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arXiv:2303.11484 · Physical Review Research

Asymptotically deterministic robust preparation of maximally entangled bosonic states

Matteo Piccolini, Vittorio Giovannetti, Rosario Lo Franco

Published Jan 19, 2024• 6 citations

Abstract

We introduce a theoretical scheme to prepare a pure Bell singlet state of two bosonic qubits, in a way that is robust under the action of arbitrary local noise. Focusing on a photonic platform, the proposed procedure employs passive optical devices and a polarization insensitive, nonabsorbing, parity check detector in an iterative process which achieves determinism asymptotically with the number of repetitions. Distributing the photons over two distinct spatial modes, we further show that the elements of the related basis composed of maximally entangled states can be divided in two groups according to an equivalence based on passive optical transformations. We demonstrate that the parity check detector can be used to connect the two sets of states. We thus conclude that the proposed protocol can be employed to prepare any pure state of two bosons which are maximally entangled in either the internal degree of freedom (Bell states) or the spatial mode (NOON states). Published by the American Physical Society 2024

DOI: 10.1103/physrevresearch.6.013073

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Linear-optical-based quantum information processing has attached much attention since photon is an ideal medium for transmitting quantum information remotely. Until now, there are some important works in quantum state remote preparation, the method for reconstructing quantum state deterministically via linear optics. However, most of the methods are protocols to prepare single-qubit states remotely via linear-optical elements. In this article, we investigate the methods to prepare two-qubit hybrid states remotely. We present a deterministic remote state preparation scheme for an arbitrary two-qubit hybrid state via a hyperentangled Bell state, resorting to linear-optical elements only. The sender rotates the spatial-mode state and polarization state of the hyperentangled photon respectively in accordance with his knowledge of the two-qubit hybrid state, and the receiver can reconstruct the original two-qubit hybrid state by applying appropriate recovery operations. Moreover, we discuss the remote state preparation scheme for the two-qubit hybrid state via partially hyperentangled Bell state.

We implement experimentally a deterministic method to prepare and measure the so-called single-photon two-qubit entangled states or single-photon Bell states, in which the polarization and the spatial modes of a single photon each represent a quantum bit. All four single-photon Bell states can be easily prepared and measured deterministically using linear optical elements alone. We also discuss how this method can be used for the recently proposed single-photon two-qubit quantum cryptography scheme.

We propose a deterministic remote state preparation scheme for photon polarization qubit states, where entanglement, local operations, and classical communication are used. By consuming one maximally entangled state and two classical bits, an arbitrary (either pure or mixed) qubit state can be prepared deterministically at a remote location. We experimentally demonstrate the scheme by remotely preparing

12

pure states and

6

mixed states. The fidelities between the desired and achieved states are all higher than

0.99

and have an average of

0.9947

.

We report an experimental implementation of deterministic preparation and measurement of single-photon two-qubit entangled states, in which the polarization and the spatial modes of a single-photon each represent a quantum bit. It is demonstrated that all four single-photon two-qubit entangled states (Bell states) can be easily prepared and measured deterministically using linear optical elements alone. We also discuss how this scheme can be used for implementing recently proposed single-photon two-qubit quantum cryptography.