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arXiv:quant-ph/0304066 · Physical Review A

Reliability of the beam-splitter–based Bell-state measurement

Yoon-Ho Kim, Warren P. Grice

Published Dec 5, 2003• 18 citations
arXivHTMLPDF

Abstract

A linear 50-50 beam splitter, together with a coincidence measurement, has been widely used in quantum optical experiments, such as teleportation, dense coding, etc., for interferometrically distinguishing, measuring, or projecting onto one of the four two-photon polarization Bell states $|{\ensuremath{\psi}}^{(\ensuremath{-})}〉.$ In this paper, we demonstrate that the coincidence measurement at the output of a beam splitter cannot be used as an absolute identifier of the input state $|{\ensuremath{\psi}}^{(\ensuremath{-})}〉$ nor as an indication that the input photons have been projected to the $|{\ensuremath{\psi}}^{(\ensuremath{-})}〉$ state.

DOI
10.1103/physreva.68.062305

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A linear 50-50 beam splitter, together with a coincidence measurement, has been widely used in quantum optical experiments, such as teleportation, dense coding, etc., for interferometrically distinguishing, measuring, or projecting onto one of the four two-photon polarization Bell states ∣\ensuremathψ(\ensuremath−)〉.|{\ensuremath{\psi}}^{(\ensuremath{-})}〉.∣\ensuremathψ(\ensuremath−)〉. In this paper, we demonstrate that the coincidence measurement at the output of a beam splitter cannot be used as an absolute identifier of the input state ∣\ensuremathψ(\ensuremath−)〉|{\ensuremath{\psi}}^{(\ensuremath{-})}〉∣\ensuremathψ(\ensuremath−)〉 nor as an indication that the input photons have been projected to the ∣\ensuremathψ(\ensuremath−)〉|{\ensuremath{\psi}}^{(\ensuremath{-})}〉∣\ensuremathψ(\ensuremath−)〉 state.
A linear 50/50 beamsplitter, together with a coincidence measurement, has been widely used in quantum optical experiments, such as teleportation, dense coding, etc., for interferometrically distinguishing, measuring, or projecting onto one of the four two-photon polarization Bell-states |/spl Psi//sup (-)/>. In this paper, we demonstrate that the coincidence measurement at the output of a beamsplitter cannot be used as an absolute identifier of the input state |/spl Psi//sup (-)/> nor as an indication that the input photons have projected to the |/spl Psi//sup (-)/> state.
Many quantum information protocols require a Bell-state measurement of entangled systems. Most optical Bell-state measurements utilize two-photon interference at a beam splitter. By creating polarization-entangled photons with spontaneous parametric down-conversion using a first-order Hermite-Gaussian pump beam, we invert the usual interference behavior and perform an incomplete Bell-state measurement in the coincidence basis. We discuss the possibility of a complete Bell-state measurement in the coincidence basis using hyperentangled states ( Phys. Rev. A, 58 (1998) R2623).
Beam splitters are optical elements widely used in modern technological applications to split the initial light beam into a required number of beams and they play a very promising role for generating entangled optical states. Here, a potential scheme is proposed to generate Bell coherent-states superpositions through the action of a beam splitter when a Glauber coherent state is injected on one input mode and vacuum state is incident on the other one. Different quantifiers are used to measure the quantumness in the output state such as concurrence entanglement, entropic quantum discord, quantum coherence, geometric measure of quantum discord, local quantum uncertainty (LQU) and local quantum Fisher information. Thereby, we derive their analytical formulas and focus more on the behavior and bounds of each measure. Besides, we have introduced the notion of "weak measurement-induced LQU" captured by weak measurements as the generalization of normal LQU defined for standard projective measurement, and we investigate the effect of the measurement strength on the estimated phase enhancement if the generated Bell cat states are the probe states in quantum metrology. Our results suggest that the sensitivity of the interferometric phase estimation depends on how strongly one perturbs the probe state and that a weak measurement does not necessarily capture more quantumness in composite system.
Bell state measurement is vital to quantum information technology. Conventional linear optical elements, however, cannot fully distinguish all polarization Bell states without assisting of additional degrees of freedom. Leveraging on a pair of binary-pixel metasurfaces, we demonstrate direct measurement of all four polarization Bell states. Each metasurface is designed to produce two output modes that linearly superpose three Bell states in the coincidence counting measurement. By rotating the polarizers, the coincidence counting measurement achieves a tunable anticorrelation between one and the other two Bell states, achieving Bell state detection efficiency of 75% in a single measurement. Complete and deterministic Bell state measurement is further realized by performing two measurements. Our work shows the advantage of utilization of metasurfaces in quantum detection schemes and is of great applicative interest for quantum dense coding, entanglement swapping, quantum teleportation protocols, and novel quantum information processing tasks.
We present our source of polarization entangled photons, which consist of orthogonally polarized and collinear parametric down converted photons sent to the same input of a nonpolarizing beam splitter. We show that a too straightforward characterization of the quantum state cannot account for all the experimental observations, in particular for the behavior of the doublecounts, which are the coincidences produced whenever both photons are dispatched by the beam splitter to the same measuring station (either Alice or Bob). We argue that in order to account for all observations, the state has to be entangled in polarization before the non-polarizing beam splitter, and we discuss the intriguing and nevertheless essential role of the time-compensation required to obtain such a polarization entanglement.
Quantum mechanical models of beam splitters1 predict interesting fourth-order interference effects when nonclassical light is used. If indistinguishable one-photon states are simultaneously input into each port of a 50/50 beam splitter, the theory predicts that each output will contain either two photons or none. A naive (particle) theory would predict a mixture of two’s and one’s. The required |1,1〉 photon state can be selected in nondegenerate parametric downconversion experiments by photon-counting coincidence detection. The disappearance of this coincidence after a beam splitter has recently been studied,1-2 and the range of path length differences over which the effect can be seen is related by Fourier transform to the photon bandwidth. In our work the bandwidth is not limited by external filters, and we have developed a theory which relates the measured photon length to the geometry of the apparatus and the detailed phase matching conditions at the parametric crystal. This theory of phase matching viewed through a beam splitter produces some unexpected results when the beam splitter is tilted and when large aperture detectors are considered.