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Questions tagged [quantum-information]

For questions about quantum information theory. In physics and computer science, quantum information is information that is held in the state of a quantum system. Quantum information is the basic entity of study in quantum information theory and can be manipulated using engineering techniques known ...

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Do the probability amplitudes of the superposition state produced by the QFT transform convey useful information?

I have been studying on Quantum Fourier Transform (QFT) by myself, and I am little bit confused about how could QFT be used. For example, if the QFT of three quantum bits is $a_1|000\rangle + ...
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Suggest, partly based upon limited numerical results, possible “elegant” exact formulas for Bures two-qubit separability probability

Lovas and Andai (https://arxiv.org/abs/1610.01410) have recently established that the separability probability (ratio of separable volume to total volume) for the nine-dimensional convex set of two-...
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Relating min-entropy with conditional entropy

Suppose we have a classical quantum state $\sum_x |x\rangle \langle x|\otimes \rho_x$, one can define the smooth-min entropy $H_\min(A|B)_\rho$ as the best probability of guessing outcome $x$ given $\...
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Rotationally invariant maximally entangled states in higher dimensions

Is there a straightforward generalization of the $\mathbb{C}^2$ Bell basis to $N$ dimensions? Is there a rotational invariant Bell state in higher dimensions? If yes, then what is the form of that ...
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Collective measurements: importance and realization

I am reading the paper Polar codes for classical-quantum channels by Wilde and Guha, and it is stated the fact that collective measurements are necessary in order to aciheve the Holevo symmetric ...
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Experimental Realization of Superactivation of Quantum Capacity

The superactivation of quantum capacity is an effect that some quantum channels present such that is two of those channels with zero capacity are combined, a non-zero channel capacity can be achieved ...
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EA-Turbo simulation package

I am working with the quantum turbo codes presented in this paper by Wilde, Hsieh and Babar, and it is claimed that a package to simulate such codes is available at ea-turbo. However, the hyperlink to ...
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How many bits do Alice and Bob needs to compare to make sure the channel is secure in BB84?

I was trying to self-study qmc by reading the Quantum Computing A Gentle Introduction book, in section 2.4 it talks about the quantum key distribution protocol BB84. After (I thought) I understood it ...
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Generalization for $n$ quantum teleportations

In Breaking Down the Quantum Swap, it is stated: Thanks to the CNOT, we can implement a xor-swap on a quantum computer. All we need to do is chain three CNOTs back and forth. In a comment to a ...
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What is the Helstrom measurement?

I have been reading the paper Belief propagation decoding of quantum channels by passing quantum messages by Joseph Renes for decoding Classical-Quantum channels and I have crossed with the concept of ...
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140 views

Is there a classical limit to quantum computing?

Why are quantum computers scalable? With the subjects of spontaneous collapse models and decoherence in mind, it seems to me that the scalability of quantum computers is something which is not only ...
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Image of a sum of positive operators contains the images of each individual operator?

In the proof of Proposition 2.52 of John Watrous' QI book, see here: https://cs.uwaterloo.ca/~watrous/TQI/TQI.2.pdf, there is the statement that $\text{im}(\eta(a))\subset\text{im}(\rho)$, where $\...
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Cloning classical data encoded into qubits

How is it possible to maintain classical data encoded into qubits, which often contains copies of information, given that the no cloning theorem prevents cloning information?
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What is continuous quantum register and how it relates to qubits?

I would like to understand what is a continuous quantum register. I know the direct definition is a quantum register that stores a real number defined by an observable with a spectrum consisting of $\...
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Simplest algorithm for intuitively demonstrating quantum speed-up?

What's the simplest algorithm (like Deutsch's algorithm and Grover's Algorithm) for intuitively demonstrating quantum speed-up? And can this algorithm be explained intuitively? Ideally this would be ...
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Estimate/determine Bures separability probabilities making use of corresponding Hilbert-Schmidt probabilities

For two-qubit states, represented by a $4\times 4$ density matrix, the generic state is described by 15 real parameters. For ease of calculation, it can help to consider restricted families of states, ...
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Breakthroughs in quantum computing using non-standard quanta [closed]

It seems that quantum computers can be classified by the type of quantum they operate on. Not entirely sure what category most common current systems fall into (eg. D-Wave, Google, IBM, Microsoft). ...
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Has anyone analyzed multi-round nonlocal games?

The traditional definition of a nonlocal game is restricted to having two players and one round (e.g., here), but it is natural to consider a more general class of games that may have more than two ...
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Advances in Quantum Channel Capacity

I have been reading about the Quantum Channel Capacity and it seems to be an open problem to find such capacity in general. Quantum capacity is the highest rate at which quantum information can be ...
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How could a global quantum network be realized?

