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Journal of Experimental and Theoretical Physics Letters

Generation of a two-photon KLM quantum channel

Sergey A. Podoshvedov

Published Oct 1, 2005• 2 citations
Publisher

Abstract

As demonstrated by E. Knill et al. [Nature 409 , 46 (2001)], quantum teleportation and quantum logic gates with a success probability close to one can be implemented using only linear optical elements, additional photons, and post-selection. To do this, it is desirable to have special quantum channels in sight before quantum teleportation performance. Here, we propose an experimental arrangement to generate a two-photon KLM state different from the well-known Bell states. This two-photon KLM state can be used to enhance the success probability of the quantum teleportation of a one-mode quantum qubit from 0.5 up to 2/3.

DOI
10.1134/1.2142878

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•Nov 25, 2004•0 citations
As demonstrated by E. Knill et al. [Nature 409 , 46 (2001)], quantum teleportation and quantum logic gates with a success probability close to one can be implemented using only linear optical elements, additional photons, and post-selection. To do this, it is desirable to have special quantum channels in sight before quantum teleportation performance. Here, we propose an experimental arrangement to generate a two-photon KLM state different from the well-known Bell states. This two-photon KLM state can be used to enhance the success probability of the quantum teleportation of a one-mode quantum qubit from 0.5 up to 2/3.
We report an experimental preparation of the so-called Knill-Laflamme-Milburn states (KLM states) that have been known to have interesting properties related to quantum information processing. Our experiment has demonstrated successful preparation of entangled two-photon four-mode KLM states using spontaneous parametric down-conversion as a source of entangled photon pairs, linear optical components, and avalanche photodiodes for single-photon detection. We have verified the successful generation of KLM states by complete quantum state tomography.
In the previous chapter we developed some of the basic aspects of quantum information processing with single photons as qubits. Apart from noting the obvious benefit of using light for quantum communication, we identified some difficulties in manipulating quantum information that is encoded in photons. In particular, it is difficult to construct two-qubit gates for photonic qubits. In this chapter we will have to face this difficulty head-on in our discussion of quantum computation with single photons and linear-optical elements. The possibility of a quantum computer based on single photons, linear optics, and photon counting was demonstrated in a landmark paper by Knill, Laflamme, and Milburn in 2001. Their protocol is commonly referred to as the ‘ klm protocol’. In subsequent years, the klm protocol has been dramatically slimmed down in terms of complexity and the necessary resources to create the universal set of quantum gates. For pedagogical reasons we give the streamlined version here, and we briefly describe the original klm protocol in Appendix 2. We will make extensive use of the results in Section 1.4 about mode transformations, and Section 2.3 about cluster-state quantum computing. We start this chapter, however, with a description of linear-optical networks, and how they fail as deterministic quantum computers. In Section 6.2 we discuss the principle of post-selection, and how this can be used to create probabilistic gates with deterministic feed-forward control.
In recent years, there has been heightened interest in quantum teleportation, which allows for the transfer of unknown quantum states over arbitrary distances. Quantum teleportation not only serves as an essential ingredient in long-distance quantum communication, but also provides enabling technologies for practical quantum computation. Of particular interest is the scheme proposed by D. Gottesman and I. L. Chuang [(1999) Nature 402:390-393], showing that quantum gates can be implemented by teleporting qubits with the help of some special entangled states. Therefore, the construction of a quantum computer can be simply based on some multiparticle entangled states, Bell-state measurements, and single-qubit operations. The feasibility of this scheme relaxes experimental constraints on realizing universal quantum computation. Using two different methods, we demonstrate the smallest nontrivial module in such a scheme--a teleportation-based quantum entangling gate for two different photonic qubits. One uses a high-fidelity six-photon interferometer to realize controlled-NOT gates, and the other uses four-photon hyperentanglement to realize controlled-Phase gates. The results clearly demonstrate the working principles and the entangling capability of the gates. Our experiment represents an important step toward the realization of practical quantum computers and could lead to many further applications in linear optics quantum information processing.
One of the earliest proposals for implementing quantum computation was based on encoding each qubit in two optical modes, each containing exactly one photon. However, it is extremely difficult to unitarily couple two optical modes containing few photons. In 2001, Knill, Laflamme, and Milburn (KLM) found a way to circumvent this restriction and implement efficient quantum computation using only passive linear optics, photodetectors, and single photon sources. This efficient linear optical quantum computing (LOQC) is distinct from other linear optical schemes that are not efficiently scalable. The technological requirements for even the simplest gates in the KLM proposal initially seemed out of reach. However, Ralph, White, Munro and Milburn soon showed that, in principle, demonstrations of key gates and techniques could be achieved with current technology. The objective of the research undertaken in this project was to produce, in three years, a prototype two-qubit gate for photons using the KLM linear optics quantum computation approach, and to develop a blue-print for a multiple qubit device that might be implemented over a longer time scale. A non-deterministic two-qubit gate was demonstrated that operates with high fidelity. A number of key tasks were demonstrated using this gate, and several theoretical investigations of short, medium, and longer term issues for the LOQC approach were successfully completed.