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685 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**

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270 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**

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**0**answers

309 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**

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143 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 $\Sigma$ ...

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215 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**

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**0**answers

78 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**

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**0**answers

20 views

### Second order term of the Fedosov quantised product

In Fedosov's version of quantisation of functions on a symplectic manifold, the product is given in terms of a symplectic connection. I have looked through Fedosov's book in deformation quantisation, ...

**3**

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219 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**

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86 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**

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210 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**

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192 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**

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**0**answers

84 views

### “Semiclassical approximation” in random matrix theory

I am reading Planar Diagrams by Brezin, Parisi, Itzykson and Zuber. If you specialize the discussion in section 5 there we seem to derive the eigenvalue distribution of $N \times N$ random Hermitian ...

**2**

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**0**answers

104 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**

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**0**answers

319 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**

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96 views

### translation invariance of the Laughlin wave function

This is a translation into math of the following question, posted on PhysicsOverflow.
Let $H:=L^2(\mathbb C)$.
For every $N$, let $\psi_N\in\Lambda^N H\cong (L^2(\mathbb C^N))^{S_N}$ be the function
...

**1**

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**0**answers

134 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) operator on $\mathbb{C}[x,y]$:
...

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152 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

**0**answers

69 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

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328 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

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609 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 ...

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41 views

### Self adjoint operator and vertex conditions in quantum graphs

Let $\Gamma$ be a metric graph with finitely many edges. Consider the operator H acting as $\frac{-d^2}{dx_e^2}$ on each edge $e$, with the domain consisting of functions that belong to $H^2(e)$ on ...

**0**

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242 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 ...