Section: New Results
Programmable projective measurement with linear optics
In  present a scheme for a universal device which can be programmed by quantum states to perform a chosen projective measurement, and its implementation in linear optics. In particular, our scheme takes a single input system (the input register), and M-1 systems all in a state psi (the program registers), whose role is to encode the measurement direction, and approximates the projective measurement with respect to the state psi on the input system. Importantly the scheme is entirely independent of the measurement basis choice psi. This is done optimally in M, if we demand the input state psi always returns the appropriate outcome, and limits to the ideal projective measurement with M. The size of the linear optical circuit we propose scales as M log M , and requires O(M log M) classical side processing. Our scheme can be viewed as an extension of the swap test to the instance where one state is supplied many times.