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arXiv:quant-ph/0609080 · Physical Review A

Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement

Marco Barbieri, Giuseppe Vallone, Paolo Mataloni, F. De Martini

Published Apr 17, 2007• 191 citations
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Abstract

A complete and deterministic Bell state measurement was realized by a simple linear optics experimental scheme which adopts two-photon polarization-momentum hyperentanglement. The scheme, which is based on the discrimination among the single photon Bell states of the hyperentangled state, requires the adoption of standard single photon detectors. The four polarization Bell states have been measured with average fidelity $F=0.889\ifmmode\pm\else\textpm\fi{}0.010$ by using the linear momentum degree of freedom as the ancilla. The feasibility of the scheme has been characterized as a function of the purity of momentum entanglement.

DOI
10.1103/physreva.75.042317

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A complete and deterministic Bell state measurement was realized by a simple linear optics experimental scheme which adopts two-photon polarization-momentum hyperentanglement. The scheme, which is based on the discrimination among the single photon Bell states of the hyperentangled state, requires the adoption of standard single photon detectors. The four polarization Bell states have been measured with average fidelity F=0.889\ifmmode±\else\textpm\fi0.010F=0.889\ifmmode\pm\else\textpm\fi{}0.010F=0.889\ifmmode±\else\textpm\fi0.010 by using the linear momentum degree of freedom as the ancilla. The feasibility of the scheme has been characterized as a function of the purity of momentum entanglement.
We propose a simple scheme for complete Bell-state measurement of photons using hyperentangled states---entangled in multiple degrees of freedom. In addition to hyperentanglement, our scheme requires only linear optics and single photon detectors, and is realizable with current technology. At the cost of additional classical communication, our Bell-state measurement can be implemented nonlocally. We discuss the possible application of these results to quantum dense coding and quantum teleportation.
We present a parametric source which allows the engineering of polarization-momentum hyperentangled two photon states based on linear optics and a single type-I nonlinear crystal. The nonlocal character of these states has been verified by various tests, including the “All Versus Nothing” test of local realism [A. Cabello, Phys. Rev. Lett. 87 , 010403 (2001)], which represents a generalization of the GHZ to the case of two entangled particles and two observers. We have also created a complete and deterministic Bell-state measurement by a novel experimental scheme which adopts polarization-momentum hyper-entanglement and requires linear optics and single photon detectors.
We present a theoretical scheme for the complete Bell state measurement (BSM) for high-dimensional hyperentangled photons in polarization and path degrees of freedom (DOFs), in which the polarization entanglement is in two-dimensional Hilbert space and the path entanglement is in four-dimensional Hilbert space. This 2×4-dimensional photonic quantum system contains 64 mutually orthogonal high-dimensional hyperentangled Bell states, which can be unambiguously discriminated by using weak cross-Kerr nonlinearity, linear optical element, and single-photon detector. This is the first complete BSM scheme for high-dimensional hyperentangled photons in two DOFs assisted by the quantum nonlinear effect, and we also demonstrate its application in the quantum superdense coding protocol, which allows the transmission of log 2 64=6 bits of classical information via just sending one photon. Moreover, our scheme only requires the achievable small nonlinear phase shift, and it can provide new avenues for other BSM-based quantum information technologies involving photonic high-dimensional hyperentanglement.
The orbital angular momentum (OAM) carried by twisted photons provides a promising playground for high-dimensional quantum information processing. While Bell-state measurement is the cornerstone for various quantum information applications, the deterministic discrimination of the complete high-dimensional Bell states with linear optics remains relatively unexplored in the OAM state space. Here, we demonstrate a theoretical scheme for the complete four-dimensional OAM Bell-state measurement by using the single-photon hyperentangled state analyzer, in which the auxiliary two-dimensional polarization entanglement and two-dimensional path entanglement are utilized. Our scheme offers an alternative route toward enhancing the channel capacity in quantum communication and increasing the robustness against deleterious noise in practical experiments with twisted photons.
Quantum logic coding efficiently enhances the noise immunity of quantum systems. A quantum logical qubit using multiple degrees of freedom (DOFs) of a photon is concise, and it can reduce resource consumption compared with a quantum logical qubit using multiple photons in one DOF. In this study, two logical Bell state measurement schemes are proposed for photon systems in momentum and polarization DOFs with linear optical elements, namely, momentum polarization logical Bell state measurement assisted by W-state and self-assisted momentum polarization logical Bell state measurement. In the first scheme, parity measurements on momentum and polarization DOFs are performed simultaneously using an auxiliary four-photon W-state. The even-parity logical Bell states can be distinguished by photon detector results, resulting in a success rate of 12.5%. The second scheme does not require an auxiliary entangled photon state, and the even-parity logical Bell states can be completely distinguished by simple linear optical elements and photon detector results with a success rate of 50%. These two linear optical momentum polarization logical Bell state measurement schemes are easier to implement experimentally than the nonlinear optical schemes, and their applications in quantum communication protocols are crucial.
It is known that it is impossible to unambiguously distinguish the four Bell states encoded in pairs of photon polarizations using only linear optics. However, hyperentanglement, the simultaneous entanglement in more than one degree of freedom, has been shown to assist the complete Bell analysis of the four Bell states (given a fixed state of the other degrees of freedom). Yet introducing other degrees of freedom also enlarges the total number of Bell-like states. We investigate the limits for unambiguously distinguishing these Bell-like states. In particular, when the additional degree of freedom is qubitlike, we find that the optimal one-shot discrimination schemes are to group the 16 states into seven distinguishable classes, and that an unambiguous discrimination is possible with two identical copies.