2022/02/03 by Wilming, Henrik, Roth, Ingo
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2202.01669
It was recently observed that in certain thermalizing many-body systems, measuring the complement of a subsystem that thermalized to infinite temperature in a suitable orthonormal basis gives rise to approximate quantum state k-designs as post-measurement states on the subsystem. We prove that this emergence of approximate k-designs holds true in every large system where some small subsystem is close to being maximally mixed. On a technical level we show that any high-dimensional purification of an approximately maximally mixed state induces an approximate quantum state k-design when measured in a suitable orthonormal basis. Moreover, we show that this is true with overwhelming probability for measurement bases chosen uniformly at random from the Haar measure.