Mathematics Stack Exchange
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Questions tagged [quantum-information]

This tag is related to Quantum information Theory.

Quantum information theory uses qubits and Quantum frame for making codes and discuss same things that we discuss in Information Theory for classical codes. For a reference one can take a look at the book Quantum Computation and Quantum Information written by Michael A. Nielsen and Isaac L. Chuang.

277 questions
4
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On the arbitrariness of the definition of completely positiveness.

For a linear (super)-operator $\Psi : \mathbb{C}^{n\times n} \to \mathbb{C}^{m\times m} $, I am wondering whethe $$ \text{Id}_{k} \otimes \Psi \text{ is positive for each } k\ge 1$$ is equivalent to $$ \Psi \otimes \text{Id}_{k} \text{ is…
Guldam
  • 934
3
votes
2 answers

The Kraus representation of a completely depolarising channel

I have an answer, but I want to know how to get from the left hand size to the right hand side: $$ \frac{1}{d^2} \sum_{i=1}^{d^2} U_i \rho U_i^{\dagger} = \operatorname{Tr}[\rho] \frac{I}{d}. $$ Here the $U_i$ are $d*d$ orthogonal unitary…
Zixuan Liu
  • 73
1
vote
0 answers

$\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{Tr[\rho M]}{Tr[\sigma M]}$ satisfies DPI

Let $\mathcal{H}_1, \mathcal{H}_2$ be a Hilbert spaces and $\rho, \sigma$ be density matrices on $\mathcal{H}_1$. Define $D(\rho||\sigma) := \sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{Tr[\rho M]}{Tr[\sigma M]}$. (1) Show that $D$ satisfies the…
wamig
  • 33
0
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0 answers

quantum guesswork of an ensemble

I am reading an article about quantum guesswork [ Guesswork of a quantum ensemble by michele Dall'Arno ] and i am wondering why he considers ensembles whose traces sum up to 1 in the introduction. I know that the trace of a density matrix is 1 but…
yosh
  • 73
0
votes
1 answer

On the Hilbert space $\mathbb{R}^2$, what is a concrete example of a positive operator-valued measure that is not a projection-valued measure?

I am looking for a purely mathematical example. I tried looking for a set of symmetric matrices $\{F_1,F_2\}$ such that $F_1+F_2=I$ but I cannot seem to find an example.
Andre of Astora
  • 745