It Takes a Quantum to Know a Quantum: Limits on Distinguishabiliy of Hyperentangled Bell States with Linear Evolution and Local Measurement
A measurement of the entangled state, or Bell state, of two particles is essential to numerous protocols in quantum communication, such as quantum teleportation, entanglement swapping, and quantum dense coding. Numerous experiments use linear evolution and local measurement to approximate Bell-state measurements; such an approach is poorly matched to the nature of the entangled states and thus can only be conditionally successful. Nevertheless, the exact limitations of this approach are relevant to many existing and planned experiments, particularly as we develop the ability to work with particles entangled simultaneously, or hyperentangled, in several degrees of freedom.
I will discuss limits on hyperentangled Bell-state distinguishability for an apparatus restricted to LELM. For two identical particles entangled in n qubit variables, I present a simple proof that, of the 4n hyperentangled Bell states, 2(n+1)-1 is the largest subset that can be reliably distinguished with LELM. This result generalizes well-known results for n =1,2, and gives us physical intuition with which to understand those limits. I will also discuss distinguishability bounds for two particles entangled in several qudit variables.
Host: Luis Orozco