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Journal of the Optical Society of America B

Concentration of multi-photon entanglement with linear optics assisted by quantum nondemolition detection

Yan‐Qiang Ji, Zhao Jin, Ai‐Dong Zhu, Hong‐Fu Wang, Shou Zhang

Published Apr 4, 2014• 4 citations
Publisher

Abstract

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.

DOI
10.1364/josab.31.000994

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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 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.
Abstract We show how to concentrate an arbitrary four-photon polarization entangled state into a maximally entangled state based on some quantum nondemolition detectors. The entanglement concentration protocol (ECP) resorts to an ancillary single-photon resource and the conventional projection measurement on photons to assist the concentration, which makes it more economical. Our ECP involves weak cross-Kerr nonlinearities, X homodyne measurement and basic linear-optical elements, which make it feasible in the current experimental technology. Moreover, the ECP considers cyclic utilization to enhance a higher success probability. Thus, our scheme is meaningful in practical applications in quantum communication.
We propose two optimal entanglement concentration protocols (ECPs) for arbitrary single-photon multi-mode W state and multi-photon polarization W state, respectively. In both ECPs, we only require one pair of partially entangled W state, and do not consume any auxiliary photon. Both ECPs are based on the linear optics which can be easily realized. On the other hand, the concentrated maximally entangled states can be remained, which are quite different from the previous ECPs. Moreover, for the concentration of the arbitrary single-photon N-mode W state or N-mode polarization W state, the total success probability is equal to Nth the modulus square of the Schmidt coefficient of the smallest magnitude. It makes both ECPs optimal than all the previous ECPs. Our ECPs may be useful in current quantum communication fields.
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 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.
We propose two efficient entanglement concentration protocols (ECPs) for arbitrary less-entangled single-photon entanglement (SPE). Different from all the previous ECPs, these protocols not only can obtain the maximally SPE, but also can protect the single qubit information encoded in the polarization degree of freedom. These protocols only require one pair of less-entangled single-photon entangled state and some auxiliary single photons, which makes them economical. The first ECP is operated with the linear optical elements, which can be realized in current experiment. The second ECP adopts the cross-Kerr nonlinearities. Moreover, the second ECP can be repeated to concentrate the discard states in some conventional ECPs, so that it can get a high success probability. Based on above properties, our ECPs may be useful in current and future quantum communication.