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Conference on Lasers and Electro-Optics

Hong-Ou-Mandel Cloning: Quantum copying without an ancilla

Irfan Ali Khan, John C. Howell

Published Jan 1, 2004• 2 citations
Publisher

Abstract

We report on the first experimental 1→2, ancilla-free, phase-covariant quantum cloner by utilizing Hong-Ou-Mandel interference to clone photon polarization states. Using only linear optics, this Fock state non-perturbative cloner is an ideal BB84 evesdropping device.
DOI
10.1364/iqec.2004.img4

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arXiv:0711.4212•Physical Review A•May 7, 2008•14 citations
In this paper we report an experimental realization of an ancilla-free $1\ensuremath{\rightarrow}2$ phase-covariant quantum cloner. The cloner is realized by interfering a linearly polarized photon, which we wish to clone with a circularly polarized photon at a beam splitter. The two-photon effect can be understood in light of Hong-Ou-Mandel interference. The fidelity of the cloner was measured as $0.829\ifmmode\pm\else\textpm\fi{}0.008$ for the 0∕900∕900∕90 basis and $0.835\ifmmode\pm\else\textpm\fi{}0.006$ for the 45∕13545∕13545∕135 basis, which is in good agreement with the theoretical prediction of 5∕65∕65∕6 fidelity. The experimental scheme is straightforward and has a high cloning success rate.
We present the results of a linear optics photonic implementation of a quantum circuit that simulates a phase covariant cloner. Input polarization qubit states are cloned into path qubit states of the same photon, which is identified as a potential eavesdropper in a quantum key distribution protocol. The device has the flexibility to simulate optimal and non-optimal cloning machines, as well as mirrored versions that optimally clone states on either the northern or southern hemispheres of the Bloch sphere. We experimentally simulate the effect of a single 1→21\rightarrow 21→2 cloner, as well as the action of a random sequence of the original cloner and its mirrored version. This procedure allows the eavesdropper to mitigate the amount of noise added to the original copy and therefore to mask its presence.
After a brief introduction to the quantum no-cloning theorem and its link with the linearity and causality of quantum mechanics, the concept of quantum cloning machines is sketched, following, whenever possible, the chronology of the main results. The important classes of quantum cloning machines are reviewed, in particular state-independent and state-dependent cloning machines. The 1-to-2 cloning problem is then studied from a formal point of view, using the isomorphism between completely positive maps and operators, which leads to the so-called double-Bell ansatz. This also yields an efficient numerical approach to quantum cloning, based on semidefinite programming methods. The derivation of the optimal N-to-M universal cloning machine in d dimensions is then detailed, as well as the notion of asymmetric cloning machines. In the second part of this review, the optical implementation of cloning machines is considered. It is shown that the universal cloning of photons can be achieved by parametric amplification of light or by symmetrization via the Hong-Ou-Mandel effect. The various experimental demonstrations of quantum cloning machines are reviewed. The cloning of orthogonally polarized photons is also considered, as well as the asymmetric and phase-covariant cloning of photons. Finally, the extension of quantum cloning to continuous variables is analyzed. The optimal cloning of coherent states of light by phase-insensitive amplification is explained, as well as the experimental realization of continuous-variable quantum cloning with linear optics, measurement, and feed-forward operations.
We present the experimental realization of optimal symmetric and asymmetric phase-covariant 1-->2 cloning of qubit states using fiber optics. The state of each qubit is encoded into a single photon which can propagate through two optical fibers. The operation of our device is based on one- and two-photon interference. We have demonstrated the creation of two copies for a wide range of qubit states from the equator of the Bloch sphere. The measured fidelities of both copies are close to the theoretical values and they surpass the theoretical maximum obtainable with the universal cloner.
We report on two optical realizations of the $1\ensuremath{\rightarrow}2$ asymmetric phase-covariant cloning machines for polarization states of single photons. The experimental setups combine two-photon interference and tunable polarization filtering, which enables us to control the asymmetry of the cloners. The first scheme involves a special unbalanced bulk beam splitter exhibiting different splitting ratios for vertical and horizontal polarizations, respectively. The second implemented scheme consists of a balanced fiber coupler where photon bunching occurs, followed by a free-space part with polarization filters. With this latter approach we were able to demonstrate very high cloning fidelities which are above the universal cloning limit.
A linear optical probabilistic scheme for the optimal cloning of a pair of orthogonally polarized photons is devised, based on single- and two-photon interferences. It consists in a partial symmetrization device realized with a modified unbalanced Mach-Zehnder interferometer, followed by two balanced beam splitters where the Hong-Ou-Mandel photon bunching occurs. This scheme has the advantage that it enables quantum cloning without the need for stimulated amplification in a nonlinear medium. It can also be modified so to make an optical two-qubit partial SWAP gate, thereby providing a potentially useful tool to linear optics quantum computing.