Linear optical and local filtering of entangled states

The problem of state discrimination is fundamental to quantum information. From a theoretical perspective, orthogonal quantum states should be perfectly distinguishable. However, we can impose restrictions on the types of operations we allow, making this problem no longer trivial. Two such restrictions are those of linear optics and local measurements. In linear optical systems, the set of allowed operations is limited to those implementable using linear optical components: beam splitters and phase shifters. For local measurements, we focus on multi-partite systems, allowing only local operations on the subsystems. In both cases, we see that these limitations create challenges for the discrimination of orthogonal states. For instance, the set of four Bell states cannot be perfectly discriminated in either case, that of linear optics and that of local measurements. However, in each case there are strategies that allow for the detection of two out of the four states, allowing the discrimination to succeed 50\% of the time. For this talk, we focus on the question of optimal discrimination of any set of basis states of the space of two qubits. Specifically, we provide a general method for optimally filtering at least two of the four states given states, given any of the four states are sent. Our method gives the optimal protocols for both linear optical and local systems simultaneously.