The Elusive Source of Quantum Speedup

We discuss two qualities of quantum systems: various correlations existing between their subsystems and the distinguishability of different quantum states. This is then applied to analysing quantum information processing. While quantum correlations, or entanglement, are clearly of paramount importance for efficient pure state manipulations, mixed states present a much richer arena and reveal a more subtle interplay between correlations and distinguishability. The current work explores a number of issues related with identifying the important ingredients needed for quantum information processing. We discuss the Deutsch-Jozsa algorithm, the Shor algorithm, the Grover algorithm and the power of a single qubit class of algorithms. In the latter, a quantity called discord is seen to be more important than entanglement. One section is dedicated to cluster states where entanglement is crucial, but its precise role is highly counter-intuitive. Here we see that the notion of distinguishability becomes a more useful concept.     

Witnessing Quantum Speedup through Mutual Information

Achieving dynamical speedup of evolution in an open quantum system plays a key role in many technological applications. However, how to detect quantum speedup is unclear. In this work, a method to witness quantum speedup through the measure of the mutual information is presented. It is shown that the speed of evolution of a quantum system, can be witnessed by calculating the mutual information variation, whose increase is a clear signature of dynamical speedup. The result is explained by considering the time evolution of two qubits under a one‐sided noisy channel, finding out that the mechanism for the quantum speedup is closely associated with the total exchange of information between the system and its environment, which can be expressed by the variation of mutual information. Quantitatively, the average speed of evolution is shown proportional to the average variation of the mutual information in an interval of time. The conclusion can not only explain why the quantum entanglement (or quantum coherence) and the classical correlation are neither necessary nor sufficient to speed up the quantum evolution, but also give a vital way of detecting quantum speedup in realistic environments.     

On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms

In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.     

Maximum Speedup in Quantum Search: O(1) Running Time

We consider the running time of the generalized quantum search Hamiltonian. We provide the surprising result that the maximum speedup of quantum search in the generalized Hamiltonian is an O(1) running time regardless of the number of total states. This seems to violate the proof of Zalka that the quadratic speedup is optimal in quantum search. However the argument of Giovannetti et al. that a quantum speedup comes from the interaction between subsystems (or, equivalently entanglement) (and is concerned with the Margolus and Levitin theorem) supports our result.     

Quantum Correlations Evolution Asymmetry in Quantum Channels

It was demonstrated that the entanglement evolution of a specially designed quantum state in the bistochastic channel is asymmetric. In this work, we generalize the study of the quantum correlations, including entanglement and quantum discord, evolution asymmetry to various quantum channels. We found that the asymmetry of entanglement and quantum discord only occurs in some special quantum channels, and the behavior of the entanglement evolution may be quite different from the behavior of the quantum discord evolution. To quantum entanglement, in some channels it decreases monotonously with the increase of the quantum channel intensity. In some other channels, when we increase the intensity of the quantum channel, it decreases at first, then keeps zero for some time, and then rises up. To quantum discord, the evolution becomes more complex and you may find that it evolutes unsmoothly at some points. These results illustrate the strong dependence of the quantum correlations evolution on the property of the quantum channels.     

Nonperturbative Quantum Field Evolution

We introduce a nonperturbative, first-principles approach to time-dependent problems in quantum field theory. In this approach, the time-evolution of quantum field configurations is calculated in real time and at the amplitude level. This method is particularly suitable for treating systems interacting with a time-dependent background field. As a test problem, we apply this approach to QED and study electron acceleration and the associated photon emission in a time- and space-dependent electromagnetic background field.     

Completing the Physical Representation of Quantum Algorithms Provides a Quantitative Explanation of Their Computational Speedup

The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: (i) extending the representation to the process of setting the problem, (ii) relativizing the extended representation to the problem solver to whom the problem setting must be concealed, and (iii) symmetrizing the relativized representation for time reversal to represent the reversibility of the underlying physical process. The third steps projects the input state of the representation, where the problem solver is completely ignorant of the setting and thus the solution of the problem, on one where she knows half solution (half of the information specifying it when the solution is an unstructured bit string). Completing the physical representation shows that the number of computation steps (oracle queries) required to solve any oracle problem in an optimal quantum way should be that of a classical algorithm endowed with the advanced knowledge of half solution.     

