Quantum circuits under sufficiently weak monitoring purify on a timescale $T_P$ exponentially long in the system size. This slowness underlies a universal purification dynamics, whose quantitative description has so far required the replica trick, with a delicate analytic continuation. We show that monitored Clifford circuits on $L$ qudits of prime dimension $q$ bypass this construction entirely: in the scaling limit at fixed $x = t/T_P(L)$, purification reduces to the Markovian decay of the density-matrix rank, an exactly solvable death process descending from infinity. We compute the full scaling functions in compact form: all R\'enyi entropies collapse onto a universal curve $\langle S(x) \rangle$. Exact stabilizer simulations at $q=2,3,5$ confirm the predictions, with no fitting parameter for the global model and $T_P$ as the only fitted scale for local brick-wall circuits. Also, the replica problem amounts to a tilted version of the same Markov process, in agreement with exact computations from the Clifford commutant. Finally, the quantization of the rank leaves two hallmarks that distinguish Clifford dynamics from generic monitored circuits: the entropy fluctuations saturate at short scaled times $x\to0$ to an $O(1)$ variance, instead of vanishing, and observables develop a temporal modulation periodic in $\log_q x$, which cannot be captured by the replica approach.
Beatrice Magni, Federico Gerbino, X. Turkeshi et al.· 1 citation
Quantum resource theories characterize distinct forms of nonclassicality in many-body quantum states, raising the question of whether these resources evolve independently under generic ergodic dynamics. Considering diagnostics quadratic in the state, we show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom. For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures, as we demonstrate for coherence, various asymmetries, and number entropies. The same relations hold, to a good approximation, under chaotic Floquet and continuous-time Hamiltonian dynamics, establishing that this dynamical resource equivalence extends beyond random circuits. We further derive an exact coherence--imaginarity relation, remarkably accurate also beyond Haar-random circuits. Our results reveal an emergent simplification of many-body dynamics, in which sufficiently strong scrambling reduces seemingly distinct quantum resources to a few common dynamical degrees of freedom.
Sreemayee Aditya, X. Turkeshi, P. Sierant· 0 citations
Pure-state entanglement rests on a single algebraic backbone: majorization of the Schmidt spectrum governs state conversion under local operations and classical communication, and constrains entanglement monotones. Here we establish a corresponding majorization law for fermionic non-Gaussianity, the resource that elevates free fermions to universal quantum computation. Under any fermionic Gaussian protocol with pure state outcomes, the Williamson spectrum of a pure state's Majorana covariance matrix is weakly majorized by its ensemble average. This spectral law mirrors that of entanglement theory. It turns computable non-Gaussianity quantifiers such as fermionic antiflatness and occupation entropies into strong monotones for fermionic non-Gaussianity, and delivers necessary conditions and converse bounds on state conversion under Gaussian protocols. When fermion parity is conserved, no catalyst can remove a majorization obstruction---unless it carries parity coherence---and asymptotic interconversion is irreversible already for pure states. All relevant quantities are accessible from two-point Majorana correlators, turning the theory developed here into experimentally observable properties of quantum matter, testable on present-day quantum devices.
X. Turkeshi, P. Sierant, P. S. Tarabunga· 0 citations