相关论文: Remarks on quantum transmutation
We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the correction of algebras of observables (and may…
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
We discuss the main points of the quantum group approach in the theory of quantum integrable systems and illustrate them for the case of the quantum group $U_q(\mathcal L(\mathfrak{sl}_2))$. We give a complete set of the functional…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
A fully relational quantum theory necessarily requires an account of changes of quantum reference frames, where quantum reference frames are quantum systems relative to which other systems are described. By introducing a relational…
We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of…
Quantum Fourier transformation is important in many quantum algorithms. In this paper, we generalize quantum Fourier transformation over the Abelian group $\mathbb{Z}_N$ from two different points to get more efficient unitary…
In this article we review some results obtained from a generalization of quantum mechanics obtained from modification of the canonical commutation relation $[q,p]={\rm i}\hbar$. We present some new results concerning relativistic…
We formulate a systematic construction of commuting quantum traces for reflection algebras. This is achieved by introducing two sets of generalized reflection equations with associated consistent fusion procedures. Products of their…
We discuss several seemingly assorted objects: the umbral calculus, generalised translations and associated transmutations, symbolic calculus of operators. The common framework for them is representations of the Weyl algebra of the…
To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…
In this paper, the quantization and generalized uncertainty relation for some quantum deformed algebras are investigated. For several deformed algebras, the commutation relation between the position and the momentum operator is shown to be…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
In this paper we compute explicit formulas for the commutation relations among quantum minors in the quantum matrix bialgebra $\cO_q(M_n(k))$.
Quantum operations provide a general description of the state changes allowed by quantum mechanics. Simple necessary and sufficient conditions for an ideal quantum operation to be reversible by a unitary operation are derived in this paper.…
In the quantum theory, it has been shown that one can see if a process has the time reversal symmetry by applying the matrix transposition and examining if it remains physical. However, recent discoveries regarding the indefinite causal…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…