Questions tagged [cq-states]
For questions about classical-quantum (CQ) states.
35
questions
3
votes
1
answer
78
views
What is the difference between classical-quantum and completely classical states?
States that are completly classical :
$$
\begin{aligned}
\tilde\rho_{A B} & =\sum_{x \in \mathcal{X}} \sum_{y \in \mathcal{Y}} p_{X, Y}(x, y)(|x\rangle \otimes|y\rangle)(\langle x| \otimes\langle ...
- 433
2
votes
0
answers
43
views
Purification of classical-quantum state
For a classical-quantum state in $\mathcal{H}_{X \otimes A}$
$$
\rho = \sum_x p(x) \vert x\rangle \langle x \vert \otimes \rho^x,
$$
I can use spectral decomposition for $ \rho^x $ to get $$
\rho^x = \...
- 21
3
votes
1
answer
75
views
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 ...
- 433
2
votes
2
answers
156
views
How should $\rho(b,b')$ be interpreted in the context of classical-quantum state
I’m trying to understand the concept of a classical-quantum state as it is used in the context of quantum cryptography. In particular, I’m looking at the expression $CL.Enc_{pk}(\rho^M)$ from page 16 ...
- 365
0
votes
1
answer
201
views
How to copy value from classical register to quantum register?
I have 1-qubit of quantum register and 2-bit of classical register.
I have this simple algorithm:
First, I'm doing simple process for q[0] with NOT.
Second, I want ...
1
vote
2
answers
457
views
Is there any real world problem where I can see quantum computing being better than classical computing?
Is there any paper or piece of code showing, on a REAL quantum computer, that a specific real world problem (possibly related to computer science, machine learning or finance and possibly NOT related ...
- 497
2
votes
0
answers
41
views
What's the map from any linear classical codes to entanglement-assisted stabilizers codes
When a linear code is self-dual, its parity check matrix can be used to easily define a stabilizer code.
From my understanding, thanks to entanglement-assisted stabilizer codes, it is possible to ...
- 1,566
4
votes
2
answers
126
views
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 ...
- 1,852
2
votes
1
answer
43
views
Showing that $S(\rho_{XB}||\sigma_{XB})=\sum_{x}p(x)D(\rho_{B}^{x}||\sigma_{B}^{x})$ for classical-quantum states
Having some trouble showing that $S(\rho_{XB}||\sigma_{XB})=\sum_{x}p(x)D(\rho_{B}^{x}||\sigma_{B}^{x})$ for $\rho_{XB}=\sum_{x}p(x)|x\rangle\langle x|\otimes\rho_{B}^{x}$ and $\sigma_{XB}=\sum_{x}p(x)...
- 1,115
2
votes
1
answer
59
views
Understanding the association rule between classical to quantum data $|x\rangle=\frac{1}{|\vec x|_2}\sum_{i=1}^d x_i|i\rangle$
I've been reading the paper on Quantum Hopfield Networks by Rebentrost et al. and I'm not sure to quite understand the association rule they mention on page 2.
Here's what they say :
Consider any $d$-...
- 117
3
votes
2
answers
312
views
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 ...
- 2,597
2
votes
1
answer
92
views
Prove that for a pure tripartite state $\rho_{ABE}$, $H(RB) = H(RE)$
Let's say we have a pure tripartite state $\rho_{ABE}$ and a completely positive map $\mathcal{R}$, which is defined as:
$$
\mathcal{R} : \rho \rightarrow \sum_j \langle\psi_j|\rho |\psi_j \rangle |\...
- 1,775
4
votes
1
answer
183
views
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 ...
- 41
5
votes
1
answer
342
views
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}) - ...
- 95
1
vote
1
answer
119
views
Trace distance of two classical-quantum state with hashing
Let's say I have a classical-quantum(cq) state $\rho_{XE}$, where the classical part $(X)$ is orthogonal. It's trace distance from another uniform density operator is defined to be:
$$
\frac{1}{2}||\...