This article from 2017 predicts the quantum internet by 2030. What are the biggest bottlenecks in the realization of a global quantum network (ie quantum internet)?
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Nielsen & Chuang Exercise 2.1 - “Linear dependence: example”

Reproduced from Exercise 2.1 of Nielsen & Chuang's Quantum Computation and Quantum Information (10th Anniversary Edition): Show that $(1, −1)$, $(1, 2)$ and $(2, 1)$ are linearly dependent. ...
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Generating algebra from commutation

In a paper I am reading, it states: For open-loop coherent controllability a quantum system with Hamiltonian $H$ is open-loop controllable by a coherent controller if and only if the algebra $\...
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What is the relationship between the Toffoli gate and the Popescu-Rohrlich box?

Background The Toffoli gate is a 3-input, 3-output classical logic gate. It sends $(x, y, a)$ to $(x, y, a \oplus (x \cdot y))$. It is significant in that it is universal for reversible (classical) ...
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Why is it harder to build quantum computers than classical computers?

Is it because we don't know exactly how to create quantum computers (and how they must work), or do we know how to create it in theory, but don't have the tools to actually execute it in practice? Is ...
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Is it possible to “calculate” the absolute value of a permanent using Boson Sampling?

In boson sampling, if we start with 1 photon in each of the first $M$ modes of an interferometer, the probability of detecting 1 photon in each output mode is: $|\textrm{Perm}(A)|^2$, where the ...
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Embedding classical information into norm of a quantum state

According to An introduction to quantum machine learning (Schuld, Sinayskiy & Petruccione, 2014), Seth Lloyd et al. say in their paper: Quantum algorithms for supervised and unsupervised machine ...
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Holveo Information Inequality

Suppose I have a classical-classical-quantum channel $W : \mathcal{X}\times\mathcal{Y} \rightarrow \mathcal{D}(\mathcal{H})$, where $\mathcal{X},\mathcal{Y}$ are finite sets and $\mathcal{D}(\mathcal{...
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Quantum Channel Models

The so called depolarizing channel is the channel model that is mostly used when constructing quantum error correction codes. The action of such channel over a quantum state $\rho$ is $\rho\...
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Violation of the Quantum Hamming bound

The quantum Hamming bound for a non-degenerate $[[N,k,d]]$ quantum error correction code is defined as: \begin{equation} 2^{N-k}\geq\sum_{n=0}^{\lfloor d/2\rfloor}3^n\begin{pmatrix}N \\ n\end{...
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Degeneracy of Quantum Error Correction Codes

The feature of quantum error correcting codes called degeneracy is that they can sometimes be used to correct more errors than they can uniquely identify. It seems that codes exhibiting such ...
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Using a fractional number of classical bits within quantum teleportation

Recently, I heard that there can be transfer of rational classical bits (for example 1.5 cbits) from one party to another via quantum teleportation. In the Standard Teleportation Protocol, 2 classical ...
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What is the use of Categorical quantum mechanics?

I recently noticed that Oxford's computer science department has started offering a grad course on Categorical quantum mechanics. Apparently they say that it is relevant for the study of quantum ...
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Accessible information of system vs system, apparatus and environment

Suppose we have a quantum system $Q$ with an initial state $\rho^{(Q)}$. The measurement process will involve two additional quantum systems: an apparatus system $A$ and an environment system $E$. We ...
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What are the real advantages of superdense coding?

In superdense coding, two qubits are prepared by Eve in an entangled state; one of them is sent to Alice and the other is sent to Bob. Alice is the one who wants to send (to Bob) two classical bits of ...
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What does “measurement in a certain basis” mean?

In the Wikipedia article about Bell states it is written: Independent measurements made on two qubits that are entangled in Bell states positively correlate perfectly, if each qubit is measured in ...
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Local operations and classical communication (LOCC) on quantum system

I'm currently busy learning about the basics of quantum information theory. Does anyone know how the measurement described in the wiki link LOCC is a measurement on the product space $\mathbb{C}^2 \...
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What is quantum gate teleportation?

Quantum state teleportation is the quantum information protocol where a qubit is transferred between two parties using an initial shared entangled state, Bell measurement, classical communication and ...
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Why is the efficiency of Ekert 91 Protocol 25%?

In Cabello's paper Quantum key distribution without alternative measurements, the author said "the number of useful random bits shared by Alice and Bob by transmitted qubit, before checking for ...
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What is the difference between signaling and non-signaling quantum correlations, and what is a signaling channel?

This article talks about correlation and causality in quantum mechanics. In the abstract, under Framework for local quantum mechanics, it says (emphasis mine): The most studied, almost epitomical, ...
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How can quantum decoherence be managed?

I've stumbled myself upon this article on Wikipedia, which says: Decoherence can be viewed as the loss of information from a system into the environment (often modeled as a heat bath), since every ...
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Purpose of using Fidelity in Randomised Benchmarking

Often, when comparing two density matrices, $\rho$ and $\sigma$ (such as when $\rho$ is an experimental implementation of an ideal $\sigma$), the closeness of these two states is given by the quantum ...