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Questions tagged [quantum-information]

Quantum information is the study of the informational content of quantum states. The most common object of study is the "qubit", the information in a two-state quantum system such as spin-1/2 or photon polarization.

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What is the physical meaning of the average value of the long product of spin operators

For the quantum one-dimensional XYZ Heisenberg model with $N$ spins $1/2$, consider the following average values of the products of successive operators $\hat{\sigma}^x$ in the ground state $$ C_j(n) =...
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What would be the outcome of an experiment wherein the spin of a qubit is measured in two or more orthogonal directions simultaneously?

Out of curiosity, I am seeing the Leonard Susskind’s Theoretical Minimum lecture series on YouTube and have just started watching the second lecture. As I understand so far, the qubit can have a spin ...
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How can a quantum gate be constructed to evaluate a blackbox function (as in the Deutsch's algorithm)?

The standard Deutsch's algorithm uses a control-U gate, which takes the control qubit state $x$ as input to get the output from a black-box function $f(x)$. And the output modifies the quantum state ...
Yuan John Jiang's user avatar
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What is the dimension considered in the Schmidt Decomposition?

In the Schmidt decomposition, is the dimension considered of each Hilbert space the complex or real one? Meaning the complex dimension of $\mathbb C^2$ has dimension $2$, not $4$. If so when you ...
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Joint measurability in quantum mechanics

Two POVMs $E= \{E_i\}$ and $F= \{F_j\}$ are said to be jointly measurable if there exists a POVM $G= \{G_{ij}\}$ such that $$E_i=\sum_j G_{ij}\quad \text{and}\quad F_j =\sum_i G_{ij}$$ From this ...
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Are states partially ordered in the same way via entanglement and Bell violations?

Recall what a partially ordered set is. Let $E(\rho)$ be an entanglement measure. Let $B(\rho) \leq 0$ be a Bell inequality. Define the Bell violation measure with respect to $B$ as $$\tilde{B}(\rho) =...
Silly Goose's user avatar
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Why we use trace-class operators and bounded operators in quantum mechanics?

The set of trace-class operators $\mathcal{B_1(H)}$ on the Hilbert space $\mathcal{H}$ is like the Banach space $l^1$, while the set of bounded operators $\mathcal{B_\infty(H)}$ is like the Banach ...
Godfly666's user avatar
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Different Bekenstein bound equations – what’s the difference?

Can someone help me understand the difference between the Beckenstein bound equations that I’ve come across? They all appear to have different dimensions. I’ve been told that if you include the ...
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Why can we not experimentally evaluate the expectation value of the CHSH operator after simplifying its expression to check entanglement?

We have the observable corresponding to the CHSH inequality given by, \begin{align} \mathcal{\hat{S}} &= \hat{Z}_1 \left(\frac{1}{\sqrt{2}} (-\hat{Z}_2 - \hat{X}_2)\right) + \hat{X}_1 \left(\frac{...
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How can the Bloch sphere, built from one complex dimension, specify 2-complex dimensional Pauli spinors?

Two-component spinors can be identified with points on the surface of the Bloch Sphere. The Bloch sphere is constructed from the 1-complex-dimensional complex plane plus the point at infinity. How ...
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Does quantum entropy take into account the quantum uncertainties present in a system?

The von Neumann entropy of a mixed state is non-zero, and this makes sense as mixed states are just statistical descriptions of quantum systems, so there's some amount of classical uncertainty causing ...
Pratham Hullamballi's user avatar
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Example of a classical correlation and a quantum correlation

I'm trying to understand the fundamental differences between classical and quantum correlations through examples of a quantum entangled state and a classically correlated state. I know that this is an ...
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How are realism, determinism, counter factual definiteness and non-contextuality related?

I have come across these terms when trying to understand the EPR paradox and its resolution. I have found that they are often used interchangeably, but when I look up their official definitions, I ...
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Multi-target CNOT gate using optical devices

I am trying to map a simple quantum circuit of two CNOT gates into optical circuits with beam splitters and phase shifters,.... specifically for GKP encoding. I want to know how the arrangement of ...
mohadeseh azari's user avatar
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High fidelity implies low entropy

I was reading the security proof of QKD by Lo-Chau. One of their main idea is to bound the entropy of the eavesdropper if the singlet states are of high fidelity. Here I summarized the first lemma: ...
JasonWS 's user avatar
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When is a state entangled?

