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 vote
1 answer
40 views

If you measure one "share" of an entangled pair, will the resulting pair be a product state?

If you do a partial measurement on one "share" of en entangled pair, will the resulting pair no longer be entangled, i.e will be a product state?
user avatar
0 votes
0 answers
37 views

Why aren't states with 3 basis vectors considered entanglements in two qubit system?

I am going to take out normalization factors for simplicity. $$|00⟩+|11⟩$$ $$|00⟩−|11⟩$$ $$|10⟩+|01⟩$$ $$|10⟩−|01⟩$$ I can see why these states are entangled but I don't see why the following states ...
user avatar
4 votes
1 answer
128 views

Necessary and sufficient conditions for operator on $\mathbb C^2$ to be a density matrix

Consider a one-qubit system with Hilbert space $\mathscr H\simeq \mathbb C^2$. Define the hermitian operator $$\rho := \alpha\, \sigma_0 + \sum\limits_{i=1}^3 \beta_i\, \sigma_i \quad , \tag{1}$$ ...
user avatar
3 votes
1 answer
61 views

Find coefficient for pure and mixed states

Consider a generic $2\times 2$ Hermitian matrix written as $$\rho =\alpha\sigma_0+\beta\hat{\vec n}\cdot\vec\sigma\quad ,$$ where $\hat{\vec n}$ is a unit vector and the coefficients are real numbers. ...
user avatar
1 vote
1 answer
101 views

How to prove that every mixed one-qubit state admits a Bloch-sphere representation? [duplicate]

A mixed state $\rho$ can be written as $$\rho=\frac{1}{2}\left(I+r_x\sigma_x+r_y\sigma_y+r_z\sigma_z\right)\qquad\left(\vec{r}:=\left(r_x,r_y,r_z\right)^T\in\mathbb{R}^3; ||\vec{r}||\leq 1\right)$$ ...
user avatar
  • 395
0 votes
1 answer
35 views

Given the Symplectic Matrix acting on phase space, find the Gaussian Unitary acting on the Hilbert space

In Gaussian Quantum Mechanics, a unitary preserving the Gaussian nature of the state is a called a Gaussian Unitary. In the phase space picture, a Gaussian state is fully characterized by its first ...
user avatar
0 votes
1 answer
36 views

Filling factors and implementation for non-Abelian models

Currently reading through Pachos' Introduction to Topological Quantum Computation, and perusing other related articles and papers online. Have seen in many places that the 5/2 filling factor for ...
user avatar
-3 votes
3 answers
166 views

Are most reals fake? Does it make a difference?

There are uncountably many reals. However, there are only countably many definable numbers. Thus, almost all reals are undefinable. Undefinable means that the shortest representation of that number ...
user avatar
  • 99
1 vote
1 answer
82 views

Qubit system coupled to a bath of quantum harmonic oscillators

It is well known that when we consider a probe harmonic oscillators (called system) that is coupled to a reservoir of N harmonic oscillators, i.e. the Hamiltonian is written as the following, the ...
user avatar
1 vote
0 answers
107 views

Repeating observations in quantum theory

Suppose we prepare a state $\psi$ in a quantum system, represented in some Hilbert space, and suppose $A$ is an observable represented by the matrix $A$ (which possibly has infinite order). QUESTION A ...
user avatar
  • 267
1 vote
0 answers
23 views

Lower bound on the spectral gap in finite size critical systems with locality

Local quantum systems tuned to criticality are gapless in the thermodynamic limit. The rate at which the ground state spectral gap approaches zero as the system size $L \rightarrow \infty$ carries ...
user avatar
  • 2,757
2 votes
1 answer
62 views

How to compute the Schmidt decomposition of a bipartite pure state?

I'm trying to work out the entropy of entanglement of my state but I'm struggling to put it into a Schmidt decomposition, i.e. in the form: $\sum_i \alpha_i |u_i \rangle |v_i \rangle$. Currently I ...
user avatar
0 votes
1 answer
34 views

Quantum walk: transition matrix, negative or positive sign in the exponent?

Why is it that in some papers the transition matrix of a continuous-time quantum walk is defined as $\exp(itH)$ and in other papers as $\exp(-itH)$?
user avatar
1 vote
1 answer
41 views

Why is the density matrix of a system has this block form?

In Ficek's paper (http://zon8.physd.amu.edu.pl/~tanas/spis_pub/pdf/04-joptb-S90.pdf), the density matrix of a two two-level atom system has a block form like this. Why does it make sense to assume ...
user avatar
1 vote
1 answer
72 views

Order parameters in topologically ordered systems

Topologically ordered phases are characterized by a non-vanishing ground-state expectation value of a non-local operator. These operators are supported on sites whose number grows with the system size....
user avatar
  • 1,180
1 vote
0 answers
54 views

Analog of the Pauli vector for $SU(4)$

In quantum mechanics and representation theory, it is well known that the Pauli matrices transform as a vector due to the special relationship between $SU(2)$ and $SO(3)$. For example, suppose we have ...
user avatar
  • 627
0 votes
0 answers
12 views

Boundary condition of dyadic Green’s function for planarly layered media

The dyadic Green’s function of free space in terms of orthonormal system for TE/TM polarized waves is: where, now by applying boundary conditions to the first equation, the dyadic Green’s function ...
user avatar
-1 votes
1 answer
54 views

Question about the energy levels of Rubidium atom - how to understand this energy level diagram?

