The concept of bilocality was introduced to study the correlations which
arise in an entanglement swapping scenario, where one has two sources which can
naturally taken to be independent. This additional constraint leads to stricter
requirements than simply imposing locality, in the form of bilocality
inequalities. In this work we consider a natural generalisation of the
bilocality scenario, namely the star-network consisting of a single central
party surrounded by $n$ edge parties, each of which shares an independent
source with the centre. We derive new inequalities which are satisfied by all
local correlations in this scenario, for the cases when the central party
performs (i) two dichotomic measurements (ii) a single Bell state measurement.
We demonstrate quantum violations of these inequalities and study both the
robustness to noise and to losses.Comment: 12 pages, 2 figure
Random access codes (RACs) are used by a party to, with limited communication, access an arbitrary subset of information held by another party. Quantum resources are known to enable RACs that break classical limitations. Here, we study quantum and classical RACs with high-level communication. We derive average performances of classical RACs and present families of high-level quantum RACs. Our results show that high-level quantum systems can significantly increase the advantage of quantum RACs over their classical counterparts. We demonstrate our findings in an experimental realization of a quantum RAC with four-level communication.
The goal of self-testing is to characterise an a priori unknown quantum system based solely on measurement statistics, i.e. using an uncharacterised measurement device. Here we develop self-testing methods for quantum prepare-and-measure experiments, thus not necessarily relying on entanglement and/or violation of a Bell inequality. We present noise-robust techniques for self-testing sets of quantum states and measurements, assuming an upper bound on the Hilbert space dimension. We discuss in detail the case of a 2 → 1 random access code with qubits, for which we provide analytically optimal self-tests. The simplicity and noise robustness of our methods should make them directly applicable to experiments. arXiv:1801.08520v2 [quant-ph]
The nature of quantum correlations in networks featuring independent sources of entanglement remains poorly understood. Here, focusing on the simplest network of entanglement swapping, we start a systematic characterization of the set of quantum states leading to violation of the so-called "bilocality" inequality. First, we show that all possible pairs of entangled pure states can violate the inequality. Next, we derive a general criterion for violation for arbitrary pairs of mixed twoqubit states. Notably, this reveals a strong connection between the CHSH Bell inequality and the bilocality inequality, namely that any entangled state violating CHSH also violates the bilocality inequality. We conclude with a list of open questions.
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