Testing Product States, Quantum Merlin-Arthur Games and Tensor Optimization

Abstract

We give a test that can distinguish efficiently between product states of n quantum systems and states that are far from product. If applied to a state | ψ 〉 whose maximum overlap with a product state is 1 − ε , the test passes with probability 1 − Θ ( ε ), regardless of n or the local dimensions of the individual systems. The test uses two copies of | ψ 〉. We prove correctness of this test as a special case of a more general result regarding stability of maximum output purity of the depolarizing channel.

Document Details

• Document Type: Pub Defense Publication
• Publication Date: Feb 01, 2013
• Source ID: 10.1145/2432622.2432625

Entities

People

• Aram Harrow
• Ashley Montanaro

Organizations

• Defense Advanced Research Projects Agency
• Engineering and Physical Sciences Research Council
• National Science Foundation
• University of Bristol

Tags

Readers

• Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
• Quantum Dot Semiconductor Device Photonics and Graphene Optoelectronic Materials and THz Physics.
• Software Engineering.

Technology Areas

• Quantum Computing