Unitary-Invariant Witnesses of Quantum Imaginarity.

Quantum theory is traditionally formulated using complex numbers. This imaginarity of quantum theory has been quantified as a resource with applications in discrimination tasks, pseudorandomness generation, and quantum metrology. In the standard formulation, a quantum state is said to have "imaginarity" if the associated density matrix is not real-valued in a given, fixed basis.

Quadratic Speedup for Spatial Search by Continuous-Time Quantum Walk.

Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a quadratic advantage over classical random walks has been an outstanding problem. Thus far, this advantage is obtained only for specific graphs or when a single node of the underlying graph is marked.

Optimal Quantum Spatial Search on Random Temporal Networks.

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs G(n,p), where p is the probability that any two given nodes are connected: After every time interval τ, a new graph G(n,p) replaces the previous one. We prove analytically that, for any given p, there is always a range of values of τ for which the running time of the algorithm is optimal, i.

Publisher's Note: Spatial Search by Quantum Walk is Optimal for Almost All Graphs [Phys. Rev. Lett. 116, 100501 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.

Spatial Search by Quantum Walk is Optimal for Almost all Graphs.

The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work, we prove that for Erdös-Renyi random graphs, i.

Disorder-assisted quantum transport in suboptimal decoherence regimes.

We investigate quantum transport in binary tree structures and in hypercubes for the disordered Frenkel-exciton Hamiltonian under pure dephasing noise. We compute the energy transport efficiency as a function of disorder and dephasing rates. We demonstrate that dephasing improves transport efficiency not only in the disordered case, but also in the ordered one.

Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs.

Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that confine the dynamics to a smaller subspace of the full Hilbert space. In this work, we use invariant subspace methods, that can be computed systematically using the Lanczos algorithm, to obtain the reduced set of states that encompass the dynamics of the problem at hand without the specific knowledge of underlying symmetries.

Multibiomarker approach in fish to assess the impact of pollution in a large Brazilian river, Paraiba do Sul.

This article examines the advantages of the use of biomarkers as environmental indicators by applying it to Paraiba do Sul watershed, one of the most important Brazilian water bodies, which is in a critical environmental situation. We use a multibiomarker approach in fish as an integrated strategy to assess the impact of pollution. It comprehends a general biomarker of fish health, the condition factor (CF), and specific biomarkers of contaminant exposure such as metallothionein (MT), acetylcholinesterase (AChE) activity and biliary polycyclic aromatic hydrocarbons (PAH) metabolites.