Bell’s inequalities for three-qubit entangled states with white noise

Arpan Das, Chandan Datta, Pankaj Agrawal

Adán Cabello, Álvaro Feito, Antı́a Lamas-Linares

Contrary to the usual assumption that the experimental preparation of pure entangled states can be described by mixed states due to white noise, a more realistic description for polarization-entangled states produced by parametric down-conversion is that they are mixed states due to decoherence in a preferred polarization basis. This distinction between white and colored noise is crucial when we look for maximal violations of Bell's inequalities for two-qubit and two-qutrit entangled states. We find that violations of Bell's inequalities with realistic noise for polarization-entangled photons are extremely robust for colored noise, whereas this is not the case for white noise. In addition, we study the difference between white and colored noise for maximal violations of Bell's inequalities for three- and four-qubit entangled states.

Kateřina Jiráková, Antonín Černoch, Karel Lemr +2 more

We demonstrate a hierarchy of various classes of quantum correlations on experimentally prepared two-qubit Werner-like states with controllable white noise. Werner states, which are white-noise-affected Bell states, are prototypal examples for studying such a hierarchy as a function of the amount of white noise. We experimentally generate Werner states and their generalizations, i.e., partially entangled pure states affected by white noise. These states enable us to study the hierarchy of the following classes of correlations: separability, entanglement, steering in three- and two-measurement scenarios, and Bell nonlocality. We show that the generalized Werner states (GWSs) reveal fundamentally different aspects of the hierarchy compared to the Werner states. In particular, we find five different parameter regimes of the GWSs, including those steerable in a two-measurement scenario but not violating Bell inequalities. This regime cannot be observed for the usual Werner states. Moreover, we find threshold curves separating different regimes of the quantum correlations and find the optimal states which allow for the largest amount of white noise which does not destroy their specific quantum correlations (e.g., unsteerable entanglement). Thus, we could identify the optimal Bell-nondiagonal GWSs which are, for this specific meaning, more robust against the white noise compared to the Bell-diagonal GWSs (i.e., Werner states).

Jianxia Qi, Xin-Wei Zha, Dong Wang

Wiesław Laskowski, Tamás Vértesi, Marcin Wieśniak

We analyze robustness of correlations of the N -qubit GHZ and Dicke states against white noise admixture. For sufficiently large N , the Dicke states (for any number of excitations) lead to more robust violation of local realism than the GHZ states (e.g. for N > 8 for the W state). We also identify states that are the most resistant to white noise. Surprisingly, it turns out that these states are the GHZ states augmented with fully product states. Based on our numerical analysis conducted up to N = 8, and an analytical formula derived for any N parties, we conjecture that the three-qubit GHZ state augmented with a product of ( N − 3) pure qubits is the most robust against white noise admixture among any N -qubit state. As a by-product, we derive a single Bell inequality and show that it is violated by all pure entangled states of a given number of parties. This gives an alternative proof of Gisin’s theorem.

Su-Kuan Chu, Chen-Te Ma, Rong-Xin Miao +1 more