Onkar Parrikar, University of Pennsylvania

"Binding complexity and multiparty entanglement"

Abstract: We will discuss "binding complexity", a notion of circuit complexity which quantifies the difficulty of distributing entanglement among multiple parties, each consisting of many local degrees of freedom. We define the binding complexity of a given state as the minimum number of quantum gates which must simultaneously act on two or more parties at a time to prepare the state, while regarding gates which act within individual parties as "free". We will first discuss some simple lower bounds satisfied by such a complexity in terms of other probes of entanglement structure such as entanglement entropy, negativity etc. Then, to better illustrate the concept, we will compute the binding complexity in a Gaussian toy model using Nielsen's approach. We will show that the result is UV-finite, and discuss how it captures the entanglement structure. Finally, we will also suggest a potential candidate for the holographic dual of binding complexity in states dual to 3d multiboundary wormholes as the volume of the wormhole interior on the bulk time-reflection symmetric slice, and make a cursory comparison with results from the Gaussian toy model.