Improved Fake-State Attack to the Quantum Key Distribution Systems

It has been showed that most commercial quantum cryptosystems are vulnerable to the fake-state attacks, which employ the loophole that the avalanche photodiodes as single photon detectors still produce detection events in the linear mode. However, previous fake-state attacks may be easily prevented by either installing a watch dog or reconfiguring the dead-time assigning component. In this paper, we present a new technique to counteract the after-pulse effect ever enhanced by the fake-state attacks, in order to lower the quantum bit error rate. Obviously, it is more difficult to detect the presented attack scheme. Indeed, it contributes to promoting of implementing a secure quantum cryptosystem in real life.     

Maximum Speed of Quantum Evolution

In this paper, we discuss the question of the minimum time needed for any state of a given quantum system to evolve into a distinct (orthogonal) state. This problem is relevant to deriving physical limits in quantum computation and quantum information processing. Here, we consider both cases of nonadiabatic and adiabatic evolution and we derive the Hamiltonians corresponding to the minimum time evolution predicted by the Margolus–Levitin theorem.     

A Note on the Stochastic Nature of Feynman Quantum Paths

We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.     

Exact Sampling of Self-avoiding Paths via Discrete Schramm-Loewner Evolution

We present an algorithm, based on the iteration of conformal maps, that produces independent samples of self-avoiding paths in the plane. It is a discrete process approximating radial Schramm-Loewner evolution growing to infinity. We focus on the problem of reproducing the parametrization corresponding to that of lattice models, namely self-avoiding walks on the lattice, and we propose a strategy that gives rise to discrete paths where consecutive points lie an approximately constant distance apart from each other. This new method allows us to tackle two non-trivial features of self-avoiding walks that critically depend on the parametrization: the asphericity of a portion of chain and the correction-to-scaling exponent.     

Symmetry and Evolution in Quantum Gravity

We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory contains an evolution equation distinct from standard Wheeler–DeWitt cosmology. Furthermore, the local symmetry principle—and corresponding observables—of the theory have a direct interpretation in terms of a conventional gauge theory, where the gauge symmetry group is that of spatial conformal diffeomorphisms (that preserve the spatial volume of the Universe). The global evolution is in terms of an arbitrary parameter that serves only as an unobservable label for successive states of the Universe. Our proposal follows unambiguously from a suggestion of York whereby the independently specifiable initial data in the action principle of General Relativity is given by a conformal geometry and the spatial average of the York time on the spacelike hypersurfaces that bound the variation. Remarkably, such a variational principle uniquely selects the form of the constraints of the theory so that we can establish a precise notion of both symmetry and evolution in quantum gravity.     

Ising Quantum Chain and Sequence Evolution

A sequence space model which describes the interplay of mutation and selection in molecular evolution is shown to be equivalent to an Ising quantum chain. Observable quantities tailored to match the biological situation are then employed to treat three fitness landscapes exactly.     

Evolution of Quantum States Simultaneously Undergoing Two Kinds of Quantum Noises

International Journal of Theoretical Physics - Using the thermal-entangled state representations, we obtain the analytical evolution of quantum states simultaneously undergoing two kinds of quantum...     

Concentration Effect of Quantum and Classical Correlations during Quantum Brachistochrone Evolution

We explore the role of quantum brachistochrone evolution to quantum and classical correlations in three-qubit systems, and show that the time-averaged correlations of three-qubit systems exhibit an obvious concentration effect, which means both the standard deviations of time-averaged quantum and classical correlations decrease with the separation angle. Furthermore, we find that the concentration effect on genuine tripartite entanglement is the most significant during the quantum brachistochrone evolution of three-qubit systems.