Abstract
Quantum tasks are quantum computations with inputs and outputs occurring at specified spacetime locations. Considering such tasks in the context of AdS/CFT has led to novel constraints relating bulk geometry and boundary entanglement. In this article we consider tasks where inputs and outputs are encoded into extended spacetime regions, rather than the points previously considered. We show that this leads to stronger constraints than have been derived in the point based setting. In particular we improve the connected wedge theorem, appearing earlier in arXiv:1912.05649, by finding a larger bulk region whose existence implies large boundary correlation. As well, we show how considering extended input and output regions leads to non-trivial statements in Poincaré-AdS2+1, a setting where the point-based connected wedge theorem is always trivial.
Highlights
To derive constraints for AdS/CFT from quantum tasks, we begin by defining a task in the bulk
We show how considering extended input and output regions leads to non-trivial statements in Poincaré-AdS2+1, a setting where the point-based connected wedge theorem is always trivial
In this article we have expanded the holographic quantum tasks framework to include inputs and outputs encoded into arbitrary access structures
Summary
We will discuss quantum tasks where Alice is given inputs that are initially recorded into extended spacetime regions, and must be output at extended output regions. A quantum system X is encoded into an access structure SX = ({AiX }i, {UXi }i) if X is localized to each of the regions {AiX }i and excluded from each of the regions {UXi }i. Bob will localize the inputs Aj to regions AiAj so long as Alice never interferes She may choose to access some region AiAj and obtain Ai, in which case Bob is no longer expected to localize Ai to regions in the future of AiAj. In the application considered below, we begin with a spacetime and use tasks as a way to probe features of that fixed geometry. It is possible to consider more general tasks, where we allow the spacetime geometry to react to Alice’s protocol, which might for instance involve distributing large numbers of qubits which change the geometry We leave considering this to future work
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
