Experimental Violation of Multisetting Bell Inequalities for Qudits using Energy-Time Entangled Photons

The non-locality of nature is one of the most profound notions of quantum mechanics (QM) and is closely related to the phenomena of entanglement. The latter occurs when a quantum state of at least two particles cannot be written as independent single particle states. The manifestation of entanglement can be observed by correlations between two systems with no classical analogue. Moreover, these correlations are capable to violate linear constraints on experimental input-output correlations derived by means of a local hidden variable (LHV) model. Such constraints are well-known as Bell inequalities [1]. Experimentally, a large number of such Bell measurements have already been performed, mostly with d = 2 dimensional states, i.e. qubits, and dichotomic measurement settings and outcomes [2]. The experimental setup we use is capable of generating and manipulating entangled d-dimensional quantum states, denoted as qudits. This allows to study multisetting Bell inequalities which allow for deeper insights into the nature of non-locality and entanglement than their 2dimensional predecessors. A generic multisetting Bell experiment involves two parties Alice (A) and Bob (B) performing independent measurements Ax and By with settings x ∈ {0,1, ..., sA} and y ∈ {0, 1, ..., sB} on a shared two-qudit state. This yields measurement outcomes a ∈ {0, 1, ..., oA} for Alice and b ∈ {0, 1, ..., oB} for Bob. In this way, a set of jointconditional probabilities P(a, b|x , y) determines a Bell parameter I sAsB oAoB and the corresponding Bell inequality