Local Tests of Global Entanglement and a Counterexample to the Generalized Area Law

We introduce a technique for applying quantum expanders in a distributed fashion, and use it to solve two basic questions: testing whether a bipartite quantum state shared by two parties is the maximally entangled state and disproving a generalized area law. In the process these two questions which appear completely unrelated turn out to be two sides of the same coin. Strikingly in both cases a constant amount of resources are used to verify a global property.

Authors

• Dorit Aharonov
• Aram W. Harrow
• Zeph Landau
• Daniel Nagaj
• Mario Szegedy
• Umesh V. Vazirani

Keywords

• Quantum entanglement
• Protocols
• Stationary state
• Testing
• Entropy
• Lattices
• Vectors
• Areas Of Law
• Global Entanglement
• Basic Questions
• Entangled State
• Distributed Fashion
• Maximally Entangled State
• Left Side
• Singular Value
• Projector
• Communication Protocol
• Quantum Information
• Test Problems
• Communication Cost
• Complex Communication
• Local Terms
• Entropy Of State
• Unit Of Randomization
• Largest Singular Value
• Constant Gap