Abstract
In this paper, we present the approach to complete Bell state analysis based on filtering mapping. The key distinctive feature of this appoach is that it avoids complications related to using either hyperentanglement or representation of the Bell states as concatenated Greenber–Horne–Zeilinger (C-GHZ) state to perform discrimination procedure. We describe two techniques developed within the suggested approach and based on two-step algorithms with two different types of filtration mapping which can be called the non-demolition and semi-demolition filtrations. In the method involving non-demolition filtration measurement the filtration process employs cross-Kerr nonlinearity and the probe mode to distinguish between the two pairs of the Bell states. In the case of semi-demolition measurement, the two states are unambiguously discriminated and hence destroyed, whereas filtraton keeps the other two states intact. We show that the measurement that destroys the single photon subspace in every mode and preserves the superposition of zero and two photons can be realized with discrete photodetection based on microresonator with atoms.
Highlights
In this paper, we present the approach to complete Bell state analysis based on filtering mapping
Mathematical structure underlying the two-step procedure can be illustrated in the simple and elegant way using the polar decomposition of positive semi-definite operators. It can be described as a completely-positive trace-preserving (CPTP) map determined by a family of positive semi-definite operators {Ax }x∈X: I = Ax
In this paper we have proposed the filtration mapping realizing complete Bell state analyzer of photonic qubits
Summary
We present the approach to complete Bell state analysis based on filtering mapping. In the method involving non-demolition filtration measurement the filtration process employs cross-Kerr nonlinearity and the probe mode to distinguish between the two pairs of the Bell states. In the case of semi-demolition measurement, the two states are unambiguously discriminated and destroyed, whereas filtraton keeps the other two states intact. The related procedure of unambiguous identification is among the key factors that determine the performance of such protocols as measurement-device-independent QKD, quantum teleportation and dense coding. It is well known that in the case of photonic systems one cannot distinguish all the four Bell states unambiguously using only linear optical elements and detectors[20,21]. According to[25], introducing 2N − 2 ancillary photons may enhance the success rate of linear-optic measurements up to 1 − 1/2N
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