Work

Exact distinguishability between real-valued and complex-valued Haar random quantum states

Year: 2026

Type: article

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.

Source: Quantum

DOI: 10.22331/q-2026-05-29-2120

Authors: Tristan Nemoz, Romain Alléaume, Peter Brown

Institutions: Télécom Paris, Institut national de recherche en sciences et technologies du numérique, Institut Polytechnique de Paris, Laboratoire Traitement et Communication de l’Information, QURIOSITY: Communication et Traitement Quantiques de l'Information

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $215

Funders: European Commission, HORIZON EUROPE Framework Programme