相关论文: Algebra for generalised quantum observables
It is commonly believed that the most general type of a quantum-mechanical measurement is one described by a positive-operator valued measure (POVM). In the present paper, this statement is proven for any measurements on quantum systems…
We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. Positive operator valued measures describe quantum observables and, similarly to quantum states, also quantum observables…
Analysing Quantum Measurement requires analysing the physics of amplification since amplification of phenomena from one scale to another scale is essential to measurement. There still remains the task of working this into an axiomatic…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
Using geometric quantization procedure, the quantization of algebra of observables for physical system with Ricci-flat phase space is obtained. In the classical case the appointed physical system is reduced to harmonic oscillator when the…
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
We revisit the representation of generalized quantum observables by establishing a geometric picture in terms of their positive operator-valued measures (POVMs). This leads to a clear geometric interpretation of Born's rule by introducing…
A review is given of recent work aimed at constructing a quantum theory of cosmology in which all observables refer to information measurable by observers inside the universe. At the classical level the algebra of observables should be…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
Observational entropy is interpreted as the uncertainty an observer making measurements associates with a system. So far, properties that make such an interpretation possible rely on the assumption of ideal projective measurements. We show…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
A reference frame F is described by the element g of the Poincare' group P which connects F with a given fixed frame F_0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have…
The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
We introduce a generalization of symmetric measurements to collections of unequinumerous positive, operator-valued measures (POVMs). For informationally complete sets, we propose construction methods from orthonormal Hermitian operator…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
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…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…