##### Department of Mathematics,

University of California San Diego

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### Quantum Information Seminar

## Nolan Wallach

#### UCSD

## Quantum non-locality without entanglement

##### Abstract:

This is joint work with Jiri Lebl and Asif Shakeel. We consider orthonormal bases in n qubits that consist of product states (unentangled orthonormal basis--UOB) and a device for each qubit that can do an arbitrary unitary transformation and a measurement on the qubit. Given a UOB and an element in the basis an LOCC protocol for determining which element we have chosen involves the following steps: 1. Set up and order for doing the local operations (unitary operation and measurement) by the devices. 2. After each local operation in this order the outcome of all of the earlier operations is communicated to the next instrument in the order and that instrument chooses it's local operation using the outcomes of all the previous operations. It has been shown that in 3 or more qubits there are UOB such that there is no protocol that can pick out a specific basis element with certainty. We show that in n qubits the generic UOB does not have this non-locality and completely classify these UOB's. Thus the ones not on our list have this non-locality.

### March 18, 2015

### 1:30 PM

### AP&M 5829

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