Learning Markov Decision Processes for Model Checking

Constructing an accurate system model for formal model verification can be both resource demanding and time-consuming. To alleviate this shortcoming, algorithms have been proposed for automatically learning system models based on observed system behaviors. In this paper we extend the algorithm on learning probabilistic automata to reactive systems, where the observed system behavior is in the form of alternating sequences of inputs and outputs. We propose an algorithm for automatically learning a deterministic labeled Markov decision process model from the observed behavior of a reactive system. The proposed learning algorithm is adapted from algorithms for learning deterministic probabilistic finite automata, and extended to include both probabilistic and nondeterministic transitions. The algorithm is empirically analyzed and evaluated by learning system models of slot machines. The evaluation is performed by analyzing the probabilistic linear temporal logic properties of the system as well as by analyzing the schedulers, in particular the optimal schedulers, induced by the learned models.Comment: In Proceedings QFM 2012, arXiv:1212.345

Enhancement of Entanglement Percolation in Quantum Networks via Lattice Transformations

We study strategies for establishing long-distance entanglement in quantum networks. Specifically, we consider networks consisting of regular lattices of nodes, in which the nearest neighbors share a pure, but non-maximally entangled pair of qubits. We look for strategies that use local operations and classical communication. We compare the classical entanglement percolation protocol, in which every network connection is converted with a certain probability to a singlet, with protocols in which classical entanglement percolation is preceded by measurements designed to transform the lattice structure in a way that enhances entanglement percolation. We analyze five examples of such comparisons between protocols and point out certain rules and regularities in their performance as a function of degree of entanglement and choice of operations.Comment: 12 pages, 17 figures, revtex4. changes from v3: minor stylistic changes for journal reviewer, minor changes to figures for journal edito

Exactness of the Original Grover Search Algorithm

It is well-known that when searching one out of four, the original Grover's search algorithm is exact; that is, it succeeds with certainty. It is natural to ask the inverse question: If we are not searching one out of four, is Grover's algorithm definitely not exact? In this article we give a complete answer to this question through some rationality results of trigonometric functions.Comment: 8 pages, 2 figure

Calculation of compressible turbulent boundary layers with pressure gradients and heat transfer

Calculation of compressible turbulent boundary layers with pressure gradients and heat transfe

Preparation of entangled states of two photons in several spatial modes

We describe a protocol capable of preparing an arbitrary state of two photons in several spatial modes using pairs of photons generated by spontaneous parametric down-conversion, linear optical elements and single-photon detectors or post-selection. The protocol involves unitary and non-unitary transformations realizable by beam splitters and phase shifters. Non-unitary transformations are implemented by attenuation filters. The protocol contains several optimization capabilities with the goal of improving overall probability of its success. We also show how entangled two-photon states required for quantum computing with linear optics can be prepared using a very simple and feasible scheme.Comment: 9 pages, 9 figures, REVTeX

Entanglement production by quantum error correction in the presence of correlated environment

We analyze the effect of a quantum error correcting code on the entanglement of encoded logical qubits in the presence of a dephasing interaction with a correlated environment. Such correlated reservoir introduces entanglement between physical qubits. We show that for short times the quantum error correction interprets such entanglement as errors and suppresses it. However for longer time, although quantum error correction is no longer able to correct errors, it enhances the rate of entanglement production due to the interaction with the environment.Comment: 7 pages, 3 figures, published versio

Disentanglement and decoherence in two-spin and three-spin systems under dephasing

We compare disentanglement and decoherence rates within two-spin and three-spin entangled systems subjected to all possible combinations of local and collective pure dephasing noise combinations. In all cases, the bipartite entanglement decay rate is found to be greater than or equal to the dephasing-decoherence rates and often significantly greater. This sharpens previous results for two-spin systems [T. Yu and J. H. Eberly Phys. Rev. B 68, 165322 (2003)] and extends them to the three-spin context.Comment: 17 page

Spin Coherence During Optical Excitation of a Single NV Center in Diamond

We examine the quantum spin state of a single nitrogen-vacancy (NV) center in diamond at room temperature as it makes a transition from the orbital ground-state (GS) to the orbital excited-state (ES) during non-resonant optical excitation. While the fluorescence read-out of NV-center spins relies on conservation of the longitudinal spin projection during optical excitation, the question of quantum phase preservation has not been examined. Using Ramsey measurements and quantum process tomography, we establish limits on NV center spin decoherence induced during optical excitation. Treating the optical excitation and ES spin precession as a quantum process, we measure a process fidelity of F=0.87\pm0.03, which includes ES spin dephasing during measurement. Extrapolation to the moment of optical excitation yields F\approx0.95. This result demonstrates that ES spin interactions may be used as a resource for quantum control because the quantum spin state can survive incoherent orbital transitions.Comment: 12 pages, 3 figure

On-demand generation of entanglement of atomic qubits via optical interferometry

The problem of on-demand generation of entanglement between single-atom qubits via a common photonic channel is examined within the framework of optical interferometry. As expected, for a Mach-Zehnder interferometer with coherent laser beam as input, a high-finesse optical cavity is required to overcome sensitivity to spontaneous emission. We show, however, that with a twin-Fock input, useful entanglement can in principle be created without cavity-enhancement. Both approaches require single-photon resolving detectors, and best results would be obtained by combining both cavity-feedback and twin-Fock inputs. Such an approach may allow a fidelity of $.99$ using a two-photon input and currently available mirror and detector technology. In addition, we study interferometers based on NOON states and show that they perform similarly to the twin-Fock states, yet without the need for high-precision photo-detectors. The present interferometrical approach can serve as a universal, scalable circuit element for quantum information processing, from which fast quantum gates, deterministic teleportation, entanglement swapping $etc.$, can be realized with the aid of single-qubit operations.Comment: To be published in PR