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International Conference on Quantum Information

A General Linear-Optical Quantum State Generator

Dmitry B. Uskov, Nickolas M. VanMeter, Pavel Lougovski, Jonathan P. Dowling, Jens Eisert, Konrad Kieling

Published Jan 1, 2007• 0 citations
Publisher

Abstract

Linear-optical quantum state generator prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and post-selection using photon counters. We solve the mathematical problem of constucting a generator for a desired state.
DOI
10.1364/icqi.2007.ithb5

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A major challenge in photonic quantum technologies is developing strategies to prepare suitable discrete-variable quantum states using simple input states, linear optics, and auxiliary photon measurements to identify successful outcomes. Fundamentally, this challenge arises from the lack of strong non-linearities on the single-photon level, meaning that photonic state preparation based on linear optics cannot benefit from the deterministic gate-based approach available to other physical platforms. Instead, the preparation of quantum states can be probabilistically implemented using single photons, linear-optical networks, and photon detection. However, determining whether an input state can be transformed into a target state using a specific measurement pattern - a problem that can be mapped to deciding the feasibility of a system of polynomial equations - is a complex problem in general. To solve it, we apply the Nullstellensatz Linear Algebra algorithm from algebraic geometry to quantum state generation; this can provide definitive no-go results by proving infeasibility when the state preparation task in question has no solution. We demonstrate this capability to validate and establish lower bounds on the physical resource requirements for the realization of several ubiquitous optical states and gates.