But today when I try to read some papers working with Alkaline atom, I couldn't figure out how they plot the Rubidium energy level. From my undergraduate study, I thought the diagram of Rubidium atom ...
user avatar
0 votes
2 answers
157 views

Finding the Kraus Operators of a Quantum Channel from its Choi Matrix

TLDR : What is the form of the projector I need to use to attain a 2X1 vector from $P_i v_k$ with which I can build my Kraus Operator? I am calculating the Kraus Operators for a Quantum Channel ...
user avatar
5 votes
1 answer
161 views

Examples of quantum systems modelled with Type II von Neumann algebras

What are the examples of quantum systems that should be modelled with a Type $II_1$ or $II_\infty$ von Neumann algebra? I am pretty much a novice at von Neumann algebra, so I have hard time finding ...
user avatar
0 votes
1 answer
56 views

How to test if a bipartite density matrix violates Bell's inequality?

For a given density matrix $$\rho = \sum_{ijkl=0}^1 r_{ijkl} |i,j\rangle \langle k,l|$$ describing a bipartite two-qubit system, how can I prove for what values $r_{ij}$ the density matrix violates ...
user avatar
  • 31
-1 votes
1 answer
50 views

Quantum Computer - Rotation Bloch Sphere [closed]

please can anyone help? What gate combination allows moving from the state between |0> and |1> states. In terms of bloch-sphere from the north pole to the south pole as an example. And how can ...
user avatar
  • 1
0 votes
0 answers
30 views

Difference in density matrix where prob. 1/2 in both $|0\rangle$ and $|1\rangle$ [duplicate]

In my course, we had an example: give the density matrix of a system arising from a proces that generates a [0> with probability 1/2 and a [1> with prob. 1/2. The answer is $1/2[0\rangle\langle0]...
user avatar
  • 101
2 votes
1 answer
41 views

In quantum computing, what's the difference between the Pauli Gate and the RZ gate?

I know that both rotate around the $z$-axis, but when would you want to use one over the other? What's the difference?
user avatar
5 votes
0 answers
52 views

How to measure the entanglement of three entangled qubits?

The entanglement of two qubits is calculated using "concurrence" and "negativity". Concurrence and negativity, however, are only used for "two" entangled qubits. Is there ...
user avatar
6 votes
2 answers
217 views

Can one incorporate quantum field theory into quantum information theory?

My understanding is that quantum information is primarily formulated in terms of non-relativistic quantum mechanics language. And it can deal pretty well with, for example, elastic scattering in ...
user avatar
1 vote
0 answers
42 views

How to correctly understand the monogamy of entanglement?

If the degree of entanglement between qubits A and B is 100% (total entanglement), then neither of them can entangle with qubit C. However, if the entanglement between A and B is partial (say 80%), ...
user avatar
2 votes
0 answers
50 views

Mutual information of a tensor network

Suppose I've got a tensor network (TN) representing some bipartite quantum state, $|\Psi\rangle$. Using the Schmidt decomposition, I can write $|\Psi\rangle = \sum_{k=1}^r \sqrt{\lambda_k}|\chi_k\...
user avatar
  • 207
1 vote
0 answers
33 views

Resources for studying quantum metrology

I want to learn about quantum metrology topics like von-Neumann hamiltonian, ABL rule etc., typical case studies of interpretation of measurement, quantum contextuality etc., discussion on what is ...
0 votes
0 answers
24 views

How to transform any pure two-mode Gaussian state into "canonical two-mode squeezed state form"?

I'm new to quantum optics and am going through a review paper by Braunstein & Loock. There, after calculating the partial von Neumann entropy for a two-mode squeezed vacuum $$\hat{S}(\zeta)|00\...
user avatar
0 votes
1 answer
46 views

Understanding the Bloch Sphere Better

Numerous times I have used the Bloch sphere and visualized gates as rotations. For Z and X rotations, it is a pretty good representation. However, today I found that this does not stand for Y/2 gate. ...
user avatar
0 votes
2 answers
101 views

States $-|0\rangle$ and $i|0\rangle$ in Bloch Sphere?

