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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 as quantum information processing. (Wikipedia)

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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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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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What exactly is an oracle?

What exactly is an "oracle"? Wikipedia says that an oracle is a "blackbox", but I'm not sure what that means. For example, in the Deutsch–Jozsa algorithm,$\hspace{85px}$,is the oracle just the box ...
16
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1answer
427 views

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 ...
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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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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 ...
12
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1answer
537 views

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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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 ...
12
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1answer
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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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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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Positive maps on pure states?

In the comments to a question I asked recently, there is a discussion between user1271772 and myself on positive operators. I know that for a positive trace-preserving operator $\Lambda$ (e.g. the ...
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1answer
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Proof of an Holevo 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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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 ...
8
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1answer
278 views

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 ...
8
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1answer
140 views

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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1answer
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How would a Quantum Computer (network) perform loophole-free Bell tests?

In a simple form, Bell's theorem states that: No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. Bell developed a series of inequalities ...
8
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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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Density matrix after measurement on density matrix

Let's say Alice wants to send Bob a $|0\rangle$ with probability .5 and $|1\rangle$ also with probability .5. So after a qubit Alice prepares leaves her lab, the system could be represented by the ...
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Controlling high-dimensional Hilbert spaces with a single qubit

In superdense coding, you can use one qubit to control the Hilbert space of two qubits and steer it into 4 mutually orthogonal states, so that measurement of both qubits together will not have a ...
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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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2answers
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Are correlations stronger than those allowed by quantum mechanics possible?

We know how a quantum correlation setup can help us with a better probability of winning games like the CHSH. But what is the upper bound that physics can allow? Is it the quantum correlation setup? ...
7
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1answer
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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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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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1answer
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Is there a relation between the factorisation of the joint conditional probability distribution and Bell inequality?

[I'm sorry, I've already posted the same question in the physics community, but I haven't received an answer yet.] I'm approaching the study of Bell's inequalities and I understood the reasoning ...
7
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1answer
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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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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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Convexity and conditional von Neumann Entropy

I have read somewhere / heard that the set of all states that have non-negative conditional Von Neumann entropy forms a convex set. Is this true? Is there a proof for it? Can anything be said about ...
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2answers
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Partial trace over a product of matrices - one factor is in tensor product form

$$Tr(\rho^{AB} (\sigma^A \otimes I/d)) = Tr(\rho^A \sigma^A)$$ I came across the above, but I'm not sure how it's true. I figured they first partial traced out the B subsystem, and then trace A, but ...
6
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1answer
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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 ...
6
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2answers
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Is the Kraus representation of a quantum channel equivalent to a unitary evolution in an enlarged space?

I understand that there are two ways to think about 'general quantum operators'. Way 1 We can think of them as trace-preserving completely positive operators. These can be written in the form $$\...
6
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1answer
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How to understand the Haar measure from a quantum information perspective?

I found it a little difficult to understand it using Wikipedia and some mathematical documents. How to understand the Haar measure from a quantum information theory perspective? Are there any ...
6
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2answers
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How should we interpret these quantum logic gates as physical observables?

In quantum mechanics each operator corresponds to some physical observable, but say we have the operators $X,Y,Z,H, \operatorname{CNOT}$. I understand how these gates act on qubits, but what do they ...
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3answers
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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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Bell Inequality violations at large distances

Could anyone point to some references examining Bell inequality violations at large distances please? I see many times, in pop science articles and research literature alike, that the quantum ...
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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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1answer
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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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1answer
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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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Will quantum computers be able to solve the game of chess?

Will it be possible to use quantum computing to one day solve the game of chess? If so, any estimate as to how many qubits it would require? The game of checkers has already been solved through back ...
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Quantum teleportation with moving Alice and Bob

I have questions regarding quantum teleportation, which keep confusing me. Suppose Alice and Bob are in the same inertial frame $K$, and at time $t$ (in $K$) Alice teleports a quantum state to Bob. ...
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Building Intuition for Relative Von Neumann Entropy

This is how I think about classical relative entropy: There is a variable that has distribution P, that is outcome $i$ has probability $p_i$ of occuring, but someone mistakes it to be of a ...
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Relation between quantum entanglement and quantum state complexity

Both quantum entanglement and quantum state complexity are important in quantum information processing. They are usually highly correlated, i.e., roughly a state with a higher entanglement corresponds ...
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Bell nonlocality and conditional independence

I've been working through the paper Bell nonlocality by Brunner et al. after seeing it in user glS' answer here. Early on in the paper, the standard Bell experimental setup is defined: Where $x, y \...
5
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2answers
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Are there disadvantages in using the inner product between states instead of the fidelity?

Would there be any disadvantages of using inner product, that is, $\mathrm{Tr}(A^{\dagger}B)$ (say making it, $\mathrm{Tr}(\sqrt A \sqrt B)$ to normalise) to quantify how far two quantum states are ...
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1answer
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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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1answer
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Quantum teleportation of a state, from one of two bases

I'm watching Christian Schaffner's talk on quantum position-based cryptography (link here) and have a question about a particular application of teleportation. At about the 16:40 mark, he seems to ...
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1answer
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Is the set of classical-quantum states convex?

I read about the classical-quantum states in the textbook by Mark Wilde and there is an exercise that asks to show the set of classical-quantum states is not a convex set. But I have an argument to ...
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1answer
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Definition of locality in Bell experiments

Continuing from my previous question on Brunner et al.'s paper; so given a standard Bell experimental setup: where independent inputs $x,y \in \{0, 1\}$ decide the measurement performed by Alice &...
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1answer
213 views

What does “bipartite” mean?

This is a really easy question, but my mother language is not English and I get confused quite a lot reading Preskill notes. What does a bipartite system mean? Is this just that it "lives" in a ...
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1answer
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Superoperator cannot increase relative entropy

Note: Cross-posted on Physics SE. So I have to show that a superoperator $\$$ cannot increase relative entropy using the monotonicity of relative entropy: $$S(\rho_A || \sigma_A) \leq S(\rho_{AB} || ...
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Kraus operator of dephasing channel

I'm trying to deduce the Kraus representation of the dephasing channel using the Choi operator (I know the Kraus operators can be guessed in this case, I want to understand the general case). The ...