Real classical shadows

Understand

Efficiently learning expectation values of a quantum state using classical shadow tomography has become a fundamental task in quantum information theory.

• In a classical shadows protocol, one measures a state in a chosen basis W after it has evolved under a unitary transformation randomly sampled from a chosen distribution U.
• In this work we study the case where U corresponds to either local or global orthogonal Clifford gates, and W consists of real-valued vectors.
• Our results show that for various situations of interest, this ``real'' classical shadow protocol improves the sample complexity over the standard scheme based on general Clifford unitaries.