Estimation of Spin-Spin Interaction by Weak Measurement Scheme

Precisely knowing an interaction Hamiltonian is crucial to realize quantum information tasks, especially to experimentally demonstrate a quantum computer and a quantum memory. We propose a scheme to experimentally evaluate the spin-spin interaction for a two-qubit system by the weak measurement technique initiated by Yakir Aharonov and his colleagues. Furthermore, we numerically confirm our proposed scheme in a specific system of a nitrogen vacancy center in diamond. This means that the weak measurement can also be taken as a concrete example of the quantum process tomography.Comment: 4 pages, 1 table, 2 figures, to appear in Europhysics Letter

Asymptotic entanglement in 1D quantum walks with a time-dependent coined

Discrete-time quantum walk evolve by a unitary operator which involves two operators a conditional shift in position space and a coin operator. This operator entangles the coin and position degrees of freedom of the walker. In this paper, we investigate the asymptotic behavior of the coin position entanglement (CPE) for an inhomogeneous quantum walk which determined by two orthogonal matrices in one-dimensional lattice. Free parameters of coin operator together provide many conditions under which a measurement perform on the coin state yield the value of entanglement on the resulting position quantum state. We study the problem analytically for all values that two free parameters of coin operator can take and the conditions under which entanglement becomes maximal are sought.Comment: 23 pages, 4 figures, accepted for publication in IJMPB. arXiv admin note: text overlap with arXiv:1001.5326 by other author

Thermodynamic formalism for dissipative quantum walks

We consider the dynamical properties of dissipative continuous-time quantum walks on directed graphs. Using a large-deviation approach we construct a thermodynamic formalism allowing us to define a dynamical order parameter, and to identify transitions between dynamical regimes. For a particular class of dissipative quantum walks we propose a quantum generalization of the the classical PageRank vector, used to rank the importance of nodes in a directed graph. We also provide an example where one can characterize the dynamical transition from an effective classical random walk to a dissipative quantum walk as a thermodynamic crossover between distinct dynamical regimes.Comment: 8 page

Study on Photon Activation Analysis of Carbon in Glasses for Fiber Amplifiers by Using the Flow Method for the Rapid Separation of ^<11>C(II. Radiochemistry)

We have studied nuclear interference from a matrix produced by (γ, n), (γ, 2n), (γ, p) and (n, γ) reactions and a flow method for ^C separation in order to develop an approach for the photon activation analysis of carbon in InF_3-based fluoride, chalcogenide and tellurite glasses for fiber amplifiers. We found that seventeen radionuclides are produced from these glasses and chemical separation is necessary to determine carbon. For the flow method, which involves the fusion of an irradiated sample with an oxidizer, the conversion of ^C into ^CO_2, and the absorption of ^C in ethanolamine solution, we used a mixture of Pb_3O_4 and B_2O_3 as the oxidizer. We also found that the reaction between ^F(γ, n) and ^Na(γ, αn) in the ethanolamine solution produced ^F contamination with fluoride and chalcogenide glasses and that this flow method can only be applied to tellurite glasses. We confirmed that the chemical yield of the flow method was close to 100 % when determining carbon in standard steel samples by using lithium carbonate as a standard sample. We determined that the carbon concentrations in two kinds of tellurite glass were 8 to 13 and 21 to 28 ppm, respectively

Optimal Covariant Measurement of Momentum on a Half Line in Quantum Mechanics

We cannot perform the projective measurement of a momentum on a half line since it is not an observable. Nevertheless, we would like to obtain some physical information of the momentum on a half line. We define an optimality for measurement as minimizing the variance between an inferred outcome of the measured system before a measuring process and a measurement outcome of the probe system after the measuring process, restricting our attention to the covariant measurement studied by Holevo. Extending the domain of the momentum operator on a half line by introducing a two dimensional Hilbert space to be tensored, we make it self-adjoint and explicitly construct a model Hamiltonian for the measured and probe systems. By taking the partial trace over the newly introduced Hilbert space, the optimal covariant positive operator valued measure (POVM) of a momentum on a half line is reproduced. We physically describe the measuring process to optimally evaluate the momentum of a particle on a half line.Comment: 12 pages, 3 figure

