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Journal of Modern Optics

Parametric downconversion and optical quantum gates: two's company, four's a crowd

Marco Barbieri, Till J. Weinhold, B. P. Lanyon, Alexei Gilchrist, Kevin J. Resch, Marcelo Pereira de Almeida, Andrew G. White

Published Jan 20, 2009• 20 citations
Publisher

Abstract

We show that the primary cause of errors in a broad class of optical quantum-logic gates are due to the higher-order photon terms in parametric downconversion sources. A model describing real-life imperfections in these entangling gates is presented and tested in an experiment where we entangle dependent photons from the same downconversion source using a controlled-z gate, and measure the state tomographically. We find good agreement between the modelled and measured results. Our investigations demonstrate that, although small, these noise terms are amplified by the intrinsic non-determinism of the gates. It is worth considering alternative schemes based on weak nonlinearities to see if they are more resilient to this degradation.

DOI
10.1080/09500340802337374

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We show that the primary cause of errors in a broad class of optical quantum-logic gates are due to the higher-order photon terms in parametric downconversion sources. A model describing real-life imperfections in these entangling gates is presented and tested in an experiment where we entangle dependent photons from the same downconversion source using a controlled-z gate, and measure the state tomographically. We find good agreement between the modelled and measured results. Our investigations demonstrate that, although small, these noise terms are amplified by the intrinsic non-determinism of the gates. It is worth considering alternative schemes based on weak nonlinearities to see if they are more resilient to this degradation.
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Imperfect photon sources degrade the performance of interference-based linear-optical entangling gates. We derive a universal fidelity law for these gates in terms of two standard source metrics: Hong-Ou-Mandel visibility and second-order coherence. We model the multiphoton component as an arbitrary overlap between noise and signal photons. While different values of the signal-noise overlap produce different error structures, associated with different physical platforms, all result in the same fidelity law. We test the model on our actively synchronized CNOT-gate experiment and against published results across different platforms, with no free parameters. This framework turns source characterization into a unified benchmark for photonic quantum computing.
The photon-number distribution of an output state from a single-photon source using gated spontaneous parametric downconversion is analyzed in detail. For an improved experimental result of {P(0),P(1),P(2)}={0.59,0.40,0.009}, it is found that P(1) is restricted by the optical loss of the signal photon path (62%) and the cause of nonzero P(2) is the imperfection of the optical shutter for gating. A method by which to reconstruct the photon-number distribution via photon-counting measurement is also presented.
The use of quantum bits (qubits) in cryptography holds the promise of secure cryptographic quantum key distribution schemes. It is based usually on single-photon polarization states. Unfortunately, the implemented “qubits” in the usual weak pulse experiments are not true two-level systems, and quantum key distribution based on these imperfect qubits is totally insecure in the presence of high (realistic) loss rate. In this work, we investigate another potential implementation: qubits generated using a process of parametric downconversion. We find that, to first (two-photon) and second (four-photon) order in the parametric downconversion small parameter, this implementation of quantum key distribution is equivalent to the theoretical version.Once realistic measurements are taken into account, quantum key distribution based on parametric downconversion suffers also from sensitivity to extremely high (nonrealistic) losses. By choosing the small parameter of the process according to the loss rates, both implementations of quantum key distribution can in principle become secure against the attack studied in this paper. However, adjusting the small parameter to the required levels seems to be impractical in the weak pulse process. On the other hand, this can easily be done in the parametric downconversion process, making it a much more promising implementation.
We describe a laboratory demonstration of a quantum error correction procedure that can correct intrinsic measurement errors in linear-optics quantum gates. The procedure involves a two-qubit encoding and fast feed-forward-controlled single-qubit operations. In our demonstration the qubits were represented by the polarization states of two single-photons from a parametric down-conversion source, and the real-time feed-forward control was implemented using an electro-optic device triggered by the output of single-photon detectors.
Optical quantum computation was limited to a few photon applications such as quantum cryptography and partial teleportation until 2001. Then the possibility of performing arbitrary logic conditional on certain detection outcomes was introduced by Knill, Laflamme and Milburn ( Nature 2001 409 46). Simple circuits consisting of single photon sources, entangled pair sources, linear optical elements and high efficiency photon counting detectors can be used to develop probabilistic two-photon logic gates. Initially such gates show a low probability of success but can approach the success rate of deterministic (non-linear) logic at the cost of added complexity. These developments have led to the emergence of a novel field of research aimed at improving the efficiency of linear logic and developing the efficient sources and detectors for its implementation. This topical issue of Journal of Optics B: Quantum and Semiclassical Optics is devoted to recent advances in this field. Key to all linear optics gates is the interference effect between separate photons that have no previous history. In this issue we include the first experiment to show such an effect (Rarity et al ), on which many later experiments are based. These interference effects can then be used to entangle separate pairs of particles into higher order entangled states (Zou et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 119–121) and also to establish entanglement between matter qubits (Kok et al ). Quantum dot single photon sources suitable for linear optics quantum logic are discussed in the paper by Unitt et al while a waveguide source of pair photons is presented by Ducci et al . The difficulties in scaling linear optics quantum computing arise from the low success probabilities of the gates. Introducing a small amount of non-linearity could allow unit efficiency gates to be designed (Munro et al ) while large non-linearities generated by the collective effects in EIT could be used to implement a wide variety of quantum logic functions (Petrosyan). The development of algorithms suitable for optical implementation is addressed by Ellinas et al . Key contributors to this issue are collaborating in the project IST:38864 RAMBOQ which has a primary goal of developing linear optics computation tools and techniques.