Quantum algorithms are known for presenting more efficient solutions to certain computational tasks than any corresponding classical algorithm. It has been thought that the origin of the power of quantum computation has its roots in non-classical cor
relations such as entanglement or quantum discord. However, it has been recently shown that even a single pure qudit is sufficient to design an oracle-based algorithm which solves a black-box problem faster than any classical approach to the same problem. In particular, the algorithm that we consider determines whether eight permutation functions defined on a set of four elements is positive or negative cyclic. While any classical solution to this problem requires two evaluations of the function, quantum mechanics allows us to perform the same task with only a single evaluation. Here, we present the first experimental demonstration of the considered quantum algorithm with a quadrupolar nuclear magnetic resonance setup using a single four-level quantum system, i.e., a ququart.
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm, which can so
lve a black-box problem faster than any classical algorithm. For $2d$ permutation functions defined on a set of $d$ elements, deciding whether a given permutation is even or odd, requires evaluation of the function for at least two elements. We demonstrate that a quantum circuit with a single qudit can determine the parity of the permutation with only one evaluation of the function. Our algorithm provides an example for quantum computation without entanglement since it makes use of the pure state of a qudit. We also present an experimental realization of the proposed quantum algorithm with a quadrupolar nuclear magnetic resonance using a single four-level quantum system, i.e., a ququart.
Correlations in quantum systems exhibit a rich phenomenology under the effect of various sources of noise. We investigate theoretically and experimentally the dynamics of quantum correlations and their classical counterparts in two nuclear magnetic r
esonance setups, as measured by geometric quantifiers based on trace-norm. We consider two-qubit systems prepared in Bell diagonal states, and perform the experiments in decohering environments resulting from Bell diagonal-preserving Markovian local noise. We then report the first observation of environment-induced double sudden transitions in the geometric quantum correlations, a genuinely nonclassical effect not observable in classical correlations. The evolution of classical correlations in our physical implementation reveals in turn the finite-time relaxation to a pointer basis under nondissipative decoherence, which we characterize geometrically in full analogy with predictions based on entropic measures.
We demonstrate that arbitrary time evolutions of many-body quantum systems can be reversed even in cases when only part of the Hamiltonian can be controlled. The reversed dynamics obtained via optimal control --contrary to standard time-reversal proc
edures-- is extremely robust to external sources of noise. We provide a lower bound on the control complexity of a many-body quantum dynamics in terms of the dimension of the manifold supporting it, elucidating the role played by integrability in this context.
We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance (NMR) setup and employing geometric discord, we evaluate the quantum correlations of a state witho
ut resorting to prior knowledge of its density matrix. The method is applicable to any (2 x d) system and provides, in terms of number of measurements required, an advantage over full state tomography scaling with the dimension d of the unmeasured subsystem. The negativity of quantumness is measured as well for reference. We also observe the phenomenon of sudden transition of quantum correlations when local phase and amplitude damping channels are applied to the state.
The GOES X1.5 class flare that occurred on August 30,2002 at 1327:30 UT is one of the few events detected so far at submillimeter wavelengths. We present a detailed analysis of this flare combining radio observations from 1.5 to 212 GHz (an upper lim
it of the flux is also provided at 405 GHz) and X-ray. Although the observations of radio emission up to 212 GHz indicates that relativistic electrons with energies of a few MeV were accelerated, no significant hard X-ray emission was detected by RHESSI above ~ 250 keV. Images at 12--20 and 50--100 keV reveal a very compact, but resolved, source of about ~ 10 x 10. EUV TRACE images show a multi-kernel structure suggesting a complex (multipolar) magnetic topology. During the peak time the radio spectrum shows an extended flatness from ~ 7 to 35 GHz. Modeling the optically thin part of the radio spectrum as gyrosynchrotron emission we obtained the electron spectrum (spectral index delta, instantaneous number of emitting electrons). It is shown that in order to keep the expected X-ray emission from the same emitting electrons below the RHESSI background at 250 keV, a magnetic field above 500 G is necessary. On the other hand, the electron spectrum deduced from radio observations >= 50 GHz is harder than that deduced from ~ 70 - 250 keV X-ray data, meaning that there must exist a breaking energy around a few hundred keV. During the decay of the impulsive phase, a hardening of the X-ray spectrum is observed which is interpreted as a hardening of the electron distribution spectrum produced by the diffusion due to Coulomb collisions of the trapped electrons in a medium with an electron density of n_e ~ 3E10 - 5E10 cm-3.
