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Quantum nonlocality
Quantum nonlocality

... Before concluding this part there is something more to say. We have used, in our formulation only the universal dynamical principle, the calibration of the experiment and the assumed correspondence of our perceptions to the definite positions of the pointers. But much more is implied. We have prove ...
Time-Space Efficient Simulations of Quantum Computations
Time-Space Efficient Simulations of Quantum Computations

Dynamical Aspects of Information Storage in Quantum
Dynamical Aspects of Information Storage in Quantum

... In this respect, the assumption of finite precision of all physically realizable state preparation, manipulation, and registration procedures is particularly important, and can even be treated as an empirical given. This premise is general enough to subsume (a) fundamental limitations imposed by the ...
The density-matrix renormalization group in the age of matrix
The density-matrix renormalization group in the age of matrix

Holographic quantum error-correcting code
Holographic quantum error-correcting code

11 Canonical quantization of classical fields
11 Canonical quantization of classical fields

... In Sections 5-10 a formalism was developed which allows to describe quantum mechanically interactions of relativistic particles. Starting with the second quantized formulation of quantum mechanics of many-particle systems we have identified in Section 6 the basic properties one-particle states shoul ...
quantum computation of the jones polynomial - Unicam
quantum computation of the jones polynomial - Unicam

The density-matrix renormalization group in the age of matrix
The density-matrix renormalization group in the age of matrix

... made in higher dimensions starting with [65] using a generalization of the MPS state class[66]. The goal of this paper cannot be to provide a full review of DMRG since 1992 as seen from the perspective of 2010, in particular given the review[7], which tries to provide a fairly extensive account of ...
Coherent states and projective representation of the linear canonical
Coherent states and projective representation of the linear canonical

4. Non-Abelian Quantum Hall States
4. Non-Abelian Quantum Hall States

... Note that the argument of the Pfaffian remains anti-symmetric, as it must. Multiplying out the Pfaffian, we see that this state contains the same number of (z ⌘) factors as (4.5), but clearly encodes the positions ⌘1 and ⌘2 of two independent objects. We will refer to these smaller objects as the qu ...
Unit 2: Lorentz Invariance
Unit 2: Lorentz Invariance

... Lie Algebra: generalized vector space (in this case, space of the generators) over a field (R1,3 in this case) with a Lie Bracket (in physics, usually commutation) and certain other axioms, which are automatically met if your Lie Bracket is commutation. ...
De finetti theorems, mean-field limits and bose
De finetti theorems, mean-field limits and bose

Strong no-go theorem for Gaussian quantum bit commitment
Strong no-go theorem for Gaussian quantum bit commitment

Algebraic Study on the Quantum Calogero Model
Algebraic Study on the Quantum Calogero Model

... Among the models in theoretical physics, exactly solvable models deserYe special interest. For instance, the problem on the hydrogen atom, which played a crucial role in bringing high credit to quantum mechanics, is a typical example of the models whose eigenvalue problems are exactly soh·able by se ...
The Thomas-Fermi Theory of Atoms, Molecules and
The Thomas-Fermi Theory of Atoms, Molecules and

... tensor product of Le(R3; C). We continue JGTlYS 1. to denote Ho” ? &‘&vs by F1,” or, when necessary, by 11o”(.s, ,..., z,~; R, ,..,, I&). Wc shall let E.,*o, the “ground state energy,” denote the infinum of the spectrum of Ho”. If N -- 1 < -&, Zj ) this infinum is known to he an eigenvalue of Ho,” 1 ...
how quantum logic differs from classical logic: following distribution
how quantum logic differs from classical logic: following distribution

Calculating Floquet states of large quantum systems: A
Calculating Floquet states of large quantum systems: A

Entanglement or Separability
Entanglement or Separability

Spin Hamiltonians and Exchange interactions
Spin Hamiltonians and Exchange interactions

Hypergroups and Quantum Bessel Processes of Non
Hypergroups and Quantum Bessel Processes of Non

... The rest of this note is structured as follows. Section 2 contains a concise summary of Biane’s construction of the quantum Bessel process; in Section 3 we recall an analogous construction of the usual Bessel process (of integer dimension). In Section 4 we provide basic definitions and terminology as ...
PyProp - A Python Framework for Propagating the Time
PyProp - A Python Framework for Propagating the Time

Types for Quantum Computing
Types for Quantum Computing

Conformal geometry of the supercotangent and spinor
Conformal geometry of the supercotangent and spinor

On the Distribution of the Wave Function for Systems in Thermal
On the Distribution of the Wave Function for Systems in Thermal

... Note that a wave function Ψ chosen at random from this distribution is almost certainly a nontrivial superposition of the eigenstates |ni with random coefficients hn|Ψi that are identically distributed, but not independent. The measure uE,δ is clearly stationary, i.e., invariant under the unitary ti ...
On quantum detection and the square
On quantum detection and the square

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Compact operator on Hilbert space

In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite-rank operators in the uniform operator topology. As such, results from matrix theory can sometimes be extended to compact operators using similar arguments. In contrast, the study of general operators on infinite-dimensional spaces often requires a genuinely different approach.For example, the spectral theory of compact operators on Banach spaces takes a form that is very similar to the Jordan canonical form of matrices. In the context of Hilbert spaces, a square matrix is unitarily diagonalizable if and only if it is normal. A corresponding result holds for normal compact operators on Hilbert spaces. (More generally, the compactness assumption can be dropped. But, as stated above, the techniques used are less routine.)This article will discuss a few results for compact operators on Hilbert space, starting with general properties before considering subclasses of compact operators.
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