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Newest 'information-theory' Questions - Quantum Computing Stack Exchange
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Learn more about TeamsQuestions tagged [information-theory]
The tag is used for questions connected with information theory in classical and/or quantum sense.
297 questions
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1
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0
answers
49
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applying Haar random unitary to projection and pure states and compute its trace
I have this question when I read the proof of Theorem 4 in This paper. Here are the settings:
\begin{align}
&|\phi\rangle^{BC}: \text{The reduction of a pure state $|\phi\rangle^{ABCD}$ where A,C ...
6
votes
0
answers
72
views
Low entropy implies far from maximally mixed
A paper I've been reading (1, just after eq. 5.1) claims that if $\rho$ is a quantum state on $n$ qubits, and $S(\rho) \le (1 - \epsilon)n$, then $$\|\rho - \tilde{I}\|_{\text{tr}} \ge \epsilon - \...
0
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0
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116
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Proof of Theorem 3 of Frenkel, and Weiner, Commun. Math. Phys. 340, 563 (2015)
Suppose Bob performs a $k$-outcome measurement, characterised by the POVM $E = \{E_j\}_{j=1}^k$, on $l$ qudits $\{\rho_i\}_{i=1}^l$ sent by Alice. This results in an $k \times l$ column-stochatstic ...
1
vote
2
answers
59
views
Is quantum conditional mutual information monotonic under conditioning?
For quantum conditional mutual information, is it true in general that:
$$
I(A:B|C) \geq I(A:B|CD)
$$
assuming they are all isomorphic quantum systems.
If not, when is the inequality satisfied?
My ...
0
votes
0
answers
59
views
Definition of a wavefunction in terms of density matrix
Given a system in the state $\vert \psi\rangle$, a wave function is given by a parametrised scalar product $\langle r \vert \psi \rangle$. Is it possible to obtain this expression using the density ...
6
votes
1
answer
128
views
Given an entangled state on two systems, when can a subsystem of one decouple from the other?
Suppose you have the following quantum state:
$$\frac{1}{\sqrt{2^n}}\sum_{i}|\bar{i}\rangle_A|i\rangle_S$$
where $\{|i\rangle_A\}$ and $\{|i\rangle_S\}$ are orthonormal bases for an $n$-qubit ancilla ...
3
votes
0
answers
48
views
Relationship Between Knill-Laflamme Conditions and Negativity
Given an error channel $\mathcal{E}$, one can state the Knill-Laflamme conditions in terms of a condition on the coherent information, e.g., this post.
Is there a version of the Knill-Laflamme ...
3
votes
1
answer
113
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Classical Analog of Information-Theoretic Version of Knill-Laflamme Conditions
One version of the Knill–Laflamme conditions for quantum error correction is stated as follows:
Theorem 9.5 in Gottesman's Quantum Error Correction Book:
Let $ \mathcal{F}: L \to Q $ be a quantum ...
2
votes
1
answer
115
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Prove the relation between trace norm and fidelity for pure states
I encountered an exercise as follows:
Consider two generic pure states ( $|\Psi\rangle$, $|\Phi\rangle $).
Prove the following exact relation between the fidelity and the trace
distance:
$$\frac{1}{2}...
2
votes
1
answer
91
views
The POVM of quantum packing lemma does not need to 'coat'
It is the exercise 16.5.4 from Quantum information theory by Mark Wilde. In the original proof of the quantum packing lemma, the POVM is defined as
\begin{align}
\Lambda_m = (\sum_{m'=1}^{|\mathcal{M}|...
1
vote
0
answers
38
views
quantum mutual information as an achievable rate for entanglement-assisted classical communication
I'm reading the proof of Corollary 21.2.1 Quantum Information Theory by Mark Wilde, and my question is about the notations in the proof.
The corollary says the quantum mutual information $I(A;B)_{\...
1
vote
1
answer
96
views
Why is it called the Petz 'transpose' map?
The Petz transpose map (also called Petz recovery map) is defined for a Channel $\Phi : \mathrm{L}(\mathcal X) \to \mathrm{L}(\mathcal Y) $ and an input reference state $\rho \in \mathrm{D}(\mathcal X ...
1
vote
2
answers
250
views
How to prove the no-cloning theorem for density matrices and quantum channels?
$\newcommand{\ket}[1]{\left|#1\right\rangle}
\newcommand{\bra}[1]{\left\langle#1\right|}
\newcommand{\ketbra}[1]{\ket{#1}\bra{#1}}$Suppose $\mathcal{E}$ is a trace-preserving quantum channel that ...
-3
votes
1
answer
150
views
Does hawking radiation leak information in a time-independent way, and could it carry charge as well as being thermal? Is this how we model it?
I’ve been working on a series of quantum circuit experiments to explore information preservation in Hawking radiation, focusing on whether injected properties like charge and spin are encoded in the ...
3
votes
1
answer
124
views
$f(p)=S(p\rho +(1-p)\sigma)$, where $S$ is Von Neumann entropy, prove $f''(p)\leq 0$
This exercise is from Quantum Computation and Quantum Information by Nielsen and Chuang. Suppose the concavity holds, then $f(\frac{1}{2})\geq\frac{1}{2}(f(0)+f(1))$, $S(\frac{\rho+\sigma}{2})\geq (S(\...
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