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Structural physical approximation (SPA) has been exploited to approximatenon-physical operation such as partial transpose. It has already been studiedin the context of detection of entanglement and found that if the minimumeigenvalue of SPA to partial transpose is less than $\frac{2}{9}$ then thetwo-qubit state is entangled. We find application of SPA to partial transposein the estimation of optimal singlet fraction. We show that optimal singletfraction can be expressed in terms of minimum eigenvalue of SPA to partialtranspose. We also show that optimal singlet fraction can be realized usingHong-Ou-Mandel interferometry with only two detectors. Further we have shownthat the generated hybrid entangled state between a qubit and a binary coherentstate can be used as a resource state in quantum teleportation.

Structural Physical Approximation make possible to realize the optimal singlet fraction with two measurements