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arXiv:quant-ph/0506269 · Physical Review Letters

Linear Optics Controlled-Phase Gate Made Simple

Nikolai Kiesel, Christian Schmid, Ulrich Weber, Rupert Ursin, Harald Weinfurter

Published Nov 18, 2005• 296 citations
arXivHTMLPDF

Abstract

Linear optics quantum logic gates are the best tool to generate multiphoton entanglement. Simplifying a recent approach [Phys. Rev. A 65, 062324 (2002); 66, 024308 (2002); Nature (London) 426, 264 (2003); Phys. Rev. Lett. 93, 080502 (2004)], we were able to implement the conditional phase gate with only one second-order interference at a polarization dependent beam splitter, thereby significantly increasing its stability. The improved quality of the gate is evaluated by analyzing its entangling capability and by performing full process tomography. The achieved results ensure that this device is well suited for implementation in various multiphoton quantum information protocols.

DOI
10.1103/physrevlett.95.210505

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Linear optics quantum logic gates are the best tool to generate multiphoton entanglement. Simplifying a recent approach [Phys. Rev. A 65, 062324 (2002); 66, 024308 (2002); Nature (London) 426, 264 (2003); Phys. Rev. Lett. 93, 080502 (2004)], we were able to implement the conditional phase gate with only one second-order interference at a polarization dependent beam splitter, thereby significantly increasing its stability. The improved quality of the gate is evaluated by analyzing its entangling capability and by performing full process tomography. The achieved results ensure that this device is well suited for implementation in various multiphoton quantum information protocols.
Linear optics two-qubit logic gates are essential tools in photonic quantum information. We describe a recently introduced simple conditional phase gate for photons, which relies on only one second order interference at a polarization dependent beam splitter, thereby making additional stability precautions dispensable. The improved quality of the gate is evaluated by performing full process tomography. The obtained process tomography data is fitted by a model based on experimental parameters of the setup which allows predictions on the performance of the gate in multi-photon experiments. .
Knill, Laflamme, and Milburn (KLM) proved that it is possible to build a scalable universal quantum computer using only linear-optics elements and conditional dynamics [Nature (London) {\bf 409}, 46 (2001)\cite{Knill}]. However, the practical realization of the quantum logic gate for the scheme is still technically difficult. A major difficulty is the requirement for sub-wavelength level stabilization of the interlocking interferometers. Following our recent experimental work[Phys. Rev. Lett.{\bf 92}, 017902 (2004)\cite{Sanaka2}], we describe a more feasible scheme to implement the gate that greatly reduces the experimental stability requirements. The scheme uses only polarizing beam splitters and half-wave plates.
We propose a linear optical scheme for direct realization of a nondestructive NNN-qubit controlled phase gate without resorting to a sequence of single- and two-qubit gates. The proposed setup involves linear optical elements, nonmaximally entangled pairs of photons, and multiphoton coincidence detection. To implement the scheme, physical qubits represented by the polarization states of single photons are probabilistically encoded into the two-photon states. Based on such encoding operation, a nondestructive NNN-qubit phase gate can be directly achieved by NNN-photon interference on an array of polarization beam splitters and NNN-photon coincidence detection.
We report the first experimental demonstration of an optical quantum controlled-NOT gate without any path interference, where the two interacting path interferometers of the original proposals have been replaced by three partially polarizing beam splitters with suitable polarization dependent transmittance and reflectance. The performance of the device is evaluated using a recently proposed method, by which the quantum process fidelity and the entanglement capability can be estimated from the 32 measurement results of two classical truth tables, significantly less than the 256 measurement results required for full quantum tomography.
Entanglement lies at the heart of quantum mechanics and challenged the intuition of physicists ever since it was discovered. At the same time, it is a powerful tool that serves as a key resource for quantum communication and quantum computation schemes. Many of these applications rely on multiparticle entanglement, whose description, generation and manipulation became therefore a very active field in theoretical and experimental quantum information science. The goals are here to classify and understand the different types of entanglement, to find new applications and to control and analyze the quantum states experimentally. In this thesis, the experimental observation and analysis of two different types of four-photon polarization entangled states is presented: The cluster state and the symmetric Dicke state with two excitations. For this purpose, experimental setups based on spontaneous parametric down conversion and linear optics with conditional detection were designed. They allowed to observe the cluster state with a fidelity of 74.1 % and the symmetric Dicke state with a fidelity of 84.4 %. The cluster state experiment included the development of a new instrument that is of interest for linear optics quantum logic in general: A probabilistic controlled phase gate that is, due to the simplification of a previous approach, highly stable and can actually be used in multiphoton experiments. The quality of the gate is evaluated by analyzing its entangling capability and by performing full process tomography. The achieved results demonstrate that this device is well suited for implementation in various multiphoton quantum information protocols. In order to study the observed quantum states, efficient analysis tools are introduced. It was possible to verify that essential properties of the ideal states are indeed reproduced in the experiment, among others, the presence of genuine four-partite entanglement. A particular focus is put on the behavior of the states under projective measurements and photon loss. Several new insights in their entanglement structure are revealed and verified experimentally. We further demonstrate properties that are characteristic for the entanglement classes of the states. These can be used to infer the applicability of the observed states for certain distributed quantum communication applications. The presented experiments are generic for the design of setups to observe cluster- and symmetric Dicke states with a higher number of photons. Furthermore, also the efficient non-tomographic methods for state analysis we employ can directly be generalized to experiments with higher qubit numbers, where the reduction of the experimental effort for state analysis is even more crucial.
Quantum logic gates are important for quantum computation and quantum information processing in numerous physical systems. Although time-bin qubits are suitable for quantum communication over optical fiber, many essential quantum logic gates for them have not yet been realized. Here, we demonstrated a controlled-phase (C-Phase) gate for time-bin qubits that uses a 2 × 2 optical switch based on an electro-optic modulator. A Hong–Ou–Mandel interference measurement showed that the switch could work as a time-dependent beam splitter with a variable splitting ratio. We confirmed that two independent time-bin qubits were entangled as a result of C-Phase gate operation with the switch.