Complete Bell measurement on Ψ−⊗Ψ−Elias Amselem1, & Mohamed Bourennane1

1Department of Physics, Stockholm University,S-10961 Stockholm, Sweden

Bell measurement is the corner stone for teleportation and entanglement swapping protocols. Still a completesetup that can distinguish all Bell sates has not been used in the realization of the protocols. We have tested a Bellmeasurement setup that can distinguish between all Bell states on a Ψ−⊗Ψ− product state.

To setup a source that can generate |Ψ−〉 ⊗ |Ψ−〉 we used a spontaneous parametric down conversion [1](SPDC) process in a 2mm Type-II β -barium borate (BBO) crystal. A uv-pulses pump beam at 390nm was usedwith an average power of 650mW. The pules was reflected back after one pass by a small 3mm diameter mirror.From the first pass the photons where emitted in the A and B modes and from the second pass the photons whereemitted in the C and D modes (see Fig. 1). After proper special (single mode fibers) and spectral (3nm FWHM)filtering we obtain the highly entangled state (|HV 〉AB(CD)−|V H〉AB(CD))/

√2. The modes A and C are brought

to local polarization analyzers. The Bell measurement between arms B and D is based on a linear optical controlsign shift gate [2] and single qubit rotations. This setup maps each Bell state to a polarization coincidences in thearms B and D, that is

(|HH〉BD−|VV 〉BD)/√

2 =⇒ |HH〉BD (1)

(|HV 〉BD−|V H〉BD)/√

2 =⇒ |HV 〉BD (2)

(|HH〉BD + |VV 〉BD)/√

2 =⇒ |V H〉BD (3)

(|HV 〉BD + |V H〉BD)/√

2 =⇒ |VV 〉BD (4)

A coincidence window of 1.7ns was used. An average of 3 per 10 second four folded coincidences was recorded.Characterization of the state of the photons in arms A and C was done with an complete quantum state tomographyfor each Bell projection in modes B and D. The state fidelity experimentally obtained is as high as F = 0.86±0.01.The entanglement properties where studied by Bell inequalities, entanglement wetness and positive partial trans-pose criteria.

Figure 1: The left part of the setup is the source of |Ψ−〉⊗ |Ψ−〉. The Bell measurement setup for the parties Band D is in the right part of the setup. The setup is based on a linear optical control sign shift gate. Also the HOMinterference dip between two vertical polarized photons from arm B and D needed for the Bell measurement. Thevisibility of the dip obtained was Vexp = 0.67±0.02 with a theoretical max of Vt = 0.8

References

[1] Paul G. Kwiat, Klaus Mattle, Harald Weinfurter, & Anton Zeilinger, New High-Intensity Source of Polarization-EntangledPhoton Pairs. Phys. Rev. Lett. 76, 722 (1996).[2] N. Kiesel, C. Schmid, U. Weber, G. Tóth , R. Ursin & H. Weinfurter, Linear optics controlled-phase gate made simple.Phys. Rev. Lett. 95, 210505 (2005).

978-1-4244-4080-1/09/$25.00 c©2009 IEEE