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Journal of Physics B Atomic Molecular and Optical Physics

A postselection-based linear optical scheme for generation of a three-photon W state

Binbin Zhang, Yu Liu

Published Sep 22, 2009• 2 citations
Publisher

Abstract

We propose a novel linear optical scheme to generate a three-photon W state, which is based on postselection of final outcome events. The success probability of our proposal has been improved to be 21/32, higher than that of the previous methods using the linear optical system. We also discuss the effects of realistic photon resources on its experimental realization and compare our scheme with the nonlinear optical approach to the three-photon W state generation. The idea of our proposal suggests a new way to improve the generation efficiency of some other entangled states and may have a promising application.

DOI
10.1088/0953-4075/42/19/195504

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We propose a novel linear optical scheme to generate a three-photon W state, which is based on postselection of final outcome events. The success probability of our proposal has been improved to be 21/32, higher than that of the previous methods using the linear optical system. We also discuss the effects of realistic photon resources on its experimental realization and compare our scheme with the nonlinear optical approach to the three-photon W state generation. The idea of our proposal suggests a new way to improve the generation efficiency of some other entangled states and may have a promising application.
A simple experimental scheme is proposed to generate a three-photon entangled WWW state and a genuine four-photon entangled state $|{\ensuremath{\chi}}^{00}⟩$ that has many interesting entanglement properties and possible applications in quantum information processing. These multipartite entangled states can be generated with a certain success probability. We show that even when the quantum efficiency of the detector is $\ensuremath{\eta}=0.75$, the success probability can reach $2.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ for WWW-state production and $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ for $|{\ensuremath{\chi}}^{00}⟩$-state production. The scheme is based only on simple linear optical elements and conventional photon detectors, which greatly decrease the experimental difficulty of implementing linear optical quantum computation.
We introduce schemes for linear-optical quantum state generation. A quantum state generator is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and postselection using photon counters. We show that this device can be concisely described in terms of polynomial equations and unitary constraints. We illustrate the power of this language by applying the Gr\"obner-basis technique along with the notion of vacuum extensions to solve the problem of how to construct a quantum state generator analytically for any desired state, and use methods of convex optimization to identify bounds to success probabilities. In particular, we disprove a conjecture concerning the preparation of the maximally path-entangled $\ensuremath{\mid}n,0⟩+\ensuremath{\mid}0,n⟩$ (NOON) state by providing a counterexample using these methods, and we derive a new upper bound on the resources required for NOON-state generation.
Multipartite entanglement is an essential quantum resource for various distributed quantum applications. One promising method for preparing multipartite entanglement is to interfere independent photons at linear optical interference setups. While heralding the successful interference and thereby the state generation is often costly, postselecting entangled states provides an achievable alternative in this framework. We introduce a family of interference schemes for postselecting symmetric qudit Dicke states, useful resources in quantum communication and variational quantum computing. We present schemes with and without ancillary photons and show that using ancillary photons can exceed the upper bound on the success probability of schemes without ancillary photons. Our results accommodate a wide range of linear optical schemes, providing multiple viable approaches for postselecting Dicke states.
A scheme is presented for generation of a multipartite WWW state for an arbitrary number of qubits. Based on a recent proposal of entanglement without touching, it serves to demonstrate the potential of particle indistinguishability as a useful resource of entanglement for practical applications. The devised scheme is efficient in design, meaning that it is built with linear optics without the need for auxiliary particles nor measurements. Yet, the success probability is shown to be highly competitive compared with the existing proposals (i.e., decreases polynomially with the number of qubits) and remains insensitive to particle statistics (i.e., has the same efficiency for bosons and fermions).
Abstract We report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon–photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups that are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability for each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that the maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to an m -tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of (1/4) m −1 .