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Journal of the Optical Society of America B

Single-photon-assisted entanglement concentration of partially entangled multiphoton W states with linear optics

Bin Gu

Published Jun 19, 2012• 54 citations
Publisher

Abstract

We propose a single-photon-assisted entanglement concentration protocol (ECP) for nonlocal N-photon systems in a partially entangled pure W-class state with linear optical elements. Only one of the N parties in quantum communication prepares an ancillary photon and operates the entanglement concentration process for picking up the standard N-photon W state from each partially entangled pure W-class state by choosing the two-mode instances from a polarization beam splitter. Compared with other ECPs for W-class states, our protocol has some advantages. First, it requires only linear optical elements. Second, it requires an N-photon system and an ancillary photon for each round of concentration, not two systems. Third, only one party asks other parties to retain or discard their photons. All these advantages make our ECP more feasible and more convenient than others.

DOI
10.1364/josab.29.001685

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We propose a nonlocal entanglement concentration protocol (ECP) for N-photon systems in a partially entangled W state, resorting to some ancillary single photons and the parity-check measurement based on cross-Kerr nonlinearity. One party in quantum communication first performs a parity-check measurement on her photon in an N-photon system and an ancillary photon, and then she picks up the even-parity instance for obtaining the standard W state. When she obtains an odd-parity instance, the system is in a less-entanglement state, and it is the resource in the next round of entanglement concentration. By iterating the entanglement concentration process several times, the present ECP has a total success probability approaching the limit in theory. The present ECP has the advantage of a high success probability. Moreover, the present ECP requires only the N-photon system itself and some ancillary single photons, not two copies of the systems, which decreases the difficulty of its implementation greatly in experiment. It may have good applications in quantum communication in the future.
We present two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons. A partially entangled photon pair can be concentrated to a maximally entangled pair with only an ancillary single photon with a certain probability, while the conventional ECPs require two copies of partially entangled pairs at least. Our first protocol is implemented with linear optics and the second protocol is implemented with cross-Kerr-nonlinearities. Compared with other ECPs, they do not need to know the accurate coefficients of the initial state. With linear optics, it is feasible with current experiments. With cross-Kerr-nonlinearities, it does not require sophisticated single-photon detectors and can be repeated to get a higher success probability. Moreover, the second protocol can get the higher entanglement transformation efficiency and it may be the most economical protocol by far. Meanwhile, both protocols are more suitable for multiphoton system concentration because they need less operations and classical communications. All these advantages make the two protocols useful in current long-distance quantum communications.
We propose an entanglement concentration protocol (ECP) for nonlocal N -electron systems in a partially entangled W state, resorting to ancillary single electrons and charge detection. Compared with other ECPs for W states, our ECP has some advantages. Firstly, only an entangled N -electron system is required in each round of entanglement concentration, not two copies. Secondly, only one of the users, say Charlie, needs to perform the protocol, while all parties should perform the same operations as Charlie in other ECPs for W -class states. Thirdly, only Charlie asks other parties to retain or discard their electrons, and they do not need to check their measurement results, which greatly simplifies the complication of classical communication. Fourthly, our ECP has a higher success probability than other ECPs for W -class states as the parties can recycle their concentration when they obtain a system in another W -class state with less entanglement. These advantages make our ECP more feasible for practical applications.
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The entanglement concentration protocols (ECPs) are presented for distilling the maximally entangled state from a known partially entangled n-photon Bell-class and W state, respectively, only resorting to the linear optical elements and quantum nondemolition detector. Different from the traditional parity check with a single photon as an ancilla, we use linear optical elements for changing the photon paths to realize the concentration. The total success probability of the concentration for n-photon entangled states is calculated. The present protocols only require a partially entangled state and do not need any single auxiliary particle. By iterating the ECP repeatedly, the maximal success probability can be increased. Meanwhile, the present protocols are more suitable for the photon system due to the simple operations.
We present a systematic entanglement concentration protocol (ECP) for an arbitrary unknown less-entangled three-photon W state, resorting to the optical property of the quantum-dot spins inside one-sided optical microcavities. In our ECP, the parties obtain not only some three-photon systems in the partially entangled with two unknown parameters when one of the parties picks up the robust odd-parity instance with the parity-check gate (PCG) on his two photons, but also some entangled two-photon systems by keeping the even-parity instance in the first step. By exploiting the above three-photon and two-photon systems with the same parameters as the resource for the second step of our ECP, the parties can obtain a standard three-photon W state by keeping the robust odd-parity instance. Meanwhile, the systems in the even-parity instance can be used as the resource in the next round of our ECP. The success probability of our ECP is largely increased by iteration of the ECP process. As it does require that all the coefficients are unknown for the parties, our ECP maybe have good applications in quantum communication network in future.