QLunch: Li Liu

Speaker: Li Liu from QMATH

Title: Explicit protocol for exact universal embezzlement of entanglement

Abstract: Embezzlement of entanglement is the procedure of producing an entangled state using only local operations and a large catalyst state. It is known that embezzlement of entanglement can only be performed exactly under the commuting operator framework with infinite dimensions. If a fixed catalyst state can embezzle any entangled states with different local operations, then this is called a universal embezzlement protocol. Recent result has shown that universal embezzlement protocol dictates the catalyst to be in the space of Type III_1 von Neumann factor, but no explicit protocol was known. In this talk, I will discuss the first known explicit construction of exact universal embezzlement protocols using the C*-algebraic model of infinite dimensional quantum systems. I will start with an explicit approximate universal embezzlement protocol that can exactly embezzle a dense set of all entangled states, and then extend it to exact universal embezzlement protocol that can exactly embezzle any states. By construction, the approximate protocol lives in a separable space whereas the exact protocol lives in a non-separable space.