High-dimensional Bell test for a continuous variable state in phase space and its robustness to detection inefficiency

We propose a scheme for testing high-dimensional Bell inequalities in phase space. High-dimensional Bell inequalities can be recast into the forms of a phase-space version using quasiprobability functions with the complex-valued order parameter. We investigate their violations for two-mode squeezed states while increasing the dimension of measurement outcomes, and finally show the robustness of high-dimensional tests to detection inefficiency.Comment: 8 pages, 2 figures; title and abstract changed, published versio

On Bell inequality violations with high-dimensional systems

Quantum correlations resulting in violations of Bell inequalities have generated a lot of interest in quantum information science and fundamental physics. In this paper, we address some questions that become relevant in Bell-type tests involving systems with local dimension greater than 2. For CHSH-Bell tests within 2-dimensional subspaces of such high-dimensional systems, it has been suggested that experimental violation of Tsirelson's bound indicates that more than 2-dimensional entanglement was present. We explain that the overstepping of Tsirelson's bound is due to violation of fair sampling, and can in general be reproduced by a separable state, if fair sampling is violated. For a class of Bell-type inequalities generalized to d-dimensional systems, we then consider what level of violation is required to guarantee d-dimensional entanglement of the tested state, when fair sampling is satisfied. We find that this can be used as an experimentally feasible test of d-dimensional entanglement for up to quite high values of d

Experimental test of high-dimensional quantum contextuality based on contextuality concentration

Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here we address this problem by identifying a family of noncontextuality inequalities whose maximum quantum violation grows with the dimension of the system. At first glance, this contextuality is the single-system version of an extreme form of multipartite Bell nonlocality. What is interesting is that the single-system version achieves the same degree of contextuality but using a Hilbert space of {\em lower} dimension. That is, contextualize "concentrates" as the degree of contextuality per dimension increases. We demonstrate the usefulness of this result by showing the experimental observation of contextuality in a single system of dimension seven. By simulating sequences of quantum ideal measurements in an all-optical setup using projective measurements on structured light, we report a violation of 68.7 standard deviations of the simplest of the noncontextuality inequalities identified. Our results advance the investigation of high-dimensional contextuality, its connection to the Clifford algebra, and its role in quantum computation.Comment: 7+5 pages, 4+2 figures. Comments are welcom

Demonstrating multilevel entanglement and optimal quantum measurements

Optimal generalised quantum measurements are important for quantum information applications in both photonic and solid state systems. However, until now, the implementations of such measurements have been optical. Entanglement is also a very important resource in quantum communication and information processing. However, highdimensional entangled states and corresponding Bell-inequality violations are challenging to detect and demonstrate experimentally. This thesis focuses on these two aspects of signal detection. A cavity quantum electrodynamics (QED) scheme to realise an optimised quantum measurement demonstrating the superadditivity of quantum channel capacity is proposed and analysed. The measurement is shown to be feasible using atoms in a cavity QED setup even in the presence of rather high levels of experimental errors. This is interesting because cavity QED realisations could potentially be more easily scaled to increase quantum coding gain. Experimental unambiguous discrimination between non-orthogonal states is also carried out for the first time in the solid state using the nuclear spin of a nitrogen atom associated with a defect in bulk diamond—an important step for implementations of solid-state quantum computing. This thesis presents a method for verifying entanglement dimension using only Bell inequality test measurements. It also shows experimental results demonstrating genuine eleven-dimensional two-photon orbital angular momentum (OAM) entanglement and violations of generalised Bell inequalities up to dimension twelve. The demonstrated highdimensional entanglement is potentially useful for closing the detection loophole in Belltest experiments and for real-world large-alphabet quantum-cryptography applications

Multidimensional quantum entanglement with large-scale integrated optics

The ability to control multidimensional quantum systems is key for the investigation of fundamental science and for the development of advanced quantum technologies. Here we demonstrate a multidimensional integrated quantum photonic platform able to robustly generate, control and analyze high-dimensional entanglement. We realize a programmable bipartite entangled system with dimension up to $15 \times 15$ on a large-scale silicon-photonics quantum circuit. The device integrates more than 550 photonic components on a single chip, including 16 identical photon-pair sources. We verify the high precision, generality and controllability of our multidimensional technology, and further exploit these abilities to demonstrate key quantum applications experimentally unexplored before, such as quantum randomness expansion and self-testing on multidimensional states. Our work provides a prominent experimental platform for the development of multidimensional quantum technologies.Comment: Science, (2018

Bell inequalities for three systems and arbitrarily many measurement outcomes

We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin Bell inequality. For a small number of outcomes, we verify that our inequalities define facets of the polytope of local correlations. We investigate the quantum violations of these inequalities, in particular with respect to the Hilbert space dimension. We provide strong evidence that the maximal quantum violation can only be reached using systems with local Hilbert space dimension exceeding the number of measurement outcomes. This suggests that our inequalities can be used as multipartite dimension witnesses.Comment: v1 6 pages, 4 tables; v2 Published version with minor typos correcte

A Zoology of Bell inequalities resistant to detector inefficiency

We derive both numerically and analytically Bell inequalities and quantum measurements that present enhanced resistance to detector inefficiency. In particular we describe several Bell inequalities which appear to be optimal with respect to inefficient detectors for small dimensionality d=2,3,4 and 2 or more measurement settings at each side. We also generalize the family of Bell inequalities described in Collins et all (Phys. Rev. Lett. 88, 040404) to take into account the inefficiency of detectors. In addition we consider the possibility for pairs of entangled particles to be produced with probability less than one. We show that when the pair production probability is small, one must in general use different Bell inequalities than when the pair production probability is high.Comment: 12 pages, revtex. Appendix completed, minor revision