All Questions
Tagged with it.information-theory mp.mathematical-physics
15 questions
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Combinatorial structure of the entanglement spectrum and quantum error correction in finite vector spaces
Let $V$ be a finite-dimensional vector space over $\mathbb{C}$ with dimension $d$. Consider a subspace $S \subset V^{\otimes n}$ representing the code subspace of a quantum error correcting code. We ...
- 11
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1
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524
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Has the von Neumann entropy ever been used in classical mechanics?
After going through an application of the von Neumann entropy(from quantum information theory) to certain problems in computational neuroscience [2], it occurred to me that this entropy might have ...
- 3,871
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6
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Revisiting the unreasonable effectiveness of mathematics
Question:
On balance, with theoretical advances in algorithmic information theory and Quantum Computation it appears that the remarkable effectiveness of mathematics in the natural sciences is quite ...
6
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0
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360
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What is the status of the Born Rule in axiomatic QM?
While physicists have tried multiple times and failed to derive the Born Rule (for example: https://arxiv.org/pdf/quant-ph/0409144.pdf). I was wondering what axiomatic Quantum Mechanics had to say ...
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Is there a mathematical and information theoretic explanation for this cube packing phenomenon?
I saw this unintuitive result on dice packing:
A jumble of thousands of cubic dice, agitated by an oscillating
rotation, can rapidly become completely ordered, a result that is hard
to produce with ...
- 13.9k
9
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1
answer
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A necessary condition for differential entropy to be finite
An ensemble corresponding to a probability distribution usually has finite free energy so it is not a great loss of generality to assume that the ensemble also has finite energy in following ...
- 8,071
15
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1
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748
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Digital physics and "Gandy-like" machines
Various physicists, famously John Wheeler, have asserted that physical information is the central object of study in physics, in the sense that an object or concept is "physically meaningful" if it ...
- 3,612
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decomposition of Hilbert space into tensor product $L^2([0,\tfrac{1}{2}]) \otimes L^2([\tfrac{1}{2},1]) \simeq L^2([0,1])$
The definition of entanglement entropy in Quantum Field Theory involves decompositing a Hilbert space into a tensor product $\mathcal{H} = \mathcal{H}_A \otimes \mathcal{H}_B$.
As an example, is it ...
- 22.8k
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567
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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 $\mathcal H$, ...
- 73
5
votes
1
answer
862
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Turing machines and Ising model
I have currently started a new research line aiming to prove a mapping between a 2-symbol Turing machine and the one dimensional Ising model. The connection is seen by recognizing that a set of ...
- 1,687
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4
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Is there a useful generalization of the Schmidt decomposition to the tensoring together of 3 or more vector spaces?
I've rewritten the question in math notation, and I've left the old version in physics bra-ket notation here.
Background
A simple consequence of the singular value decomposition is that any vector $...
- 846
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Does BQP^P = BQP ? ... and what proof machinery is available?
Update #3:
Over on TCS StackExchange, I have rated as "accepted" an ingenious construction by Luca Trevisan, which answers a two-part question (as reframed by Tsuyoshi Ito) that is in essence "Do ...
- 1,389
2
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0
answers
1k
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Can we pass to the limit in Poincaré-Jaynes-Bretthorst interpolation and deconvolution?
In Science and Hypothesis, chapter XI, The calculus of probabilities, Henri Poincaré deals informally with the fundamental problem of interpolation. He concludes (see http://ia600308.us.archive.org/21/...
3
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1
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632
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What is the entropy of a density matrix which is the sum of two unitarily equivalent projectors?
Construction
Suppose I have a density matrix $\rho$ which is proportional to a projector $P$ formed by tensoring together $N$ small projectors $P^{(i)}$ of rank 2:
$P^{(i)} = |a\rangle_i\langle a| + |...
- 846
1
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2
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Quantum channels, question 2: tensor products and composition of functions
Please be kind. I've been working on this for a long time and can't find an answer. Feel free to edit for clarity if you think the question can be better worded.
Background
It may help to see a ...
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