Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations

Understand

Schur-Weyl duality is a ubiquitous tool in quantum information.

• At its heart is the statement that the space of operators that commute with the tensor powers of all unitaries is spanned by the permutations of the tensor factors.
• In this work, we describe a similar duality theory for tensor powers of Clifford unitaries.
• The Clifford group is a central object in many subfields of quantum information, most prominently in the theory of fault-tolerance.