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New Journal of Physics

Probabilistically cloning two single-photon states using weak cross-Kerr nonlinearities

Wen Zhang, Pinshu Rui, Ziyun Zhang, Qun Yang

Published Aug 8, 2014• 16 citations

Abstract

By using quantum nondemolition detectors (QNDs) based on weak cross-Kerr nonlinearities, we propose an experimental scheme for achieving probabilistic quantum cloning (PQC) of a single-photon state, secretly choosing from a two-state set. In our scheme, after a QND is performed on the to-be-cloned photon and the assistant photon, a single-photon projection measurement is performed by a polarization beam splitter (PBS) and two single-photon trigger detectors (SPTDs). The measurement is to judge whether the PQC should be continued. If the cloning fails, a cutoff is carried out and some operations are omitted. This makes our scheme economical. If the PQC is continued according to the measurement result, two more QNDs and some unitary operations are performed on the to-be-cloned photon and the cloning photon to achieve the PQC in a nearly deterministic way. Our experimental scheme for PQC is feasible for future technology. Furthermore, the quantum logic network of our PQC scheme is presented. In comparison with similar networks, our PQC network is simpler and more economical.

DOI: 10.1088/1367-2630/16/8/083019

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By using quantum nondemolition detectors (QNDs) based on weak cross-Kerr nonlinearities, we propose an experimental scheme for achieving probabilistic quantum cloning (PQC) of a single-photon state, secretly choosing from a two-state set. In our scheme, after a QND is performed on the to-be-cloned photon and the assistant photon, a single-photon projection measurement is performed by a polarization beam splitter (PBS) and two single-photon trigger detectors (SPTDs). The measurement is to judge whether the PQC should be continued. If the cloning fails, a cutoff is carried out and some operations are omitted. This makes our scheme economical. If the PQC is continued according to the measurement result, two more QNDs and some unitary operations are performed on the to-be-cloned photon and the cloning photon to achieve the PQC in a nearly deterministic way. Our experimental scheme for PQC is feasible for future technology. Furthermore, the quantum logic network of our PQC scheme is presented. In comparison with similar networks, our PQC network is simpler and more economical.

We propose a three-party scheme for quantum information splitting (QIS) of an arbitrary single-photon polarization state based on weak cross-Kerr nonlinearity combined with linear optics elements such as polarization beam splitters (PBSs) and half wave plates (HWPs). The scheme is generalized to the arbitrary-party case. With the help of quantum nondemolition (QND) measurements, our schemes can be accomplished in an almost deterministic way. The two schemes are feasible with the current technology.

A scheme for teleporting an unknown single-qubit photonic state in a nearly deterministic and controlled manner is proposed via the weak cross-Kerr nonlinearities.The functions of the complicated CNOT operations and Bell-state analysis can be realized easily with the help of quantum nondemolition measurement technique.This improvement makes the present scheme more efficient than the schemes using nonunitaxy projective measurements.Discussions about this scheme show that it is feasible with the current experimental technology in optics.

Scheme for teleporting an unknown single-qubit photonic state is revisited. With the help of quantum nonde-molition measurements, the scheme now can be achieved in an almost deterministic way. The weak-cross-Kerrnonlinearities-based quantum nondemolition measurement acts as an entangler as well as the Bell-state analyzer, and thus plays a similar role as the CNOT gate in the teleportation process. This improvement makes the present scheme more efficient than the schemes using nonunitary projective measurements and feasible with the current experimental technology.

In this paper, with the weak cross-Kerr nonlinearity, we first present a special experimental scheme called controlled-path gate with which the realization of all possible bipartite positive-operator-value measurements of two-photon polarization states may be nearly deterministic. Following the same technique, the realization of quantum control gates, including the controlled-NOT gate, Fredkin gate, Toffoli gate, arbitrary controlled-U gate, and even arbitrary multicontrolled-U gate, are proposed. The corresponding probabilities are

1∕2

,

1∕8

,

2∕23

, etc., respectively. Only the coherent states are required but not any ancilla photons, and no coincidence measurement are required, which results in these gates being scalable. The structures of these gates are very simple, therefore we think they are feasible with the current experimental technology in optics.

We present three protocols for directly measuring the concurrence of two-photon polarization-entangled states, including pure states and mixed states. Two signal photon pairs in the same polarization-entangled states are needed in each detection round, and the signal photons will pass through polarization-independent beam splitters simultaneously. The concurrence of the photon pairs will be encoded in the total probability of picking up the balanced states in the two output modes of the beam splitter, which can be directly measured by single-photon detectors. The photon detection efficiency can be further enhanced with the help of the weak cross-Kerr nonlinearity, and the signal photons will not be absorbed. The third scheme using the bilateral nondemolition measurements can measure the concurrence of both pure and mixed states with high efficiency and high fidelity and is robust against the copy error of the state to be measured. The sophisticated controlled-not operation of the previous schemes is not required here, so our protocols are more feasible within the current experimental technology.

Schemes for two-qubit and three-qubit controlled gates based on cross-Kerr nonlinearity are proposed in this paper. The probability of the success of these gates can be increased by quantum nondemolition detectors, which are used to judge which paths the signal photons pass through. These schemes are almost deterministic and require no ancilla photon. The advantages of these gates over the existing ones include less resource consumption and a higher probability of success, which make our schemes more feasible with current technology.