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.

Filter by
Sorted by
Tagged with
-1 votes
0 answers
26 views

Does wave function collapse imply the creation of information? [closed]

I ask this question as a complete layperson, so do mind my inevitable misunderstandings here. I hope this makes enough sense for you good people to provide some insights, however. I got to thinking ...
-3 votes
0 answers
17 views

entangled qubits weaving space-time [closed]

Can somebody explain this article https://knowablemagazine.org/article/physical-world/2019/quantum-origin-spacetime simply since I do not really understand it and I roughly understand quantum ...
1 vote
0 answers
21 views

Duality transformation in Kitaev's quantum double models

In Kitaev's quantum double models (https://arxiv.org/pdf/quant-ph/9707021.pdf), it is well known that the vertex operators $A_g$ and the plaquette operators $B_h$ are dual to each other, so there ...
  • 144
1 vote
1 answer
69 views

Lindblad operators of $n$-qubits local dephasing noise process

I know that Lindblad operator for $1$-qubit dephasing quantum channel is $L = \sqrt{\gamma} \sigma_z$ so that the corresponding master equation is $\dot{\rho} = \sigma_z \rho \sigma_z - \rho$ (e.g., ...
1 vote
0 answers
37 views

Does the holographic principle allow realistically-sized universe simulation?

I was reading about the holographic principle and a question came up to my mind which I can't find an answer to. My understanding is that the holographic principle states that the description volume ...
  • 311
1 vote
0 answers
56 views
+50

Interpreting a Density Matrix Resulting from Decoherence of a GHZ State

This questions extends on this question and on the given answer. What this question is about: Decoherence model. Consider a simple decoherence process modelled by $$\mathcal{E}\left(\rho\right)=p_0\...
  • 659
2 votes
2 answers
64 views

Local symplectic transformations on Gaussian states

According to Eqn. $(18)$ of this paper, given a two mode Gaussian state with the $4 \times 4$ covariance matrix $\sigma$, it is possible to find a symplectic matrix $S = S_1 \oplus S_2$, where $S_{1, ...
  • 336
0 votes
1 answer
64 views

Is entanglement the only way to get mixed state that is consistent with the Schrödinger equation?

If we treat our entire system (say an electron and a bunch of atoms) quantum mechanically then all possible interactions will be unitary transformations. Thus any state that I describe will always be ...
1 vote
0 answers
33 views

Representation of $d$-dim maximally mixed state in different bases

Consider the maximally entangled state in $d$ dimensions, $|\Psi\rangle:= \frac{1}{\sqrt{d}} \sum_{i=0}^{d-1} |i,i\rangle^{AB}$, where $|i\rangle^{AB} := |i\rangle^{A}\otimes|i\rangle^{B}$ and $\{|i\...
  • 465
1 vote
1 answer
110 views

Is quantum cloning $|\psi\rangle|\psi_1\rangle|\psi_2\rangle|C\rangle\to e^{i\alpha}|\phi\rangle|\psi\rangle|\psi\rangle|C'\rangle$ prohibited?

I think the no-cloning theorem is too restrictive, as in, $$|\psi\rangle |\phi\rangle\to e^{i\alpha}|\psi\rangle|\psi\rangle \tag{1}$$ does not allow for any arbitrariness in the final state. Instead, ...
  • 5,705
0 votes
0 answers
16 views

Are functions of commuting measurement operators equivalent to the same functions on the outcomes of those operators?

I.e., is it the case that for all states $\hat{\rho}$, we have that $F(\hat{A}_i, \hat{A}_j, \hat{A}_k, \hat{\rho}) \equiv F(a^{(l)}_i, a^{(m)}_j, a^{(n)}_k)$, where $a^{(l)}_i, a^{(m)}_j$ and $a^{(n)}...
  • 1,213
3 votes
1 answer
125 views

Dephasing noise as a decoherence model - Effect on a generalized GHZ state

Some input: Consider a decoherence process modelled by $$\mathcal{E}\left(\rho\right)=p_0\rho+(1-p_0)\sigma_z\rho\sigma_z$$ with $p_0=(1+e^{-\gamma t})/2$. One can readily find that this leads to $\...
  • 659
3 votes
0 answers
82 views

Measuring quantum states without violating no-cloning

In Nielsen and Chuang exercise 2.64, the following problem is given: Suppose Bob is given a quantum state chosen from a set $\{ \lvert \psi_1 \rangle, \ldots , \lvert \psi_m \rangle \}$ of linearly ...
  • 131
3 votes
4 answers
171 views

Does $\exp(-i \theta \sigma_m \otimes \sigma_n)$ represent a rotation operator?

It is well known that $\exp(-i \sigma_k \theta)$ where $\sigma_k$ $(k=x,y,z)$ is a Pauli matrix, represents the rotation operator about $k$-th axis. What physical interpretation does $\exp(-i \theta \...
  • 246
1 vote
0 answers
38 views

Quantum State Tomography with Machine Learning [closed]

So, I am new to this area. I know a little bit on Machine Learning and Neural Networks and I'm a Physics student and recently I started studying Quantum Information Theory. I found some papers and ...
2 votes
1 answer
55 views

Is the following map linear over the space of density matrices?

