Tomographic test of Bell’s inequality for a time-delocalized single photon

Abstract

Time-domain balanced homodyne detection is performed on two well-separated temporal modes sharing a single photon. The reconstructed density matrix of the two-mode system is used to prove and quantify its entangled nature, while the Wigner function is employed for an innovative tomographic test of Bell's inequality based on the theoretical proposal by Banaszek and Wodkiewicz (Phys. Rev. Lett. 82, 2009Lett. 82, (1999). Provided some auxiliary assumptions are made, a clear violation of Banaszek-Bell's inequality is found.

Homodyne detection of non-Gaussian quantum steering

“…For the most complete descriptions of CV states, one generally resorts to quasi-probability distributions. However, it is highly challenging to use such objects to study quantum correlations (Bell inequalities for a notable exception [49,50]). The techniques in Section II B provide a useful way to analytically study the presence of metrologically useful non-Gaussian quantum steering based purely on the marginal of the Wigner function.…”

Coherent Superpositions of Photon Creation Operations and Their Application to Multimode States of Light

“…A total of 10 6 quadrature measurements for each mode, equally distributed over the range [0, π] of ϕ, allows the reconstruction of the two-mode density matrix of the quantum state truncated to a maximum number of Fock state contributions of n = 2, for a total of 3 4 = 81 density matrix elements. With a full reconstruction of the density matrix from homodyne quadrature measurements, the entanglement of this kind of state was clearly demonstrated [29,44].…”

Nonclassicality and Decoherence of Photon-added Thermo-invariant Coherent State

“…When the m-PATICS evolves in the thermal channel, the evolution of the density matrix can be described by [35] where κ represents the dissipative coefficient andn denotes the average thermal photon number of the environment. Whenn = 0, (17) reduces to the master equation describing the photon-loss channel [36,37]. In [38] Hu and Fan have derived the evolution formula of WF in laser process by using entangled state representation, the case in (17) as its a special example, i.e.,…”