I have read from What's the difference between an entangled state, a superposed state and a cat state? that an entangled state is one that cannot be expressed as product state. Suppose we have the ...
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Operator systems in functional analysis & quantum mechanics: intuition

I saw this concept of operator systems in here but I am not sure if I want to get deep into it before knowing roughly what it is used for in, say, quantum information or quantum mechanics. My very ...
Evangeline A. K. McDowell's user avatar
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What exactly does the quantum mutual information measure? [duplicate]

Quantum mutual information (QMI) is often said to be the quantum mechanical analog of Shannon mutual information (MI). I realize they can be written with the same formula: $$S_x+S_y-S_{xy} \ ,$$ where ...
Mat's user avatar
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What does the superposition of fields mean in the context of the convolution of two Glauber-Sudarshan $P$-representations?

In his 1963 paper, in which he introduces his formulation of the Glauber-Sudarshan $P$-representation (https://doi.org/10.1103/PhysRev.131.2766), Glauber refers to the convolution of the $P$-...
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Is von Neumann entropy symmetric? [closed]

In a multiparty system, Shannon entropy is symmetric with respect to exchange of two parties. Is this also true for von Neumann entropy in case of a multiparty density matrix? If yes, is there any ...
asu's user avatar
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Multiplication of $\mathrm{U}(3)$ matrices [closed]

On this page of this paper: I am unable to understand how they multiplied the $3\times 3$ $\mathrm{U}(3)$ matrix with $T_{3,2}$, which is a $2\times 2$ matrix, in Eqs. (26) to (28). Can anyone please ...
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How is information defined when considering locality in quantum mechanics?

$\newcommand{\ket}[1]{|#1\rangle}$ My question is a follow-up from this discussion about the presence of non-local correlations in a theory that is deemed local. The first answer talks about the ...
UVcatastrophe's user avatar
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Are squeezed vacuum states classical?

After calculating their photon-number variance I tried to compute their second order coherence function, but it turns out larger than 3, implying it is a classical state. Is it wrong? I expected it to ...
Daniel Janjani's user avatar
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2 answers
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Simple examples of computing the quantum discord

I'm looking for a relatively simple, nontrivial example of computing quantum discord (if such an example exists). Could anyone provide such an example?
Mat's user avatar
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Loss of coherence in the double-slit experiment

Let's suppose we perform the double-slit experiment, using two detectors to detect which slit the particle has passed through. I describe the detectors using quantum mechanics, so they are represented ...
daniele's user avatar
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Problem in quantum superpositions meaning in a special case

In this article, which is the theory behind Orbital Angular Momentum (OAM) mode sorter, there is the observation of the fact that if we have a superposition of two OAM modes (which are orthogonal to ...
amir moghaddam's user avatar
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3 answers
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Is that right that about trace of the two density matrices multiply to each other? [closed]

We have: $$\mathrm{Tr}\,(\rho \rho^{\prime})=1$$ then, is it right to say $\rho=\rho^{\prime}$?
xhian's user avatar
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Time evolution keeps a certain product state always a product state. Is there a time-independent factorizable evolution for this state?

I am typically thinking of quantum spin chains in the following of some length $L$. I am OK without any locality in the assumptions on $H$. I have a product state $|\psi\rangle$ and a potentially very ...
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Is the tensor product injective on pure quantum state vectors?

I am reading lecture notes on quantum information/computing, and the tensor product of two pure qubit states $|b_1\rangle\otimes |b_2\rangle\in\mathbb{C}^{2\times2}$ was introduced as the "...
td12345's user avatar
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Operational meaning of mode dependence of mode-entanglement

In this paper, Vedral shows that the entanglement in second quantized states can depend on the choice of modes. As a simple example, he points out that the ground state of two non-interacting harmonic ...
Varun Immanuel's user avatar
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Monogamy of entanglement and Quantum Cryptography

I would like to understand thoroughly the monogamy of entanglement and its use in Quantum Cryptography. The literal phrasing is that : "Whenever two systems A and B are maximally entangled, a ...
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Is there any restriction for locally mapping a given 2-qubit density matrix into a desired 2-qubit density matrix with lower entanglement?

Suppose we're given a 2-qubit density matrix($\rho_{4\times4}$). we can apply two local maps on each of these qubits seperatly. So the output is density matrix($\rho^{\prime}_{4\times4}$). I'm ...
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Quantum sensing using Ion penning traps[[ODF, Dicke states and pi/2 pulse]]

I am reading the article https://www.science.org/doi/full/10.1126/science.abi5226 It's about Quantum sensing in ion penning traps. Question 1. Does the axial mode of the penning trap have nothing to ...
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Seperable Quantum States

Some similar questions have been ask before, but I still don't really get the definition of seperable states in quantum mechanics. Consider a bell state of a two qubit system. \begin{align} \left|\Psi\...
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Is this an alternative realization of Deutsch's algorithm? [closed]

