Preparation of entangled states by quantum Markov processes

Abstract

We investigate the possibility of using a dissipative process to prepare a quantum system in a desired state. We derive for any multipartite pure state a dissipative process for which this state is the unique stationary state and solve the corresponding master equation analytically. For certain states, like the Cluster states, we use this process to show that the jump operators can be chosen quasi-locally, i.e. they act non-trivially only on a few, neighboring qubits. Furthermore, the relaxation time of this dissipative process is independent of the number of subsystems. We demonstrate the general formalism by considering arbitrary MPS-PEPS states. In particular, we show that the ground state of the AKLT-model can be prepared employing a quasi-local dissipative process.

Quantum states and phases in driven open quantum systems with cold atoms

“…While the present work has focused on condensed matter aspects of realizing nonequlibirium (quasi-)condensates of interacting bosons and paired fermions in optical lattices, the present ideas are readily extended to spin systems, and promise a new avenue towards preparing interesting entangled states of qubits for quantum information [16]. On the atomic physics side, control via external fields offers interesting new possibilities of engineering a broad class of quantum jump operators (3), one example being phase imprinting a i → a i e iφi with a laser.…”

“…the dark state is an eigenstate of the set of quantum jump operators with zero eigenvalue, which will be compatible with the dynamics induced by the Hamiltonian if (ii) H |D = E |D . Uniqueness of the dark state is guaranteed if there is no other subspace of the system Hilbert space which is invariant under the action of the operators c ℓ [15,16]. In fact, it can be shown that for any given pure state there will be a master equation so that this state becomes the unique steady state [16].…”

“…While in quantum optics we know several examples of preparing single particle pure states dissipation, including dark state laser cooling to subrecoil temperatures [17,18], it is of interest to extend these ideas to many body systems, dissipatively driving the system into entangled states of interest, or preparing non-equilibrium quantum phases in condensed matter systems. Furthermore, for the example of a dissipative driven Bose Einstein condensate (BEC) discussed below, but also for stabilizer states in a system of spins-1/2 or qubits living on a lattice [16], the dissipation can be chosen to be quasi-local, i.e. the jump operators act non-trivially only on a small neighborhood of particles.…”

Simulation of single-qubit open quantum systems

“…This formalism offers a natural setting for the simulation of open quantum systems and arXiv:1405.6049v3 [quant-ph] 28 May 2017 research in this direction has resulted in successful experimental demonstrations of the dissipative simulation of complex many-body spin models [27,28]. In addition, dissipative quantum computation has allowed for alternative approaches to state preparation [29]- [38] and universal quantum computation [39,40]. Importantly however, it has recently been shown that dissipative quantum computing is no more powerful than the traditional circuit model -the so called "Dissipative Church Turing Thesis" [41].…”

Thermodynamic formalism for dissipative quantum walks

“…Quantum fluctuations alone can give origin, at zero temperature, to quantum phase transitions [2] whose effects can experimentally be observed in a critical region at small but finite temperatures. Away from thermodynamic equilibrium engineered open quantum systems provide a more recent source of interest [3][4][5]. In these latter settings a controlled environment can be used to drive the system to a steady state whose properties depend on system and environment parameters.…”