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New Journal of Physics

The entanglement of the four-photon cluster state

Christoph Schmid, Nikolai Kiesel, Witlef Wieczorek, Harald Weinfurter

Published Jul 17, 2007• 12 citations
Publisher

Abstract

Measurement based quantum computation draws its power from the remarkable entanglement properties of the cluster states. This contribution analyses the entanglement and its persistency of an experimentally realized four-photon cluster state. We describe how spontaneous parametric down conversion together with linear optics quantum logic can be used for the experimental study.

DOI
10.1088/1367-2630/9/7/236

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Measurement based quantum computation draws its power from the remarkable entanglement properties of the cluster states. This contribution analyses the entanglement and its persistency of an experimentally realized four-photon cluster state. We describe how spontaneous parametric down conversion together with linear optics quantum logic can be used for the experimental study.
Entangled photons are a crucial resource for linear optical quantum communication and quantum computation. Besides the remarkable progress of photon state engineering using atomic memories (Kimble (2008); Yuan et al. (2008)) the majority of current experiments is based on the production of photon pairs in the process of spontaneous parametric down-conversion (SPDC), where the entangled photon pair is concluded from post-selection of randomly occurring coincidences. Here we present new insights into the heralded generation of photon states (Barz et al. (2010); Wagenknecht et al. (2010)) that are maximally entangled in polarization (Schrodinger (1935)) with linear optics and standard photon detection from SPDC (Kwiat et al. (1995)). We utilize the down-conversion state corresponding to the generation of three pairs of photons, where the coincident detection of four auxiliary photons unambiguously heralds the successful preparation of the entangled state (Śliwa & Banaszek (2003)). This controlled generation of entangled photon states is a significant step towards the applicability of a linear optics quantum network (Nielsen & Chuang (2000)), in particular for entanglement distribution (Bennett et al. (1996)), entanglement swapping (Kaltenbaek et al. (2009); Pan et al. (1998)), quantum teleportation (Bouwmeester et al. (1997)), quantum cryptography (Bennett & Brassard (1984); Ekert (1991); Jennewein et al. (2000)) and scalable approaches towards photonics-based quantum computing schemes (Browne & Rudolph (2004); Gottesman & Chuang (1999); Knill et al. (2001)).
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.
High fidelity, high count rate four qubit linear cluster states have been realized by using two photons that are entangled both in polarization and linear momentum. Their properties have been investigated by evaluating the entanglement witness and carrying out a "stronger two observer all versus nothing" test of quantum nonlocality. The experimental results concerning the realization of single qubit rotations demonstrates the feasibility of one-way quantum computation by using these states.