Exact distinguishability between real-valued and complex-valued Haar random quantum states
Abstract
Haar random states are fundamental objects in quantum information theory and quantum computing. We study the density matrix resulting from sampling t copies of a d -dimensional quantum state according to the Haar measure on the orthogonal group. In particular, we analytically compute its spectral decomposition. This allows us to compute exactly the trace distance between t -copies of a real Haar random state and t -copies of a complex Haar random state. Using this we show a lower-bound on the approximation parameter of real-valued state t -designs and improve the lower-bound on the number of copies required for imaginarity testing.
Fields of Study & Subjects
Quantum Mechanics and Applications
Quantum Information and Cryptography
Publication details
- Journal / source
- Quantum
- Publisher
- Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
- Volume
- 10
- Pages
- 2120–2120
- Publication date
- 29 May 2026
- Language
- EN