Complex joint probabilities as expressions of determinism in quantum mechanics

The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex conditional probabilities that describe the fundamental relation between precise statements about the three different observables. Since such transformations merely change the representation of the quantum state, these conditional probabilities provide a state-independent definition of the deterministic relation between the outcomes of different quantum measurements. In this paper, it is shown how classical reality emerges as an approximation to the fundamental laws of quantum determinism expressed by complex conditional probabilities. The quantum mechanical origin of phase spaces and trajectories is identified and implications for the interpretation of quantum measurements are considered. It is argued that the transformation laws of quantum determinism provide a fundamental description of the measurement dependence of empirical reality.Comment: 12 pages, including 1 figure, updated introduction includes references to the historical background of complex joint probabilities and to related work by Lars M. Johanse

Weak Values with Decoherence

The weak value of an observable is experimentally accessible by weak measurements as theoretically analyzed by Aharonov et al. and recently experimentally demonstrated. We introduce a weak operator associated with the weak values and give a general framework of quantum operations to the W operator in parallel with the Kraus representation of the completely positive map for the density operator. The decoherence effect is also investigated in terms of the weak measurement by a shift of a probe wave function of continuous variable. As an application, we demonstrate how the geometric phase is affected by the bit flip noise.Comment: 17 pages, 3 figure

Closed timelike curves via post-selection: theory and experimental demonstration

Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can in principle interact with its former self in the past. CTCs appear in many solutions of Einstein's field equations and any future quantum version of general relativity will have to reconcile them with the requirements of quantum mechanics and of quantum field theory. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we explore an alternative quantum formulation of CTCs and show that it is physically inequivalent to Deutsch's. Because it is based on combining quantum teleportation with post-selection, the predictions/retrodictions of our theory are experimentally testable: we report the results of an experiment demonstrating our theory's resolution of the well-known `grandfather paradox.Comment: 5 pages, 4 figure

Coined quantum walks on percolation graphs

Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well-studied on regular structures and also shown to be sensitive to defects and imperfections in the lattice. As a simple example of a disordered system, we consider percolation lattices, in which edges or sites are randomly missing, interrupting the progress of the quantum walk. We use numerical simulation to study the properties of coined quantum walks on these percolation lattices in one and two dimensions. In one dimension (the line) we introduce a simple notion of quantum tunneling and determine how this affects the properties of the quantum walk as it spreads. On two-dimensional percolation lattices, we show how the spreading rate varies from linear in the number of steps down to zero, as the percolation probability decreases to the critical point. This provides an example of fractional scaling in quantum walk dynamics.Comment: 25 pages, 14 figures; v2 expanded and improved presentation after referee comments, added extra figur

Ammonium regulates the development of pine roots through hormonal crosstalk and differential expression of transcription factors in the apex

Ammonium is a prominent source of inorganic nitrogen for plant nutrition, but excessive amounts can be toxic for many species. However, most conifers are tolerant to ammonium, a relevant physiological feature of this ancient evolutionary lineage. For a better understanding of the molecular basis of this trait, ammonium‐induced changes in the transcriptome of maritime pine (Pinus pinaster Ait.) root apex have been determined by laser capture microdissection and RNA sequencing. Ammonium promoted changes in the transcriptional profiles of multiple transcription factors, such as SHORT‐ROOT, and phytohormone‐related transcripts, such as ACO, involved in the development of the root meristem. Nano‐PALDI‐MSI and transcriptomic analyses showed that the distributions of IAA and CKs were altered in the root apex in response to ammonium nutrition. Taken together, the data suggest that this early response is involved in the increased lateral root branching and principal root growth, which characterize the long‐term response to ammonium supply in pine. All these results suggest that ammonium induces changes in the root system architecture through the IAA‐CK‐ET phytohormone crosstalk and transcriptional regulation.This study was funded by Spanish Ministerio de Ciencia e Innovación, grant numbers BIO2015‐73512‐JIN MINECO/AEI/FEDER, UE; RTI2018‐094041‐B‐I00 and EQC2018‐004346‐P. Funding for open access charge: Universidad de Málaga/CBUA. FO was supported by grants from the Universidad de Málaga (Programa Operativo de Empleo Juvenil vía SNJG, UMAJI11, FEDER, FSE, Junta de Andalucía) and BIO‐114, Junta de Andalucí