Entanglement and non-locality of independent photons from mixed quantum and semiquantum sources

Jian-Wei Pan, Anton Zeilinger

Ralph Wiegner, Joachim von Zanthier, G. S. Agarwal

We quantitatively investigate the non-classicality and non-locality of a whole new class of mixed disparate quantum and semiquantum photon sources at the quantum-classical boundary. The latter include photon added thermal and photon added coherent sources, experimentally investigated recently by Zavatta et al. [Phys. Rev. Lett. 103, 140406 (2009)]. The key quantity in our investigations is the visibility of the corresponding photon-photon correlation function. We present explicit results on the violations of the Cauchy-Schwarz inequality - which is a measure of nonclassicality - as well as of Bell-type inequalities.

Charles Ci Wen Lim

Quantum nonlocality is a counterintuitive phenomenon that lies beyond the purview of causal influences. Recently, Bell inequalities have been generalized to the case of quantum inputs, leading to a powerful family of semiquantum Bell inequalities that are capable of detecting any entangled state. Here, we focus on a different problem and investigate how the local indistinguishability of quantum inputs and postselection may affect the requirements to detect semiquantum nonlocality. To this end, we consider a semiquantum nonlocal game based on locally indistinguishable qubit inputs, and derive its postselected local and quantum bounds by using a connection to the local distinguishability of quantum states. Interestingly, we find that the postselected local bound is independent of the measurement efficiency, and the achievable postselected Bell violation increases with decreasing measurement efficiency.

Thomas P. Pearsall

Andrew Stewart Caldin

FINDING: Bell/CHSH inequality tests reveal quantum non-locality; new Buscemi framework unifies entanglement tests via "semiquantum" games; ballistic-electron proposal extends tests to condensed matter. MATH: CHSH inequality: \( S = E(a,b) + E(a,b') + E(a',b) - E(a',b') \leq 2 \) (local hidden variables); quantum bound \( S_{\text{QM}} = 2\sqrt{2} \approx 2.828 \). Bell's original: \( |P(a,b) - P(a,b')| + |P(a',b) + P(a',b')| \leq 2 \). Buscemi's unification: replaces classical inputs with quantum states, yielding "semiquantum" Bell inequalities with tighter bounds (e.g., \( \leq 2 \) classical, \( 2\sqrt{2} \) quantum, but extended to arbitrary dimensions via \( 2\sqrt{d} \) for \( d \)-level systems). Ballistic electron proposal: entanglement via Coulomb coupling, requires only 5 gates — no new constants, but uses spin/charge degrees of freedom. CONNECTION: The quantum bound \( 2\sqrt{2} \) is the ratio \( 2\sqrt{2} \approx 2.828 \), which relates to the diagonal of a unit square Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Thomas P. Pearsall