Speaker
Description
Symmetry is a fundamental concept in physics and appears in a wide variety of contexts. Quantum information processing is no exception, with many theorems being well-known, such as the Wigner-Araki-Yanase (WAY) theorem, which imposes limitations on measurements, and the Eastin-Knill theorem, which restricts error correction codes.
In this talk, we give an inequality that captures the trade-off structure between symmetry, irreversibility, and quantum coherence, and show that this inequality can unify and extend the symmetry-induced limitations. The examples of the applications are as follows:
• A unification of the WAY theorem for the measurements, the Eastin-Knill theorem for covariant codes, and the WAY theorem for unitary gates
• The existence of a class of Gibbs-preserving maps that require infinite implementation coherence costs
• A trade-off relationship between measurement time and error in finite-time measurements, implying that zero-error measurements require infinite measurement time.