I have a map $\mathcal{N}$ from the space of two-qubit subnormalised density matrices $\mathcal{S}(\mathcal{H}_2 \otimes \mathcal{H}_2)$ to itself (positive operators with trace between 0 and 1). ...
  • 23
2 votes
2 answers
82 views

Why is this the right form for the density operator in "classical" mixture cases?

It is well known that the set of density operators $\{\rho\}$ for a quantum theory form a convex set. As I have seen them defined, we simply say that a state corresponds to some linear operator $\rho$ ...
  • 661
2 votes
0 answers
121 views

Showing there are infinitely many decompositions of a non-pure state [duplicate]

Consider Problem 2.10 from Ballentine (paraphrased): Show (by constructing an example depending on a continuous parameter) that this can be done in infinitely many ways. I'm not sure how to proceed. ...
  • 661
1 vote
0 answers
82 views

On the correspondence rules between the physical world and mathematical frameworks (quantum mechanics)

At the start of Chapter 2 of his Quantum Mechanics: A modern development, Ballentine gives the framework which sets the stage for the questions I have: Every physical theory involves some basic ...
  • 661
1 vote
1 answer
63 views

Entanglement Entropy and Entanglement Negativity for pure/mixed separable/entangled state

My question is how is Entanglement Entropy (EE) and Entanglement Negativity (N) related to the combinations of pure/mixed and separable/entangled states? That is for pure separable (PS), pure ...
1 vote
0 answers
41 views

The action of $50:50$ quantum beam splitter

I have a question regarding the action of the $50:50$ beam splitter. According to Peter Knight's book, the action is: $B=\frac{1}{\sqrt{2}}\begin{pmatrix}1 & \iota\\ \iota & 1 \end{pmatrix}$ ...
  • 11
1 vote
1 answer
113 views

What is the fundamental reason why information is on the event horizon of a black hole?

I don't know the mathematics behind black holes and information theory but is there a simple explanation of why information is on the event horizon. Why can't it be elsewhere?
user avatar
0 votes
0 answers
41 views

Collapse postulate in the density operator formalism [duplicate]

To the extent that the collapse postulate holds, textbooks will almost invariably restrict the discussion to contexts in which states are represented by normalized kets, so that the collapse postulate ...
  • 661
-1 votes
0 answers
31 views

I have a quantum gate and I need to decompose it in tensor products of qiskit native gates, how do I do it?

I have the following unitary and I need to decompose it in products of Qiskit native gates (I guess phase and CNOT is the customary universal set but I'm not sure): $$ \begin{pmatrix} \cosh(\frac{\...
2 votes
1 answer
26 views

Photon polarization transformations

Photon polarization states form a qubit $(\cos \theta ~ \sin \theta)^{T}$ - characterized by a parameter $\theta$. Obviously, such a state can be rotated by some transformation matrix $R_{\theta} = (...
  • 246
1 vote
0 answers
73 views

Quantumly hard problem but classically easy [closed]

It is usually said that the quantum computer can solve classically hard problem but quantumly easy. See for example the Preskill video. Are there important problems of the opposite: the classical ...
1 vote
1 answer
98 views

A theorem in Sakurai's QM book (section 1.4)

I was trying to understand the theorem 1.2 in Sakurai's Modern QM, it is on page 29 (the second edition): Suppose that $A$ and $B$ are compatible observables, and the eigenvalues of $A$ are ...
3 votes
3 answers
173 views

Do the states in a decomposition $\rho=\sum_i p_i |\phi_i\rangle\!\langle \phi_i|$ need to be orthonormal?

On Wikipedia it says: Let $\mathcal H_S$ be a finite-dimensional Hilbert space, and consider a generic (possibly mixed) quantum state $\rho$ defined on $\mathcal H_S$, and admitting a decomposition ...
0 votes
1 answer
49 views

Bell's Original Paper - Local hidden variable theories correlations smaller than entanglement

I'm having trouble following Bell's derivation of equation 22 in his original paper. Particularly, how to go from $$ | \overline{P} (\vec{a}, \vec{b}) - \overline{P}(\vec{a}, \vec{c}) | \leq 1 + \...
0 votes
1 answer
50 views

How are the particles constituting a black hole entangled with Hawking radiation?

On the horizon of a black hole negative energy (frequency) states of virtual particles are separated from positive energy states, while staying entangled. The negative energy states (particles or anti-...
3 votes
1 answer
103 views

Commutativity of $\rho_{AB}$ and $\mathbb{I}_A\otimes\rho_B$

Suppose the density operator of a composite system $AB$ is given by $\rho_{AB}$ and $\rho_B =\mathrm{Tr}_A(\rho_{AB})$ the marginal density operator of the sub-system $B$. I have some doubt whether $\...
  • 33
0 votes
1 answer
38 views

Black hole and entropies

In their paper The entropy of Hawking radiation, Juan Maldacena et al. write : «In other words, if the black hole degrees of freedom together with the radiation are producing a pure state, then the ...
1 vote
1 answer
76 views

Can a particle be entangled with itself?

