Single-entity violation of Bell-CHSH inequality and no-signaling conditions

Silvio Paolo sorella

Diederik Aerts, Massimiliano Sassoli de Bianchi

We describe a simple experimental setting where joint measurements performed on a single (classical or quantum) entity can violate both the Bell-CHSH inequality and the marginal laws (also called no-signaling conditions). Once emitted by a source, the entity propagates within the space of Alice’s and Bob’s detection screens, with the measurements’ outcomes corresponding to the entity being absorbed or not absorbed in a given time interval. The violation of the marginal laws results from the fact that the choice of the screen on the side of Alice affects the detection probability on the side of Bob, and vice versa, and we show that for certain screen choices, the Bell-CHSH inequality can be violated up to its mathematical maximum. Our analysis provides a clarification of the mechanisms that could be at play when the Bell-CHSH inequality and marginal laws are violated in entangled bipartite systems, which would not primarily depend on the presence of a bipartite structure but on the fact that the latter can manifest as an undivided whole.

Andrew Stewart Caldin

FINDING: Bell/CHSH inequalities define the boundary between classical local-hidden-variable theories and quantum correlations; recent work (Buscemi) reformulates them as a unified family of "rules" covering entanglement and nonlocality, and new physical platforms (ballistic electrons in semiconductor quantum wires) are proposed as testbeds. MATH: - CHSH inequality (classical bound): |E(a,b) − E(a,b′) + E(a′,b) + E(a′,b′)| ≤ 2 - Quantum (Tsirelson) bound: same expression ≤ 2√2 ≈ 2.828 - Quantum/classical ratio: 2√2 / 2 = √2 ≈ 1.4142 - Maximal violation angle for singlet state: correlations E(a,b) = −a·b; optimal settings at 45° increments give S = 2√2 - General Bell functional: S = Σ_{x,y} w_{xy} P(a,b|x,y); local polytope bounded by facet inequalities; quantum set Q strictly contains local polytope L, strictly contained in no-signaling set NS - Buscemi's unification: inequalities expressed via conditional min-/max-entropy constraints — "new rules" generalize CHSH to entropy-based Bell Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Silvio Paolo sorella

Karol Bartkiewicz, Bohdan Horst, Karel Lemr +1 more

It is well known that the violation of Bell's inequality in the form given by Clauser, Horne, Shimony, and Holt (CHSH) in two-qubit systems requires entanglement, but not vice versa, i.e., there are entangled states which do not violate the CHSH inequality. Here we compare some standard entanglement measures with violations of the CHSH inequality (as given by the Horodecki measure) for two-qubit states generated by Monte Carlo simulations. We describe states that have extremal entanglement according to the negativity, concurrence, and relative entropy of entanglement for a given value of the CHSH violation. We explicitly find these extremal states by applying the generalized method of Lagrange multipliers based on the Karush-Kuhn-Tucker conditions. The found minimal and maximal states define the range of entanglement accessible for any two-qubit states that violate the CHSH inequality by the same amount. We also find extremal states for the concurrence versus negativity by considering only such states which do not violate the CHSH inequality. Furthermore, we describe an experimentally efficient linear-optical method to determine the highest Horodecki degree of the CHSH violation for arbitrary mixed states of two polarization qubits. By assuming to have access simultaneously to two copies of the states, our method requires only six discrete measurement settings instead of nine settings, which are usually considered.

Jeremy Karich