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arXiv:quant-ph/0702049 · Physical Review A

Demonstration of deterministic and high fidelity squeezing of quantum information

Jun–ichi Yoshikawa, Toshiki Hayashi, Takayuki Akiyama, Nobuyuki Takei, Alexander Huck, Ulrik L. Andersen, Akira Furusawa

Published Dec 11, 2007• 97 citations
arXivHTMLPDF

Abstract

By employing a recent proposal [R. Filip, P. Marek, and U.L. Andersen, Phys. Rev. A 71, 042308 (2005)] we experimentally demonstrate a universal, deterministic, and high-fidelity squeezing transformation of an optical field. It relies only on linear optics, homodyne detection, feedforward, and an ancillary squeezed vacuum state, thus direct interaction between a strong pump and the quantum state is circumvented. We demonstrate three different squeezing levels for a coherent state input. This scheme is highly suitable for the fault-tolerant squeezing transformation in a continuous variable quantum computer.

DOI
10.1103/physreva.76.060301

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By employing a recent proposal [R. Filip, P. Marek, and U.L. Andersen, Phys. Rev. A 71, 042308 (2005)] we experimentally demonstrate a universal, deterministic, and high-fidelity squeezing transformation of an optical field. It relies only on linear optics, homodyne detection, feedforward, and an ancillary squeezed vacuum state, thus direct interaction between a strong pump and the quantum state is circumvented. We demonstrate three different squeezing levels for a coherent state input. This scheme is highly suitable for the fault-tolerant squeezing transformation in a continuous variable quantum computer.
By employing at recent proposal (R. Filip, P. Marek and U.L. Andersen, Phys. Rev. A {\\bf 71}, 042308 (2005)), we experimentally demonstrate a high-fidelity, deterministic and universal squeezing transformation of a quantum state. The approach circumvents a direct interaction between a strong pump and the quantum state, but relies only on linear optics, homodyne detection, feedforward and an ancillary squeezed vacuum state. We demonstrate three different squeezing operations with attained fidelities of 94%, 89% and 78%.
Most quantum computation schemes propose encoding qubits in two-level systems. Others exploit the use of an infinite-dimensional system. In "Encoding a qubit in an oscillator" [Phys. Rev. A 64, 012310 (2001)], Gottesman, Kitaev, and Preskill (GKP) combined these approaches when they proposed a fault-tolerant quantum computation scheme in which a qubit is encoded in the continuous position and momentum degrees of freedom of an oscillator. One advantage of this scheme is that it can be performed by use of relatively simple linear optical devices, squeezing, and homodyne detection. However, we lack a practical method to prepare the initial GKP states. Here we propose the generation of an approximate GKP state by using superpositions of optical coherent states (sometimes called "Schrödinger cat states"), squeezing, linear optical devices, and homodyne detection.
One-way quantum computation is a very promising candidate to fulfill the capabilities of quantum information processing. Here we demonstrate an important set of unitary operations for continuous variables using a linear cluster state of four entangled optical modes. These operations are performed in a fully measurement-controlled and completely unconditional fashion. We implement three different levels of squeezing operations and a Fourier transformation, all of which are accessible by selecting the correct quadrature measurement angles of the homodyne detections. Though not sufficient, these linear transformations are necessary for universal quantum computation.
We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection, and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock state of $n\ensuremath{\leqslant}4$, and conjecture that this can be generalized for an arbitrary nnn Fock state. We describe our experimental demonstration of this scheme using coherent input states and measuring experimental fidelities that are only achievable using quantum resources.
We propose feasible implementations of basic continuous-variable (CV) interactions (squeezer, parametric amplifier, and quantum nondemolition interaction) between light modes without the requirement for in-line nonlinear couplings in a strongly pumped optical medium. The method is based entirely on linear optics, homodyne detection, and off-line squeezed ancillary states and therefore represents the CV analog of the measurement-induced nonlinearity approach, previously used in single-photon qubit experiments to probabilistically implement a controlled-NOT gate.
The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature components of two light modes. We experimentally demonstrate a QND sum gate, employing the scheme by R. Filip, P. Marek, and U. L. Andersen [Phys. Rev. A 71, 042308 (2005)10.1103/PhysRevA.71.042308], solely based on off-line squeezed states, homodyne measurements, and feedforward. The results are verified by simultaneously satisfying the criteria for QND measurements in both conjugate quadratures.