Suppose I had a single particle with a four-dimensional Hilbert space $\mathcal{H}$ spanned by the states $\{ |1\rangle,|2\rangle,|3\rangle,|4\rangle\}$ and suppose I prepared the particle in the ...
  • 3,498
2 votes
3 answers
129 views

What is the difference between nonlocality and entanglement?

I'm a bit confused about the difference and relation between (quantum) nonlocality and entanglement. To give some context about my confusion, I was reading this paper: Brunner, Nicolas, et al. "...
  • 37
1 vote
0 answers
32 views

Applying a simple noise model to the ghz state

I want to calculate the effect of a specific noise model on the GHZ state but fail to do so. I think I am missing some basic rules established for working with operations on density matrices. More on ...
  • 659
1 vote
1 answer
50 views

"Elimination" of terms in Simon's Algorithm

I've started to study Quantum Information Technology and I stumbled upon a rather confusing statement while studying about Simon's Algorithm. I am pretty sure this isn't just something that is related ...
6 votes
2 answers
273 views

Non-physical state in tomography

In tomography, we can use Pauli operators to estimate the qubit state, and by performing a substantial number of measurements one can estimate their expectation values. Define the estimates as $\bar\...
  • 107
0 votes
1 answer
73 views

Reduced density matrix computation generalization

I just recently completed a problem in which I had a Hilbert space of the form $$ H = H_1 \otimes H_2 \otimes H_3 $$ and was tasked with finding the reduced density matrix for the system in the ...
3 votes
1 answer
400 views

Why do physical quantum maps need to be completely positive? [duplicate]

It has been a real question for me why exactly for studying open quantum systems it is not sufficient for the dynamical maps to be positive and must be completely positive. what is the physical ...
  • 107
10 votes
4 answers
609 views

On the definition of positive linear superoperators on Hilbert spaces

Consider a linear map between linear maps of a Hilbert space, $\mathcal{E}: \mathcal{L}(\mathcal{H})\to\mathcal{L}(\mathcal{H})$. The standard definition I have encountered is that $\mathcal{E}$ is ...
  • 123
2 votes
1 answer
38 views

What barriers have prevented us from using Landau levels to make qubits?

Landau levels allow us to jam all electrons into nearly identical quantum states - these states share the same quantum numbers (e.g. orbital and spin) except for the guiding center. Furthermore, the ...
  • 543
1 vote
1 answer
58 views

Can excited high spin states be used as qubits?

What the title says. I was wondering if we can use excited high spin states formed by enhanced intersystem crossing for qubits? like intramolecular quartets formed by a doublet and an intersystem ...
0 votes
2 answers
105 views

Why are the number of one qubit quantum gates uncountably infinite?

I keep running into this statement everywhere I go, and the source is never quoted. Is it because the entries for the matrix representing the gate are complex numbers and hence uncountably infinite? ...
0 votes
1 answer
52 views

3 Eigenstates for $X$? [closed]

Unless I have made an error, the Pauli $X$ operator has 3 eigenstates. Qiskit lists the two eigenstates for $X:|+\rangle= \frac 1{\sqrt2}(|1\rangle + |0\rangle)$ and $|-\rangle = \frac 1{\sqrt 2}|0\...
1 vote
0 answers
47 views

Fuzz Ball hypothesis of Black holes [closed]

A little help please. How does the fuzz ball hypothesis using string theory solve the information paradox? I have heard people who know the subject far better than me say that it in fact does but i ...
0 votes
1 answer
55 views

General Relativity downfall point/radius in BH physics [closed]

Studying GR, sometimes one asks himself/herself where GR fails to describe physics. For simplicity, take a Schwarzschild solution (nonrotating chargeless black holes), what of the following conditions ...
  • 6,027
0 votes
1 answer
67 views

How many subsystems does an abstract quantum system have?

Given an abstract quantum system, for example, the four-state system (ququart), is it possible to calculate all different ways to split the system state space into tensor product of subsystems' state ...
  • 723
3 votes
2 answers
161 views

Does The Classical Limit of Quantum Computing Exists?

In any standard college book on quantum mechanics and field theory, one for sure has encountered some expressions like " the classical limit corresponds to setting hbar to zero" or quantum ...
1 vote
0 answers
38 views

Inverse participation ratio (IPR) literature

I am curently working with the inverse participation ratio (IPR) as a measure of localization but I can't find literature that just explains why and how exactly it relates to localization. I get the ...
-2 votes
1 answer
100 views

What is the relation between Dirac spinors and qubit spin? [closed]

Dirac Spinors is a 4 element vector, and a qubit state vector is two element vector. Two spinors are positive(1 and 4) and negative values (3 and 2), being the first value the spin up and the second ...

1
2 3 4 5
63