Universal Continuous-Variable State Orthogonalizer and Qubit Generator

Open Access

Universal Continuous-Variable State Orthogonalizer and Qubit Generator

Antonio S. Coelho, Luca S. Costanzo, Alessandro Zavatta, Catherine Hughes, M. S. Kim, and Marco Bellini

Phys. Rev. Lett. 116, 110501 – Published 17 March 2016

Abstract

We experimentally demonstrate a universal strategy for producing a quantum state that is orthogonal to an arbitrary, infinite-dimensional, pure input one, even if only a limited amount of information about the latter is available. Arbitrary coherent superpositions of the two mutually orthogonal states are then produced by a simple change in the experimental parameters. We use input coherent states of light to illustrate two variations of the method. However, we show that the scheme works equally well for arbitrary input fields and constitutes a universal procedure, which may thus prove a useful building block for quantum state engineering and quantum information processing with continuous-variable qubits.

Received 30 July 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.110501

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Entanglement production Quantum information processing with continuous variables Quantum measurements Quantum state engineering

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Antonio S. Coelho^1,‡, Luca S. Costanzo^1,2, Alessandro Zavatta^1,2, Catherine Hughes³, M. S. Kim^3,*, and Marco Bellini^1,2,†

¹Istituto Nazionale di Ottica (INO-CNR), Largo E. Fermi 6, 50125 Florence, Italy
²LENS and Department of Physics, University of Firenze, 50019 Sesto Fiorentino, Florence, Italy
³QOLS, The Blackett Laboratory, Imperial College London, SW7 2AZ, United Kingdom

^*m.kim@imperial.ac.uk
^†bellini@ino.it
^‡Present address: Departamento de Engenharia, Centro Universitário UNINOVAFAPI, 64073-505 Teresina, Piauí, Brazil.

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand

Issue

Vol. 116, Iss. 11 — 18 March 2016

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Conceptual experimental scheme of the orthogonalizer and CV qubit generator based on photon addition by heralded stimulated PDC. A click in the single-photon-counting module (SPCM) normally heralds a single photon addition to the generic input $| ψ ⟩$ state. However, if the PDC idler mode is mixed with a coherent state $| β ⟩$ on a beam splitter (BS) prior to detection, a superposition of the photon creation operator and the identity with adjustable weights and phases can be obtained. In the actual experiments we used coherent states $| α ⟩$ as the input states and the operator superposition was implemented by using polarization modes (see the Supplemental Material [9] for details). HD is a time-domain homodyne detector triggered by SPCM clicks [11]. (b) Raw measured $x$ quadrature distributions (marginals of the Wigner function) for the input coherent states (ribbon-style curves) and for the corresponding results of the orthogonalization procedure (shaded areas) with $| α | = 0.5$ , 1.0, 2.0.
Reuse & Permissions
Figure 2
Wigner functions for different balanced superpositions of states $| α ⟩$ and $| α_{⊥} ⟩$ with $| α | = 1.0$ , as reconstructed by correcting for a detection efficiency of 70%. Panels (a) and (b) correspond to states $1 / \sqrt{2} (| α ⟩ \pm | α_{⊥} ⟩)$ and panels (c) and (d) correspond to states $1 / \sqrt{2} (| α ⟩ \pm i | α_{⊥} ⟩)$ , respectively. The experimental fidelities $F$ of the generated states to the ideal CV superpositions are also shown. Different values of $F$ are mainly connected to the different level of stability in the experimental superposition phase for the different states.
Reuse & Permissions
Figure 3
(a) Conceptual experimental scheme for the orthogonalizer based on the photon number operator. The HTBSs are high-transmittivity beam splitters; $C$ is a coincidence logic circuit. (b) Experimental homodyne detection traces for the original input coherent state $| α ⟩$ (left panel) and for the state obtained by the orthogonalization procedure (right panel). The input amplitude was $| α | = 0.78$ , and ten different values of the local oscillator phases were used. (c) Wigner functions of the input coherent state and of its orthogonal (a displaced single-photon Fock state) as reconstructed from the homodyne data after correcting for the limited (70%) detection efficiency. The same color scale as for Fig. 2 is used here.
Reuse & Permissions
Figure 4
Calculated Wigner functions of results of applying different orthogonalizing operations to cat and squeezed states. (a1) $| α ⟩ + | - α ⟩$ . (a2) ${\hat{O}}_{a^{†}} (| α ⟩ + | - α ⟩)$ .(a3) ${\hat{O}}_{n} (| α ⟩ + | - α ⟩)$ . (b1) $\hat{S} (ζ) | 0 ⟩$ . (b2) ${\hat{O}}_{a^{†}} \hat{S} (ζ) | 0 ⟩$ . (b3) ${\hat{O}}_{n} \hat{S} (ζ) | 0 ⟩$ . For plots (a1)–(a3) we take $α = 1$ , while for plots (b1)–(b3) we take $ζ = 0.4$ . Here, the normalization is omitted in the expressions, but the figures are properly normalized.
Reuse & Permissions

Physical Review Letters