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arXiv:1604.08289 · Quantum Information Processing

Construction of quantum states with special properties by projection methods

Xuefeng Duan, Chi-Kwong Li, Diane Christine Pelejo

Published Nov 1, 2020• 1 citation
arXivHTMLPDF
DOI
10.1007/s11128-020-02881-5

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Projection operators associated with antiunitary time-reversal symmetry differ from the usual orthogonal projections encountered in Hilbert space. Operators that act in Fock space and project parts of a single-mode state of the electromagnetic field that can be identified as its quadratures are defined and their properties are verified by consideration of their action on single-mode coherent states. The fact that their construction involves, in an essential way, not one but two parameters is discussed and a weakened form of orthogonal projection that is specialized to a particular Fock state superposition is identified. The question of whether or not such orthogonal projections are universal is raised. In passing, it is noted that the possibility of classifying states as well as operators according to their time-reversal symmetry properties is relevant to the analysis of nonlinear wave interactions between waves with rationally related frequencies.
Methods proposed so far for measuring the canonical phase probability distribution of light are very difficult to implement. In particular the method of projection synthesis, which synthesizes a phase state projector, involves the use of a beam splitter and a specially engineered reference state. Here we extend this method by use of an additional beam splitter to synthesize phase sine and cosine operators. This allows the measurement of all the moments needed to construct the phase distribution. The reference state required for operator synthesis is, remarkably, just an easily prepared coherent state.