相关论文: Quantum Advantage without Entanglement

A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms.…

This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we analyze their main characteristics,…

The speed-up provided by quantum algorithms with respect to their classical counterparts is at the origin of scientific interest in quantum computation. However, the fundamental reasons for such a speed-up are not yet completely understood…

In 1985, David Deutsch challenged the Church-Turing thesis by stating that his quantum model of computation "could, in principle, be built and would have many remarkable properties not reproducible by any Turing machine". While this is…

Although a precise description of microscopic physical problems requires a full quantum mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which…

We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…

That superpositions of states can be useful for performing tasks in quantum systems has been known since the early days of quantum information, but only recently has quantitative theory of quantum coherence been proposed. Here we apply that…

Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…

We analyze utility of communication channels in absence of any short of quantum or classical correlation shared between the sender and the receiver. To this aim, we propose a class of two-party communication games, and show that the games…

We present a scheme to efficiently simulate, with a classical computer, the dynamics of multipartite quantum systems on which the amount of entanglement (or of correlations in the case of mixed-state dynamics) is conveniently restricted.…

Not all quantum protocols require entanglement to outperform their classical alternatives. The nonclassical correlations that lead to this quantum advantage are conjectured to be captured by quantum discord. Here we demonstrate that discord…

In the black-box model, problems constrained by a `promise' are the only ones that admit a quantum exponential speedup over the best classical algorithm in terms of query complexity. The most prominent example of this is the Deutsch-Jozsa…

We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…

Coherently manipulating multipartite quantum correlations leads to remarkable advantages in quantum information processing. A fundamental question is whether such quantum advantages persist only by exploiting multipartite correlations, such…

We observe that fault-tolerant quantum computers have an optimal advantage over classical computers in approximating solutions to many NP optimization problems. This observation however gives nothing in practice.

We demonstrate that quantum entanglement can help separated individuals in making decisions if their goal is to find each other in the absence of any communication between them. We derive a Bell-like inequality that the efficiency of every…

One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed…

Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm'…

In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…

The mathematical structure of quantum entanglement is studied and classified from the point of view of quantum compound states. We show that t he classical-quantum correspondences such as encodings can be treated as dia gonal (d-)…