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)

Filter by
Sorted by
Tagged with
8
votes
3answers
389 views

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
votes
1answer
296 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 ...
17
votes
1answer
2k views

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 ...
13
votes
3answers
2k views

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 ...
7
votes
3answers
353 views

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 ...
7
votes
2answers
198 views

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 ...
5
votes
3answers
316 views

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 \...
6
votes
3answers
141 views

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 ...
2
votes
1answer
253 views

What is a complementary map?

I have a quantum map described by the following Kraus operators $$A_0 = c_0 \begin{pmatrix} 1 & 0\\ 0 & 1 \end{pmatrix}, \qquad A_1 = c_1 \begin{pmatrix} ...
12
votes
1answer
547 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 ...
7
votes
2answers
245 views

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
votes
2answers
447 views

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 ...
4
votes
0answers
39 views

Motivation for the definition of k-distillability

Definition of k-distillability For a bipartite state $\rho$, $H=H_A\otimes H_B$ and for an integer $k\geq 1$, $\rho$ is $k$-distillable if there exists a (non-normalized) state $|\psi\rangle\in ...
10
votes
1answer
127 views

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{...
6
votes
2answers
158 views

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). ...
6
votes
2answers
139 views

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 $$\...
5
votes
1answer
112 views

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 &...
4
votes
2answers
467 views

How to show a density matrix is in a pure/mixed state?

Say we have a single qubit with some density matrix, for example lets say we have the density matrix $\rho=\begin{pmatrix}3/4&1/2\\1/2&1/2\end{pmatrix}$. I would like to know what is the ...
10
votes
3answers
314 views

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 ...
8
votes
1answer
273 views

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\...
7
votes
0answers
112 views

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, ...
6
votes
1answer
199 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 ...
5
votes
1answer
58 views

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} || ...
4
votes
1answer
519 views

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, ...
4
votes
2answers
122 views

Shannon entropy is least when Measurement basis = Mixture basis

For a one qubit system, take a basis. Call this the mixture basis. Consider only basis states and classical mixtures of these basis states. Definition of Shannon Entropy used here: Defined with ...
3
votes
1answer
146 views

How does the vectorization map relate to the Choi and Kraus representations of a channel?

I know that the Choi operator is a useful tool to construct the Kraus representation of a given map, and that the vectorization map plays an important role in such construction. How exactly does the ...
3
votes
0answers
31 views

Are X-state separability and PPT- probabilities the same for the two-qubit, qubit-qutrit, two-qutrit, etc. states?

On p. 3 of "Separability Probability Formulas and Their Proofs for Generalized Two-Qubit X-Matrices Endowed with Hilbert-Schmidt and Induced Measures" (https://arxiv.org/abs/1501.02289), it is ...
2
votes
0answers
29 views

What proportions of certain sets of PPT-two-retrit states are bound entangled or separable?

For two particular (twelve-and thirteen-dimensional) sets of two-retrit states (corresponding to 9 x 9 density matrices with real off-diagonal entries), I have been able to calculate the Hilbert-...
0
votes
1answer
53 views

Transmission of information over long distances

I am reading that entangled particles can share information across long distances and the speed is usually faster than the speed of light...so am I right in assuming that future communications in the ...