Linear optics

Marcel Wellner

Emanuel H. Knill

Fermionic linear optics is efficiently classically simulatable. Here it is shown that the set of states achievable with fermionic linear optics and particle measurements is the closure of a low dimensional Lie group. The weakness of fermionic linear optics and measurements can therefore be explained and contrasted with the strength of bosonic linear optics with particle measurements. An analysis of fermionic linear optics is used to show that the two-qubit matchgates and the simulatable matchcircuits introduced by Valiant generate a monoid of extended fermionic linear optics operators. A useful interpretation of efficient classical simulations such as this one is as a simulation of a model of non-deterministic quantum computation. Problem areas for future investigations are suggested.

Mark M. Wilde, Hari Krovi, Jonathan P. Dowling +1 more

We provide experimental proposals for coherent communication with linear optics. The first proposal suggests a linear-optical scheme for coherent superdense coding. The second proposal gives a linear-optical coherent teleportation scheme.

Christopher R. Moylan

Yosep Kim, Kang-Hee Hong, Joonsuk Huh +1 more

Linear optical computing (LOC) with thermal light has recently gained attention because the problem is connected to the permanent of a Hermitian positive semidefinite matrix (HPSM), which is of importance in the computational complexity theory. Despite the several theoretical analyses on the computational structure of an HPSM in connection to LOC, the experimental demonstration and the computational complexity analysis via the linear optical system have not been performed yet. We present, herein, experimental LOC for estimating the permanent of an HPSM. From the linear optical experiments and theoretical analysis, we find that the LOC efficiency for a multiplicative error is dependent on the value of the permanent and that the lower bound of the computation time scales exponentially. Furthermore, our results are generalized and applied to LOC of permanents of unitary matrices, which can be implemented with a multiport quantum interferometer involving single photons at the input ports. We find that LOC with single photons, for the permanent estimation, is on average less efficient than the most efficient classical algorithm known to date, even in ideal conditions.