Realization of the optimal universal quantum entangler (4 pages)

Jaroslav Novotný

Rui Duan, Yuan Feng

M. A. Jafarizadeh, Fahimeh Naghdi, M. R. Bazrafkan

Fabio Sciarrino, F. De Martini, Vladimír Bužek

We present an experimental demonstration of the ``optimal'' and ``universal'' quantum entangling process involving qubits encoded in the polarization of single photons. The structure of the ``quantum entangling machine'' consists of the quantum injected optical parametric amplifier by which the simultaneous realization of the $1\ensuremath{\rightarrow}2$ universal quantum cloning and of the universal NOT (U-NOT) gate has also been achieved.

Yale Yauk, Lucas Hackl, Alexander Hahn

We study bipartite entanglement statistics in one-dimensional anyon chains, whose Hilbert spaces are constrained by fusion rules of unitary pre-modular categories. Our setup generalizes previous frameworks on symmetry-resolved entanglement entropy for non-abelian Lie group symmetries to the setting of quantum groups. We derive analytical expressions for the average anyonic entanglement entropy and its variance. Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(\sqrt{L})$ or $O(1)$ symmetry-type corrections except for a subleading topological correction term that produces a Page curve asymmetry. We further show that the variance decays exponentially with system size, establishing the typicality. Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions, supporting the use of eigenstate entanglement as a diagnostic of quantum chaos. Our results establish the anyonic Page curve as an appropriate chaotic benchmark in topological many-body systems and connect anyonic entanglement to Page-type universality in quantum many-body physics.

Siddhardh C. Morampudi, Anushya Chandran, Chris R. Laumann

Constraints play an important role in the entanglement dynamics of many quantum systems. We develop a diagrammatic formalism to exactly evaluate the entanglement spectrum of random pure states in large constrained Hilbert spaces. The resulting spectra may be classified into universal "phases" depending on their singularities. The simplest class of local constraints reveals a nontrivial phase diagram with a Marchenko-Pastur phase which terminates in a critical point with new singularities. We propose a certain quantum defect chain as a microscopic realization of the critical point. The much studied Rydberg-blockaded or Fibonacci chain lies in the Marchenko-Pastur phase with a modified Page correction to the entanglement entropy. Our results predict the entanglement of infinite temperature eigenstates in thermalizing constrained Floquet spin chains, as we confirm numerically.