- 1,775
5
votes
1
answer
70
views
Does the quantum Jensen-Shannon divergence appear in any quantum algorithms or texts on quantum computing?
The generalization of probability distributions on density matrices allows to define quantum Jensen–Shannon divergence (QJSD), which uses von Neumann entropy. Does QJSD appear in any quantum ...
- 947
2
votes
0
answers
317
views
What is the relation between density matrices and phase-space probability distributions?
According to its tag description, a density matrix is the quantum-mechanical analogue to a phase-space probability measure (probability distribution of position and momentum) in classical statistical ...
- 947
2
votes
0
answers
45
views
Quantum analogues of information theoretic measures: are log probabilities replaced with the density matrix?
Below is a question and an answer.
How does quantum information relate to, diverge from or reduce to
Shannon information, which used log probabilities?
What people are more often interested in are ...
- 947
2
votes
1
answer
175
views
Relating quantum max-relative entropy to classical maximum entropy
The quantum max-relative entropy between two states is defined as
$$D_{\max }(\rho \| \sigma):=\log \min \{\lambda: \rho \leq \lambda \sigma\},$$
where $\rho\leq \sigma$ should be read as $\sigma - \...
- 947
2
votes
1
answer
85
views
Is "classical information" the same as "Shannon information"?
does Shannon meet Feynman?
Bits underlie classical information measurements in information theory, while qubits underlie quantum information measurements in, what I can only assume to be called, ...
- 947
2
votes
1
answer
60
views
Counting Achievable Operations
I'm struggling to find an analytic way to solve this problem.
There are $4! = 24$ possible classical operations on the four 2-Cbit basis states. How many of these are achievable via the classical ...
- 21
4
votes
0
answers
377
views
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 ...
2
votes
0
answers
34
views
Question about the practical use of super dense coding in information transmission [duplicate]
Question about the practical use of super dense coding in information transmission:
We know that by using super dense coding it is possible to transmit 2n classical bits transmitting n qubits, ...
- 21
4
votes
2
answers
145
views
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 ...
- 191
2
votes
1
answer
49
views
The effect of available information on random quantum channels
This question is about the effect of available information on random quantum channels.
Suppose there are two black box devices.
Device 1.
We have a black box device with a single qubit in it. Once ...
- 21
3
votes
1
answer
113
views
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 ...
- 947
2
votes
0
answers
78
views
Quantum Optimization algorithms
The Harrow-Hassidim-Lloyd (HHL) algorithm for quantum matrix inversion (linear algebra) bridges classical math to quantum math and has been adopted for quantumizing many classical applications, such ...
- 947
2
votes
2
answers
262
views
Translating classical math and code to quantum math and code
I am starting to see a lot of classical quantitative problems such as linear regression being represented in quantum math, which suggests that almost anything based on frequentist statistics could be ...
- 947
1
vote
3
answers
3k
views
How to initialize classical register in Qiskit?
I'm working on a Hybrid classical-quantum linear solver. For this, they make a loop on a quantum circuit (ie. below), and each time they change the value of the classical register and apply a X gate ...
- 461
3
votes
1
answer
147
views
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? ...
- 131
3
votes
1
answer
1k
views
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 ...
- 133
3
votes
1
answer
295
views
Trace distance of two classical-quantum states
I have these two classical-quantum states:
$$\rho = \sum_{a} \lvert a\rangle \langle a\lvert \otimes q^a \\
\mu = \sum_{a} \lvert a\rangle \langle a\lvert \otimes r^a $$
Where $a$ are the classical ...
- 1,775
1
vote
1
answer
100
views
Better Way Of Separating Two CQ-States
I have this cq-state:
$$\frac{1}{2} \times (|0\rangle \langle0|_A \otimes \rho^0_E + |1\rangle \langle1|_A \otimes \rho^1_E)$$
Where Alice (A) is classical and an adversary Eve (E) has some ...
- 1,775
5
votes
0
answers
511
views
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 $\rho_x^B$, ...
6
votes
1
answer
628
views
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 ...
- 61