Abstract
Linear optical systems acting on photon number states produce many interesting evolutions, but cannot give all the allowed quantum operations on the input state. Using Toponogov’s theorem from differential geometry, we propose an iterative method that, for any arbitrary quantum operator U acting on n photons in m modes, returns an operator widetilde{U} which can be implemented with linear optics. The approximation method is locally optimal and converges. The resulting operator widetilde{U} can be translated into an experimental optical setup using previous results.
Highlights
Linear optical devices under quantum light show a rich behaviour and have different applications in experiments on the foundations of quantum optics and quantum infor- 314 Page 2 of 18J
While they can be built with relatively simple optical elements like beam splitters and phase shifters [4,5,6,7,8], their behaviour for photon number states cannot be accurately reproduced by any classical system
We have previously presented an inverse method which can tell if any desired quantum evolution on n photons can be achieved with a linear optical system or not, giving the corresponding system when it is possible [19]
Summary
There are many results on the synthesis of linear systems from their classical description [4,7,8] and that analyze the evolution of multiple photons in those devices [10,11,12,13,14,15,16,17,18]. We have previously presented an inverse method which can tell if any desired quantum evolution on n photons can be achieved with a linear optical system or not, giving the corresponding system when it is possible [19]. We complete this design method with a procedure that gives the best possible approximation to any quantum unitary that cannot be achieved using only photon preserving linear optical systems.
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