Port-based teleportation for arbitrary systems

Sergii Strelchuk ( University of Cambridge (Dept. Applied Mathematics & Theoretical Physics) )

Port-based teleportation (PBT), which was introduced in 2008, is a scheme where Alice and Bob share a number of EPR pairs (ports) and the teleported state ends up in one of Bob’s ports without any unitary correction. Its performance is well understood when the dimension of the teleported state d=2 and N>2. When d>2 and N>2, calculating the probability of success and the teleportation fidelity requires exponential overhead.

In our work we find a complete solution for the fidelity of transmission and other quantities of interest for all PBT protocols which characterize them in all dimensions and all performance regimes. Moreover, through unexpected connections to algebra of partially transposed operators, we gain conceptual insights about features of the PBT and their fundamental limitations.

In addition, new mathematical tools that we develop can be used to characterize quantum systems with partial symmetries. Quantum states occurring in the PBT protocol are one such example. Systems with partial symmetries are widespread (e.g. when studying square-root measurements for mixed states, integrability of GL(m,n) spin chains) but in contrast to their permutational-invariant counterparts very little is known about how to efficiently estimate their properties.