Related papers: Quantum computational logic with mixed states
It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or…
The concrete schemes to realize three types of basic quantum logical gates using linear quadripartite cluster states of optical continuous variables are proposed. The influences of noises and finite squeezing on the computation precision…
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…
We introduce QuAlg, an open-source symbolic algebra package for quantum information. QuAlg supports working with qubit-states, qudit-states, fock-states and even wave-functions in infinite dimenional Hilbert spaces. States can have…
If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting…
Quasi-set theory was proposed as a mathematical context to investigate collections of indistinguishable objects. After presenting an outline of this theory, we define an algebra that has most of the standard properties of an orthocomplete…
In this article, we develop an algebraic framework of axioms which abstracts various high-level properties of multi-qudit representations of generalized Clifford algebras. We further construct an explicit model and prove that it satisfies…
It is well-known that a Hilbert-style deduction system for first-order classical logic is sound and complete for a model theory built using all Boolean algebras as truth-value algebras if and only if it is sound and complete for a model…
We investigate some forms of quantum logic arising from the standard and the unsharp approach.
The aim of this paper is to apply a contextual probabilistic model (in the spirit of Mackey, Gudder, Ballentine) to represent and to generalize some results of quantum logic about possible macroscopic quantum-like (QL) behaviour. The…
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that…
We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
We provide here a general mathematical framework to model attitudes towards ambiguity which uses the formalism of quantum theory as a ``purely mathematical formalism, detached from any physical interpretation''. We show that the…
We formalize the quantum arithmetic, i.e. a relationship between number theory and operator algebras. Namely, it is proved that rational projective varieties are dual to the $C^*$-algebras with real multiplication. Our construction fits all…
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…