Positive-operator-valued-measure receiver for quantum cryptography

Claim 1

A positive-operator-valued-measure receiver, comprising: a Wollaston prism for receiving a photon having a polarization state |ψ> given by |ψ>=α|u>+β|v>, where α and β are arbitrary real constants and the polarization of state |u> makes an angle θ with that of state |v>; wherein the photon exits the Wollaston prism in a state |ψ 1 >=2 -1/2 (α+β)(1+cos θ) 1/2 |e u+v > for the path between the Wollaston prism and a first beam splitter and |ψ 2 >=2 -1/2 (α-β)(1-cos θ) 1/2 |e u-v > for the path between the Wollaston prism and a mirror, where |e u+v > and |e u-v > denote unit kets corresponding to polarization vectors e u+v and e u-v , respectively; the first beam splitter for receiving the photon in the state |ψ 1 > and having a reflection coefficient of tan 2 (θ/2); wherein the photon exits the first beam splitter in a transmitted state of |ψ 3 >=(α+β)(cos θ) 1/2 |e u+v > corresponding to the path between the first beam splitter and a first photodetector, and a reflected state of |ψ 4 >=i2 -1/2 (α+β)(1-cos 74) 1/2 |e u+v > corresponding to the path between the first beam splitter and a second beam splitter; the first photodetector for detecting the photon in the state |ψ 3 > corresponding to an inconclusive event; the mirror for receiving the photon in the state |ψ 2 > and reflecting the photon therefrom; a ninety degree polarization rotator for receiving the photon reflected from the mirror and rotating the photon polarization to a state |ψ 5 >=-2 -1/2 (α-β)(1-cos θ) 1/2 |e u+v >; the second beam splitter having a reflection coefficient of 0.5; the second beam splitter for receiving a photon in the state |u/ 4 > from the first beam splitter and the state |ψ 5 > from the ninety degree polarization rotator wherein both optical path lengths from the Wollaston prism to the second beam splitter are equal; and wherein the photon exits the second beam splitter in a state |ψ 6 >=-α(1-cos θ) 1/2 |e u+v > corresponding to the path between the second beam splitter and a second photodetector, and |ψ 7 >=iβ(1-cos θ) 1/2 |e u+v > corresponding to the path between the second beam splitter and a third photodetector; and the second and third photodetectors for detecting photons in the states |ψ 6 > corresponding to an incident u-polarized photon and |ψ 7 > corresponding to an incident v-polarized photon, respectively.