sets of higher-order conditions for bipartite entanglement in terms of continuous variables. One corresponds to an extension of the well-known Duan inequalities from second to higher moments describing a kind of…

The violation of a Bell inequality implies the existence of nonlocality, making device-independent randomness certification possible. This paper derives a tight upper bound for the maximal quantum violation of Gisin's elegant Bell…