The dynamical evolution of a quantum register of arbitrary length coupled to an environment of arbitrary coherence length is predicted within a relevant model of decoherence. The results are reported for quantum bits (qubits) coupling individually to different environments (“independent decoherence”) and qubits interacting collectively with the same reservoir (“collective decoherence”). In both cases, explicit decoherence functions are derived for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: We show that this sensitivity is a characteristic of both types of coupling (collective and independent) and not only of the collective coupling, as has been reported previously. A nontrivial behavior (“recoherence”) is found in the decay of the off-diagonal elements of the reduced density matrix in the specific situation of independent decoherence. Our results lead to the identification of decoherence-free states in the collective decoherence limit. These states belong to subspaces of the system’s Hilbert space that do not get entangled with the environment, making them ideal elements for the engineering of “noiseless” quantum codes. We also discuss the relations between decoherence of the quantum register and computational complexity based on the dynamical results obtained for the register density matrix.

We show that the quantum phase transition arising in a standard radiation-matter model (Dicke model) belongs to the same universality class as the infinitely coordinated, transverse-field XY model. The effective qubit-qubit exchange interaction is shown to be proportional to the square of the qubit-radiation coupling. A universal finite-size scaling is derived for the corresponding two-qubit entanglement (concurrence) and a size-consistent effective Hamiltonian is proposed for the qubit subsystem.

We show that the topological phase transition for a Kitaev chain embedded in a cavity can be identified by measuring experimentally accessible photon observables such as the Fano factor and the cavity quadrature amplitudes. Moreover, based on density matrix renormalization group numerical calculations, endorsed by an analytical Gaussian approximation for the cavity state, we propose a direct link between those observables and quantum entropy singularities. We study two bipartite entanglement measures, the von Neumann and Rényi entanglement entropies, between light and matter subsystems. Even though both display singularities at the topological phase transition points, remarkably only the Rényi entropy can be analytically connected to the measurable Fano factor. Consequently, we show a method to recover the bipartite entanglement of the system from a cavity observable. Thus, we put forward a path to experimentally access the control and detection of a topological quantum phase transition via the Rényi entropy, which can be measured by standard low noise linear amplification techniques in superconducting circuits. In this way, the main quantum information features of Majorana polaritons in photon-fermion systems can be addressed in feasible experimental setups.

We propose a nanostructure switch based on nuclear magnetic resonance which offers reliable quantum gate operation, an essential ingredient for building a quantum computer. The nuclear resonance is controlled by the magic number transitions of a few-electron quantum dot in an external magnetic field.

We investigate the non-equilibrium quantum dynamics of a canonical light–matter system—namely, the Dicke model—when the light–matter interaction is ramped up and down through a cycle across the quantum phase transition. Our calculations reveal a rich set of dynamical behaviors determined by the cycle times, ranging from the slow, near adiabatic regime through to the fast, sudden quench regime. As the cycle time decreases, we uncover a crossover from an oscillatory exchange of quantum information between light and matter that approaches a reversible adiabatic process, to a dispersive regime that generates large values of light–matter entanglement. The phenomena uncovered in this work have implications in quantum control, quantum interferometry, as well as in quantum information theory.