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2
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1answer
349 views

a question about geometric quantization background

I don't understand why for geometric description of a regular system, we take always the classical phase space as a symplectic manifold?
1
vote
1answer
26 views

Average entropy of quantum system in bipartite pure state for finite temperature

[I got halfway through writing this when I found the paper that answers the question in (essentially) the affirmative. I'll post it anyways in case anyone is interested.] Background: If a random ...
19
votes
0answers
624 views

conjectures regarding a new Renyi information quantity

In a recent paper http://arxiv.org/abs/1403.6102, we defined a quantity that we called the "Renyi conditional mutual information" and investigated several of its properties. We have some open ...
8
votes
0answers
239 views

Uncertainty principle in Entropy terms

Math Questions: Consider Hilbert space $L_2(\mathbb{R})$ with a standard norm $ ||\psi|| = ( \int_{\mathbb{R}}{ |\psi(t)|^2 dt } )^{1/2}, $ and Fourier transform $ (F\psi)(\xi) = ...
7
votes
0answers
297 views

Quantizations in quantum mechanics

Perhaps this is not an appropriate question for MO, but having just discovered this site I wanted to ask it. Is there a rigorous definition as to what "a quantization" of a Hamiltonian dynamical ...
6
votes
0answers
133 views

From 3-framings on $\Sigma$ to $\mathrm{Spin}^c$-structures on $\mathrm{Loc}_G(\Sigma)$?

Here is my question, below that some motivation: For $G$ a compact abelian Lie group and $\Sigma$ a surface, with $M_G = \mathrm{Loc}_G(\Sigma)$ denoting the space of flat $G$-connections on $\Sigma$ ...
6
votes
0answers
210 views

Lovász function of the Möbius ladder

Quantum motivation Noncontextuality inequalities (and in particular Bell inequalities) can be mapped into graphs, in such a way that its relevant properties can be calculated via some simple ...
4
votes
0answers
60 views

$q$-deformations of fundamental equation of information and entropies

Classical information theory: fundamental equation of information In classical information theory, the information $I(A)$ of an event $A$ (any element of the $\sigma$-algebra $\mathcal F$ of a ...
3
votes
0answers
156 views

Why is geometric quantization (esp. Berezin-Toeplitz quantization) interesting for a symplectic geometer/topologist?

I know that many symplectic geometers are interested in quantization as well. From what I understood, quantization isn't expected to be used as a tool to answer symplectic questions (as in ...
3
votes
0answers
81 views

Is there a known generalization of the Schmidt decomposition based on a maximal set of “locally orthogonal” vectors?

I came across the following unusual generalization of the Schmidt decomposition in my work, which I describe below. I would like to know if this structure has been studied before so I can read more ...
3
votes
0answers
204 views

is there any connection between the consistent histories interpretation of quantum mechanics and kripke semantics?

Kripke semantics interpret intuitionistic logic by a partially ordered set of worlds/situations. Consistent histories interpretation of QM elaborates the copenhagen interpretation where a consistent ...
3
votes
0answers
186 views

Bell polytopes with nontrivial symmetries

Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, r_i}$, possibly in a nondeterministic manner. We are interested in joint ...
2
votes
0answers
102 views

Three body problem with two fermions and a different particle

I'm studying the three body problem with two fermions of unitary mass and another different particle. I need references of the HVZ theorem in this case. Is there someone who knows them?
2
votes
0answers
313 views

Quantum sheaves

Are the following definitions known? Consider H a Hilbert space. A "quantum topology" on H is a set Sigma of closed subspaces satisfying the following conditions: (a) {0} and H lie in Sigma (b) If ...
1
vote
0answers
116 views

The Moyal action of a planar vector field

Let $X=P\frac{\partial}{\partial x}+Q\frac{\partial}{\partial y}$ be a polynomial vector field on $\mathbb{R}^{2}$. Consider the following (Moyal) derivation on $\mathbb{C}[x,y]$: ...
1
vote
0answers
146 views

A “coarse” version of position operator and its properties

I am wondering if someone has ever studied the following operator in the context of quantum mechanics: $$Q : L^2(\mathbb{R}) \to L^2(\mathbb{R})$$ $$(Q f)(x) := s(x) f(x),$$ where $s(x)$ is the ...
1
vote
0answers
59 views

Discretization model for Dirac equation in higher dimensions

I'm wondering if there are cases of discretization models (in lattices or graphs) that converge toward the non-linear Dirac equations? While there is a paper on the 2-d and 3-d cases ...
1
vote
0answers
289 views

How to estimate the quantum fidelity between two given states

There is a well-known theorem, firstly obtained by Denes Petz, in quantum information theory, which is described as follows: $\mathbf{Theorem.}$ Let $\rho$ and $\sigma$ be two states on $\mathcal H$, ...
1
vote
0answers
599 views

Tensor products as isomorphic functors in category theory

An earlier question that I posed sought to define a category with a set of quantum channels as arrows and the C$^{*}$-algebra that these channels map from and to as the object. So, for example, my ...
0
votes
0answers
85 views

Quantum Bayesian update and Bayesian update of a model category

We know that we can have internal categories in a model category. We also know that there is a notion of Quantum Bayesian update in a monoidal category. Does the Quantum Bayesian update (equation ...
0
votes
0answers
211 views

Functional Analysis and Differential Manifold incompatibility

From the mathematical point of view, where is the idea of the incompatibility between functional analysis, at the basis of quantum mechanics, and differential geometry, at the basis of general ...