Optimal Settings for Amplification and Estimation Of Small Effects In Postselected Ensembles

Abstract

To describe the pre-and postselected quantum ensembles, a complex quantity called the weak value of an operator is used. The weak value is highly controversial due to the fact that it is not bounded by the possible eigenvalues of the corresponding operator. Nevertheless, the obtaining of the anomalous weak value is regarded as a powerful technique in the quantum interferometry nowadays. Here it is shown that the postselection of a quantum system recovers a completely hidden interference effect in the measurement apparatus. Studying the interference pattern shows the optimal settings for the amplification and the parameter estimation. It also proves that the weak value is not an element of reality. Using single photons, it is investigated how a postselected photon can impart a 𝝅 phase shift (the peak of the amplification) to a photon interacting weakly with it in a nonlinear optical medium. The increasing of the degree of the entanglement lies behind the effectiveness of the postselection in the parameter estimation. In particular, arranging to postselect on pure entangled states can optimize the signal-to-noise ratio, allowing to achieve high-sensitive measurements using low input power.

Essential Role of Destructive Interference in the Gravitationally Induced Entanglement

“…In addition to what we have already seen here, the pure nonmaximally entangled state has been shown to be more efficient than the maximally entangled state in many applications. It can lead to the maximal violation of several Bell inequalities [32] or help in: reducing of the required detector efficiency for a loophole-free test of quantum nonlocality, [33,34] the simulation of entanglement, [35] increasing the efficiency in quantum cryptography, [36] optimal quantum estimation of phases, [17] and the complete and perfect quantum teleportation. [37] Not to forget that the non-maximally entangled state is also easier to prepare in the lab than the maximally entangled one.…”

“…Above all, I would like to refer to the recent paper [17] which can provide a photonic quantum simulation for the BMV proposal. It discusses the generation of a pure entangled state between two photons (initially prepared in a product state) using their cross-Kerr interaction in a non-linear optical medium.…”