# Questions tagged [information-theory]

The tag is used for questions connected with information theory in classical and/or quantum sense.

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### Why the "Close Images" problem is QIP-complete

The following problem is known as the "close images" problem: the input is two circuits $Q_0$, $!_1$, with the same number of input and output qubits (The circuits are allowed to add ancilla ...
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### How can one impliment Bennett's partial measurement onto a binomial subspace for state distillation?

I'm reading the seminal paper on entanglement distillation by Bennett et. al. The idea is that Alice and Bob have $n$ identical copies of an imperfect (but pure) Bell state. The initial state is ...
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### What are explicit examples of smoothed conditional min(max) entropies?

Some general discussion of smoothed entropic quantities is found for example in Watrous notes, and an overview and discussion on its operational interpretations in (Koenig et al. 2008). It seems the ...
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### In what sense is the "conditional min-entropy" a conditional entropy?

$\newcommand{\H}{\mathsf{H}}\newcommand{\Hmin}{\H_{\rm min}}\newcommand{\D}{\mathsf{D}}\newcommand{\Dmax}{\D_{\rm max}}$Consider the conditional min-entropy $\Hmin(A|B)_\rho$, discussed e.g. in this ...
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Consider the $\epsilon$-smoothed relative max-entropy of $\rho$ with respect to $Q$, defined as (following Watrous' notation from these notes): $$\mathrm D_{\rm max}^{\epsilon}(\rho\|Q) = \min_{\xi\in ... • 19.6k 3 votes 1 answer 76 views ### References of group theory for quantum information theory Now that quantum information theory (QIT) reaches the point that group theory have deeply combined with its applications and theoretical understandings, such as random benchmarking, quantum scrambling,... • 655 2 votes 1 answer 43 views ### General Proof of the Statement that You Need 1 Ebit and 2 Bits to Teleport 1 Qubit? I understand from the standard teleportation protocol that 1 ebit is used up in teleporting 1 qubit and thus, cannot be used again -- and thus, we need 1 fresh ebit of shared entanglement between ... • 185 1 vote 0 answers 66 views ### How much information can be stored in a system with synthetic dimensions? [closed] Okay this is a completely serious question and keep in mind I have a PhD in theoretical condensed matter physics, in which I have somewhat of a specialization in Floquet physics. So as the title says, ... 1 vote 1 answer 99 views ### 2 ebits + 1 bit  = 2 bits? The Set-Up Let's say Alice and Bob share k ebits, i.e., they have one-qubit each of each of the k Bell states \frac{\vert 00\rangle+\vert 11\rangle}{\sqrt{2}}. Now, Alice wants to send 2n bits ... • 185 2 votes 2 answers 162 views ### Is it possible to prevent quantum communication detection? From what I understood, one of the advantages of quantum communication is that one can (mathematically/physically) prove that the quantum communication/message has not been intercepted/tampered with. (... • 123 1 vote 0 answers 13 views ### Entanglement-assisted communication ability of a quantum depolarizing channel vs. a classical binary symmetric channel Consider a quantum qubit depolarizing channel which takes a quantum state \rho to output$$N(\rho) = (1-p)\rho + p\frac{\mathbb{1}_2}{2}.$$If I restrict \rho to be either \vert0\rangle\langle 0\... • 2,169 4 votes 2 answers 217 views ### Classical Information Theory vs. Quantum Information Theory I am quite familiar with the basic concepts of information theory (sources, alphabets, simbols, strings, information, Shannon's entropy, noisy channels, Shannon's theorems, etc.). I always thought of ... • 141 1 vote 2 answers 115 views ### What is the conditional min-entropy for diagonal ("classical") matrices? The conditional min-entropy, discussed e.g. in these notes by Watrous, as well as in this other post, can be defined as$$\mathsf{H}_{\rm min }(\mathsf{X} \mid \mathsf{Y})_{\rho}\equiv -\inf _{\sigma \...
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It is known that for degradable channels $\mathcal{N}$ and $\mathcal{M}$, the single-letter quantum capacity is aditive (Potential Capacities of Quantum Channels), i.e. \begin{equation} Q^{(1)}(\...
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### What role does Landauer's principle play in quantum reversibility?

In section 3.2.5 of Nielsen and Chuang (starting page 153) they talk about Landauer’s principle, where they discuss the lower bound on the thermodynamic cost of erasing information. In irreversible ...
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### contraction related Bit flip channel

Studying the bit flip channel using the Nielsen & Chuang's. And ran into the picture with the caption stating y-z plane is uniformly contracted by a factor of 1-2p. I don't quite understand how ...
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### Is there a non-deterministic protocol for entanglement generation between distant parties?

I'm aware that one can imperfectly clone entanglement that's shared between two parties (i.e. Bell pairs) using deterministic quantum cloning machines to produce two, lower fidelity entangled states. ...
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### Is there a non one-way quantum computer?

Be it theoretical proposal or anything else, is there even a definition for non one-way (or non measurement-based) quantum computer/computation?
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### Derivation of the linear cross entropy

I'm looking at cross-entropy benchmarks and there's much that I'm reading at the moment but I'm stuck on one detail: how to derive the linear cross-entropy formula from the cross-entropy formula. The ...
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### Can one define a Choi state for a a classical channel?

Suppose one has a classical channel $W(y|x)$ that is a conditional probability distribution. Can one define a Choi state for this channel? My guess is that one should think of it as a special case of ...
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### Tapering off qubits

Suppose you have a Hamiltonian of the form $$H = ZXXX + YXXX + XXXX$$ where $Z,X,Y$ are the usual Pauli matrices with $ZXXX = Z \otimes X \otimes X \otimes X$ and similar for the other two terms. ...
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### Is it possible to extract $x_1$ and $x_2$ from $|\phi\rangle=\frac1{\sqrt2}(|x_1,0^n\rangle+|0^n,x_2\rangle)$ with non-negligible probability?

Let $\left\vert \phi\right\rangle=\frac 1{\sqrt2}\left\vert x_1,0^n\right\rangle+\frac1{\sqrt2}\left\vert 0^n,x_2\right\rangle$ be a $2n$-bit quantum state for some unknown $x_1,x_2\in\{0,1\}^n$. My ...
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### Is it possible to efficiently measure outer products of quantum states, of the form $|a\rangle\langle b|$?

I am looking at a matrix reconstruction algorithm that, given singular values $\sigma_i$ and quantum states $|u_i\rangle$ and $|v_i\rangle$ that are efficiently prepared on a quantum computer, ...
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