The standard Deutsch's algorithm uses two qubits and a control-$U_f$ gate, which transforms the two qubits, $|x\rangle |-\rangle \rightarrow (-1)^{f(x)}\, |x\rangle |-\rangle $. To realize the ...
Yuan John Jiang's user avatar
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Proof that $\mathrm{Tr} _ {\mathcal{Y}}[(\hat{X} \otimes \mathbf{1} _ {\mathcal{Y}}) \hat{\rho}] = \hat{X} \mathrm{Tr} _ {\mathcal{Y}} (\hat{\rho})$ [closed]

I've been trying to prove a partial trace identity that I need to prove something related to the Stinespring representation of a Completely Positive map, but I haven't been successful. (For some ...
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1 vote
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What happens to a coherent state when it passes through an optical amplifier?

I learned from this article that when a quantum state passes through an optical amplifier based on stimulated emission (e.g., EDFA), the variance of its quadrature becomes: $(\Delta X)^2 = G(\Delta ...
Godfly666's user avatar
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How are uncertainties of the quantum state/wavefunctions themselves modeled?

This question might be confusing so let me try to clarify this carefully. The wavefunction is a tool that allows us to calculate probability distributions that model uncertainties. Thus makes sense. ...
Maximal Ideal's user avatar
1 vote
2 answers
299 views

Problem with logarithm of tensor product of matrices

In the book of From Classical to Quantum Shannon Theory, in exercise 11.8.1, there is a property of logarithm of a tensor products of two matrices, defined as follows: $$\log ( A \otimes B) = \log(A) \...
JasonWS 's user avatar
1 vote
3 answers
81 views

Mach-Zehnder interferometer and superposition

I've a doubt on interpretation of superposition in the interferometer Is it correct to say that in the Mach-Zehnder interferometer, the photon exists in a state of quantum superposition of the two ...
daniele's user avatar
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What is a $ZZ$-interaction physically?

To me it is clear that a Hamiltonian of the form $H = J \sigma_x$ corresponds to a rotation of a qubit around the $x$-axis. I can substitute the above Hamiltonian into the Schrodinger equation, choose ...
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Is two degree quantum entanglement possible? And by two degree of entanglement I mean one in space and other in time? [closed]

Whenever we try to entangle two particles, the entanglement lasts for a very short period. If we observe our present universe we can see that all the matters present in our universe are finely ...
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Are all types of noise a result of lack of complete knowledge about the given system? What does this say about the physicality about information?

I am currently studying the basics of quantum information theory. When we study a system (classical or quantum), any undesirable influence out of our control is usually referred to as noise, and this ...
Pratham Hullamballi's user avatar
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1 answer
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Applying operators to quantum states

I am reading a primer on quantum proofs (without having a background in QM) ("Quantum Proofs" by Thomas Vidick and John Watrous, pages 11 and 15) and have a question. For an operator $A\in L(...
Rincewind's user avatar
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Does information always gravitate?

I'm trying to wrap my head around Bekenstein's loose argument that a bit of information added to the black hole corresponds to an added Planck surface area to its horizon. In it, he argues that one ...
Lourenco Entrudo's user avatar
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Why are PEPS more frequently used when simulatind 2D systems rather than branching MERA?

From what I've read it seems that PEPS is a go-to method while simulating 2D quantum systems. Why is it the preferred method rather than branching MERA? The contraction of PEPS is a #P-complete ...
brzepkowski's user avatar
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Is there a non-negative normalized Wigner function that doesn't correspond to a physical state?

This is related to Is the Wigner function non-negative only for convex mixtures of Gaussian states? and Can the characteristic function $\chi_\rho(\beta)={\rm tr}[\rho D(\beta)]$ be an indicator ...
glS's user avatar
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Prove that the conditional von Neumann entropy satisfies $S(A|C)=-S(A|B)$ if computed on a pure $\rho_{ABC}$

Can someone show me how to prove this relation? If $\rho_{ABC}$ is a pure state, then $S(A|C)=-S(A|B)$ I already know that $S(A|B)=S(\rho_{AB})-S(\rho_{B})$ and that I should somehow use that $S(\...
Synonym's user avatar
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Is the Wigner function non-negative only for convex mixtures of Gaussian states?

Hudson's theorem, the result usually cited in this context, tells us that for a pure state, the Wigner is non-negative iff the state is Gaussian, but doesn't in general say anything about mixed states....
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How is the inner product of two quantum states related to their associated Bloch vectors?

I have a doubt about how two equivalent ways of calculating the inner product between two states seem to not be actually equivalent, as they should. In particular, I'm interested in the case where the ...
Sebastián Torres's user avatar

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