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arXiv:0706.2429 · Physical Review A

Universal discriminator for completely unknown optical qubits

Bing He, János A. Bergou, Yuhang Ren

Published Sep 4, 2007• 30 citations
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Abstract

We propose an experimental setup that is capable of unambiguously discriminating any pair of linearly independent single photon polarization qubits, about which we do not have any knowledge except that an extra pair of these unknown states are provided as the reference. This setup, which is constructed with optical controlled-NOT (CNOT) gates, weak cross Kerr nonlinearities, Bell state analyzers, and other linear optical elements, transforms the unknown triple photon input states to the corresponding single photon states to be deterministically processed by a linear optics circuit. The optimal discrimination of the unknown states is achieved by this setup.

DOI
10.1103/physreva.76.032301

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We propose an experimental setup that is capable of unambiguously discriminating any pair of linearly independent single photon polarization qubits, about which we do not have any knowledge except that an extra pair of these unknown states are provided as the reference. This setup, which is constructed with optical controlled-NOT (CNOT) gates, weak cross Kerr nonlinearities, Bell state analyzers, and other linear optical elements, transforms the unknown triple photon input states to the corresponding single photon states to be deterministically processed by a linear optics circuit. The optimal discrimination of the unknown states is achieved by this setup.
We propose a setup that transforms a photon pair in arbitrary rank-four mixed state, which could also be unknown, to a Bell state. The setup involves two linear optical circuits processing the individual photons and a parity gate working with weak cross-Kerr nonlinearity. By the photon number resolving detection on one of the output quantum bus or communication beams, the setup will realize a near deterministic transformation to a Bell state for every entangling attempt. With the simple threshold detectors, on the other hand, the system can still reach a considerable success probability of 50% per try. The decoherence effect caused by photon absorption losses in the operation is also discussed.
Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum information processing. However, photons, one of the best candidates for qubits, suffer from a lack of strong nonlinear coupling, which is required for quantum logic operations. Here we show how this drawback can be overcome by reporting a proof-of-principle experimental demonstration of a nondestructive controlled-NOT (CNOT) gate for two independent photons using only linear optical elements in conjunction with single-photon sources and conditional dynamics. Moreover, we exploit the CNOT gate to discriminate all four Bell states in a teleportation experiment.
In this paper, we present a linear optical scheme for optimal unambiguous discrimination among nonorthogonal quantum states in terms of the multiple-rail and polarization representation of a single photon. In our scheme, discriminated quantum states are expressed by using the spatial degree of freedom of a single photon while the polarization degree of freedom of the single photon is used to act as an auxiliary qubit. The optical components used in our scheme are only passive linear optical elements such as polarizing beam splitters, wave plates, polarizers, single photon detectors, and single photon source.
Quantum information processing using linear optics is challenging due to the limited set of deterministic operations achievable without using complicated resource-intensive methods. While techniques such as the use of ancillary photons can enhance the information processing capabilities of linear optical systems, they are technologically demanding. Therefore, determining the constraints posed by linear optics and optimizing linear optical operations for specific tasks under those constraints, without the use of ancillae, can facilitate their potential implementation. Here, we consider the task of unambiguously discriminating between Bell-like states using linear optics and without the use of ancillary photons. This is a basic problem relevant in diverse settings, for example, in the measurement of the output of an entangling quantum circuit or for entanglement swapping at a quantum repeater station. While it is known that exact Bell states of two qubits can be discriminated with an optimal success probability of 50%, we find, surprisingly, that for Bell-like states the optimal probability can be only 25%. We analyze a set of Bell-like states in terms of their distinguishability, entanglement as measured by concurrence, and parameters of the beam-splitter network used for unambiguous discrimination. Further, we provide the linear optical configuration comprising single-photon detectors and beam splitters with input-state-dependent parameters that achieves optimal discrimination in the Bell-like case.
Abstract We propose an efficient method to construct an optical four-photon |χ〉 state analyzer via the cross-Kerr nonlinearity combined with linear optical elements. In this protocol, two four-qubit parity-check gates and two controlled phase gates are employed. We show that all the 16 orthogonal four-qubit |χ〉 states can be completely discriminated with our apparatus. The scheme is feasible and realizable with current technology. It may have useful potential applications in quantum information processing which based on |χ〉 state.