Haar randomness is the standard null model for quantum typicality, scrambling, and random-matrix formulations of thermalization. In many physical settings, however, randomness is naturally constrained to subspaces of Hilbert space. This structure arises, in particular, both in systems with symmetry-resolved sectors and in the Eigenstate Thermalization Hypothesis (ETH), where mesoscopic energy windows define subspaces in which nearby energy eigenstates are mixed. Motivated by these settings, we consider a Block-Unitary Ensemble consisting of independently Haar-random unitaries acting on each subspace. We develop a constructive Weingarten Calculus for this ensemble, providing a unified framework across quantum information and many-body physics. This construction reveals a symmetry-resolved Schur-Weyl duality, where the relevant commutant is not the ordinary permutation algebra, but the one of color-preserving permutations. We apply this framework to quantum states under symmetry constraints and to energy-resolved ensembles for ETH.
We develop a framework to construct large decoherence-free subspaces with a non-trivial structure. The construction is based on hybrid quantum systems in which quantum matter is coupled to a dissipative bosonic mode. Dissipation imposes a global constraint on the matter by selecting the matter null states in the long-t...
Black holes are conjectured to be maximally chaotic, with their quantum spectra expected to exhibit universal random-matrix correlations. This expectation, however, has so far rested largely on holographic descriptions or on many-body models in which randomness is introduced rather than derived from the microscopic deg...
Matchgate circuits describe classically tractable dynamics in a physically relevant setting while nonetheless exhibiting features characteristic of complex quantum systems, such as high amounts of magic. This invites the broader question: to what extent are typical complexity measures saturated under trivial dynamics?...
Gregory A. L. White, Jens Eisert, Neil Dowling· 1 citation
We study the one-sided time evolution of thermofield double (TFD) states in random matrix theory, where the Hamiltonian is taken to be a $D\times D$ random matrix drawn from a unitarily invariant emsemble of Hermitian matrices. We argue that the Krylov basis with the maximally entangled state taken as the initial vecto...
Random unitary operations are a fundamental resource for quantum information processing, yet provably generating them with experimentally available controls remains challenging. Existing approaches often require calculating higher-order operator expectation values, relying on statistical assumptions about the experimen...
Oscar Scholin, Apollonas S. Matsoukas-Roubeas, Sathyawageeswar Subramanian· 0 citations
We study the emergent randomness in projected ensembles generated by dual-unitary circuits. Specifically, we consider evolution by solvable dual-unitary brickwork circuits followed by measurements on part of the system, which induce an ensemble of states on the unmeasured subsystem. Previous work has established that t...
Rahul Arvind, Nicholas Hunter-Jones· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
