For questions about classical-quantum (CQ) states.
Questions tagged [cq-states]
35 questions
8
votes
1 answer
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 show it is a convex set. I wonder whether I made a…
qquery
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6
votes
1 answer
Prove that the conditional entropy of a classical-quantum state is non-negative
Let $\rho_{XA}$ be a classical-quantum state, i.e., $\rho_{XA} = \sum_{x} p(x) |x\rangle \langle x| \otimes \rho_A^x$.
How to prove that the conditional von Neumann entropy $S(X|A) = S(\rho_{XA}) - S(\rho_A)$ is non-negative?
user297646
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5
votes
1 answer
Does the quantum Jensen-Shannon divergence appear in any quantum algorithms or texts on quantum computing?
The generalization of probability distributions on density matrices allows to define quantum Jensen–Shannon divergence (QJSD), which uses von Neumann entropy. Does QJSD appear in any quantum algorithms or texts on quantum computing?
develarist
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4
votes
1 answer
What does superposition do for quantum probabilistic sampling?
The idea of a qubit being able to exist for several values between 0 and 1 (superposition) makes it sound like it can do alot for probabilistic math problems, but for one task that comes instantly to mind, probabilistic sampling, or random number…
develarist
- 995
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- 15
4
votes
1 answer
Can a quantum computer run classical algorithms?
I realize that fundamentally speaking quantum and classical computers might as well be apples and oranges, and that for very specific problems such as integer factorization with Shor's algorithm quantum computers blow conventional computers out of…
Steve Mucci
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4
votes
1 answer
Trace distance of two classical-quantum states
I have these two classical-quantum states:
\begin{align*}\rho &= \sum_{a} | a\rangle \langle a| \otimes q^a \\
\mu &= \sum_{a} | a\rangle \langle a| \otimes r^a \end{align*}
where $a$ are the classical basis vectors, $q^a, r^a$ are arbitrary…
QuestionEverything
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4
votes
0 answers
Real-life examples of classical-quantum channels
In quantum information theory, classical-quantum channels are considered to be channels whose input is the realizations $x\in\mathcal{X}$ of a classical random variable to a quantum state $\rho_x^B$, that is
$$W:x\rightarrow\rho_x^B$$
where each…
Josu Etxezarreta Martinez
- 4,136
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4
votes
1 answer
What is the difference between classical-quantum and completely classical states?
States that are completly classical :
$$
\begin{aligned}
\tilde\rho_{A B} & =\sum_{x \in \mathcal{X}} \sum_{y \in \mathcal{Y}} p_{X, Y}(x, y)(|x\rangle \otimes|y\rangle)(\langle x| \otimes\langle y|)_{A B} \\
& =\sum_{x \in \mathcal{X}} \sum_{y \in…
IamKnull
- 493
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4
votes
1 answer
Is Classical-Classical-Quantum state equivalent to Classical-Quantum state?
Suppose we have the following CQ-state between two parties Alice & Bob
$$
\rho_{A B}^{\otimes n}=\sum_{x^n} p^n\left(x^n\right)\left|x^n\right\rangle\langle\left. x^n\right|^A \otimes \rho_{x^n}^B \tag{1}
$$
where…
IamKnull
- 493
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- 10
4
votes
2 answers
Can error correction for a classical algorithm with bit flips be easier than for a general quantum circuit?
Assume one runs a purely classical algorithm on $n$ logical qubits on a physical device with some bit flip probability.
Can implementing error correction in this case be any easier than in the case of a general quantum circuit?
I guess, given that…
mavzolej
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4
votes
1 answer
What is the general form of a classical-quantum state?
In the literature, one comes across the following situation: Alice holds two registers $X$ and $A$ and it is given that $X$ is a classical register.
What is the most general way to write down Alice's state? Is it just $\sigma_{XA} = \sum_i p_i \vert…
Polya
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4
votes
0 answers
What is known about the quantum version of Schoening's algorithm for 3SAT?
Schoening's algorithm for 3SAT can be converted to a quantum algorithm. The classical circuit representing a 3SAT expression in CNF form can be converted to a quantum version involving reversible unitary gates and a lot of ancillary qubits.…
Cristian Dumitrescu
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4
votes
2 answers
Example of a quantum algorithm better than its classical counterpart which involves only $1$ qubit?
I was reading over the proof of the Deutsch-Jozsa algorithm, which in its simplest case, involves at least 2 qubits.
Is there an example of a quantum algorithm that is better than it's classical counterpart which only involves a single qubit?
If…
Pranav Jain
- 191
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3
votes
1 answer
Classical and quantum limits to classical copying?
The no-cloning theorem can be sharpened to give quantitative bounds on the fidelity with which an arbitrary quantum state can be copied. Is there a similar picture available for classical copying? This breaks down into two
Questions:
In classical…
Tim Campion
- 131
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3
votes
2 answers
Bounding diamond norm distance using probability of error in transmission of classical information
Let us consider an encode, noisy channel and a decoder such that classical messages $m\in\mathcal{M}$ can be transmitted with some small error. That is, for a message $m$ that is sent by Alice, Bob guesses $\hat{m}$ and the average error satisfies…
user1936752
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