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Unitary realizations of the ideal phase measurement

Buscemi, F, D'Ariano, G M, Sacchi, M F

We explicitly construct a large class of unitary transformations that allow to perform the ideal estimation of the phase-shift on a single-mode radiation field. The ideal phase distribution is obtained by heterodyne detection on two radiation modes after the interaction.

Apr 10, 20032 citations

Quantum Phase Measurement

Z. Hradil

Springer eBooksJan 1, 19951 citation

The issue of phases in quantum measurement theory

Arun Kumar Pati

Acta Physica Slovaca Reviews and TutorialsJan 1, 19993 citations

Nonunitary Gates Using Measurements Only

Daniel Azses, Jonathan Ruhman, Eran Sela

Measurement-based quantum computation (MBQC) is a universal platform to realize unitary gates, only using measurements that act on a preprepared entangled resource state. By deforming the measurement bases, as well as the geometry of the resource state, we show that MBQC circuits always transmit and act on the input state but generally realize nonunitary logical gates. In contrast to the stabilizer formalism that is often used for unitary gates, we find that ZX-calculus is an ideal computation method for these nonunitary gates. As opposed to unitary gates, nonunitary gates cannot be applied with certainty, due to the randomness of quantum measurements. We maximize the success probability of realizing nonunitary gates and discuss applications including imaginary time evolution, which we demonstrate on a noisy intermediate-scale quantum device.Measurement-based quantum computation (MBQC) is a universal platform to realize unitary gates, only using measurements that act on a preprepared entangled resource state. By deforming the measurement bases, as well as the geometry of the resource state, we show that MBQC circuits always transmit and act on the input state but generally realize nonunitary logical gates. In contrast to the stabilizer formalism that is often used for unitary gates, we find that ZX-calculus is an ideal computation method for these nonunitary gates. As opposed to unitary gates, nonunitary gates cannot be applied with certainty, due to the randomness of quantum measurements. We maximize the success probability of realizing nonunitary gates and discuss applications including imaginary time evolution, which we demonstrate on a noisy intermediate-scale quantum device.

arXiv:2312.17325Physical Review LettersDec 26, 20240 citations

Ideal Quantum Measurement

Springer eBooksDec 12, 20050 citations

Unitary equivalence between ideal and feasible phases

Masashi Ban

Unitary equivalence between the ideal and feasible phases is proven. The ideal phase can be described by the phase operator D${\mathrm{^}}_{\mathrm{RNS}}$, constructed from the relative-number states, and the feasible phase considered here is characterized by the Shapiro-Wagner phase operator D${\mathrm{^}}_{\mathrm{SW}}$. The unitary operator W^ satisfying D${\mathrm{^}}_{\mathit{S}\mathit{W}}$=W^D${\mathrm{^}}_{\mathrm{RNS}}$W^ $^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ and D${\mathrm{^}}_{\mathrm{RNS}}$=W^ $^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$D${\mathrm{^}}_{\mathrm{SW}}$W^ is derived. :Unitary equivalence between the ideal and feasible phases is proven. The ideal phase can be described by the phase operator D${\mathrm{^}}_{\mathrm{RNS}}$, constructed from the relative-number states, and the feasible phase considered here is characterized by the Shapiro-Wagner phase operator D${\mathrm{^}}_{\mathrm{SW}}$. The unitary operator W^ satisfying D${\mathrm{^}}_{\mathit{S}\mathit{W}}$=W^D${\mathrm{^}}_{\mathrm{RNS}}$W^ $^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ and D${\mathrm{^}}_{\mathrm{RNS}}$=W^ $^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$D${\mathrm{^}}_{\mathrm{SW}}$W^ is derived. :

Physical Review ASep 1, 199423 citations

Unitary realizations of the ideal phase measurement

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