Remote state preparation of spatial qubits

TL;DR

This paper explores remote state preparation of spatial qubits encoded in single photons, introducing a new measurement strategy that improves fidelity and purity over traditional methods, with potential applications in quantum communication.

Contribution

The authors propose a generalized measurement strategy for remote state preparation of spatial qubits that enhances performance metrics compared to standard spatial postselection.

Findings

The new strategy improves preparation probability, fidelity, and purity.

It increases classical communication and resource requirements.

Modified version can prepare arbitrary pure states of spatial qudits.

Abstract

We study the quantum communication protocol of remote state preparation (RSP) for pure states of qubits encoded in single photons transmitted through a double slit, the so-called spatial qubits. Two measurement strategies that one can adopt to remotely prepare the states are discussed. The first strategy is the well-known spatial postselection, where a single-pixel detector measures the transverse position of the photon between the focal and the image plane of a lens. The second strategy, proposed by ourselves, is a generalized measurement divided into two steps: the implementation of a two-outcome positive operator-valued measurement (POVM) followed by the spatial postselection at the focal plane of the lens by a two-pixel detector in each output of the POVM. In both cases we analyze the effects of the finite spatial resolution of the detectors over three figures of merit of the protocol, namely, the probability of preparation, the fidelity and purity of the remotely prepared states. It is shown that our strategy improves these figures compared with spatial postselection, at the expense of increasing the classical communication cost as well as the required experimental resources. In addition, we present a modified version of our strategy for RSP of spatial qudits which is able to prepare arbitrary pure states, unlike spatial postselection alone. We expect that our study may also be extended for RSP of the angular spectrum of a single-photon field as an alternative for quantum teleportation which requires very inefficient nonlinear interactions.