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arXiv:2501.02986 · Annalen der Physik

Bidirectional Controlled Quantum State Preparation in High‐Dimensional Quantum System

S. X. Du, Hai‐Rui Wei

Published Jan 6, 2025• 3 citations
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Abstract

Abstract High‐dimensional quantum system exhibits unique advantages over the qubit system in some quantum information processing tasks. A program is presented for implementing deterministic bidirectional controlled remote quantum state preparation (BCRSP) in arbitrary ‐dimensional (quNit) system. By introducing two generalized Greenberger–Horne–Zeilinger (GHZ) states as quantum channels, two communication parties can simultaneously prepare a single‐particle high‐dimensional state at each other's site under the control of Charlie. Compared with the previous counterparts, the significant advantage of our scheme is that the high‐dimensional CNOT operations are not required. Moreover, the performance of this scheme is evaluated. The evaluation of the performance shows that if the quNit is encoded in the spatial mode of single photons, this scheme can be accomplished solely using only linear optical elements.

DOI
10.1002/andp.202400360

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Abstract A high‐dimensional system, so‐called quNit (‐level quantum system with ), provides several unique advantages, and high‐precision manipulation of arbitrary single‐quNit is demonstrated. In this study, a program to construct arbitrary qubit‐quNit quantum computation up to a global phase, and an efficient construction that requires single‐particle and generalized controlled (GCX) gates in the worst case are proposed. Moreover, by encoding the computing basis in polarization and spatial degrees of freedom of a single‐photon state, the optical architectures to implement the elementary‐gate library GCX, single‐partite rotation in a high‐dimension system are designed using linear optics. The necessary single‐photon polarization state and flexibility of linear optical elements make the quantum circuit feasible with current experimental technologies.