I am new on quantum computing and starting reading a book about it. Going through it, the Bloch sphere was described for two states. My question about is: where are the states $-|0\rangle$ and $i|0\...
user avatar
  • 103
1 vote
1 answer
57 views

Show $I+\tau\mathcal{L}$ is completely positive when $\tau \leq 1/\lambda_{\mathrm{max}}(\mathcal{L})$

I am not very well-versed when in comes to open quantum systems which is why I need some help. In a paper, I encountered the following situation: Let $\mathcal{L}$ be a Lindbladian so the time ...
user avatar
  • 337
5 votes
2 answers
314 views

How does this experiment "rule out real-valued standard formalism of quantum theory"?

I came cross this paper: https://arxiv.org/abs/2103.08123 To be frank I don't understand most of it, but the summary seems a bit shocking. I found it rather strange. There have been multiple ...
user avatar
0 votes
0 answers
15 views

The derivation of the quantum information no-hiding theorem, question 2

I am reading Samuel L. Braunstein, Arun K. Pati, Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox. The paper purportedly proves ...
user avatar
  • 723
0 votes
1 answer
53 views

Use polarization identity to prove a linear operator over a finite-dimensional Hilbert space is completely specified by its expectations on a sphere

This is from the book Quantum Theory from First Principles: An Informational Approach, which I thought I'd give a read as I found the authors' two papers on the same subject to be rather impenetrable. ...
user avatar
-1 votes
4 answers
127 views

Expected value of a state $\psi$, with two eigenstates [closed]

If a state is generally given as $$\vert{\psi}\rangle=a\vert0\rangle+b\vert1\rangle$$ then what is ( If the question makes sense ) the expected value of this state? I know about the expected value of ...
user avatar
0 votes
0 answers
51 views

How to derive the equation of Gibbs state?

I am new to the quantum mechanics. The Gibbs state is defined as the invariant state under future evolution of the system. I am confusing about how the Gibbs state is derived. Given the Hamiltonian $H$...
user avatar
5 votes
2 answers
339 views

Measurement on mixed states

I have a conflict between my lecture notes on quantum mechanics, where it is stated that the probability of measuring an eigenvalue $a_i$ on a mixed state with desnsity matrix $\rho$ is $$ \...
user avatar
  • 483
1 vote
1 answer
41 views

Is there a limit of size for superpositions?

Can objects be always in superposition if there were no environment for decoherence to occur.
user avatar
2 votes
1 answer
129 views

On the Bell's Theorem / Bell-type Inequalities and the Kochen-Specker Theorem

It appears to me that the Kochen-Specker theorem, if not Gleason’s theorem already, seals the fate of realism / value definiteness (with possibly the additional assumption of non-contextuality, ...
user avatar
0 votes
0 answers
78 views

Expectation value of $\mathrm{SU(1, 1)}$ parity operator

The $\mathrm{su(1, 1)}$ Lie algebra is spanned by the generators $K_+$, $K_−$ and $K_0$, which satisfy the commutation relations: $$[K_0, K_{±}] = ±K_{±}, [K_−, K_+] = 2K_0.$$ We can define the ...
user avatar
  • 61
0 votes
0 answers
85 views

The derivation of the quantum information no-hiding theorem, question 1

I am reading Samuel L. Braunstein, Arun K. Pati, Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox. I am puzzling over the derivation ...
user avatar
  • 723
1 vote
0 answers
18 views

Algorithm that checks if a subspace of states contains a product state

Suppose I have two identical qudits, the full Hilbert space is $\mathcal{H}=(\mathbb{C}^{d})^{\otimes 2}$. Say I'm given a supspace of states $\Lambda\subset \mathcal{H}$. What is the fastest ...
user avatar
  • 743
0 votes
1 answer
56 views

Higher derivatives of the log-partition function?

I need higher derivatives of the log-partition function $Z(z)=\log \sum_i \exp(z_i)$, has anyone derived the formula? Looking at concrete values of derivatives up to order 8, evaluated at $z=(1,1,1)$ ...
user avatar
3 votes
1 answer
176 views

Does a subsystem being mixed imply the state is entangled?

If a pure state, $\rho_{AB}$, has subsystems described by mixed density matrices, the overall state is entangled (as far as I understand). Can you conclude the same with an initially mixed bipartite ...
user avatar
  • 99
1 vote
0 answers
33 views

Concurrence between 2 qubits of tripartite system

If we consider a tripartite system (say of 3 qubits) described by density matrix $\rho_{ABC}$, does the concurrence $C(\rho_{BC})$ still accurately measure the entanglement between subsystems B and C? ...
user avatar
  • 99
1 vote
1 answer
40 views

Coupled systems and quantum configuration space?

I was watching this PBS Spacetime video. He mentions that quantum particles / wavefunctions (he uses electrons as his example) all have their own set of separate 3D coordinates in a coupled system. ...
user avatar
1 vote
1 answer
50 views

Can bond dimension vary from bond to bond?

Consider a bipartite system composed of subsystems $A$ and $B$, with corresponding Hilbert spaces $\mathcal{H}_A$ and $\mathcal{H}_B$, spanned by $\{\chi_1,...,\chi_n\}$ and $\{\phi_1,...,\phi_m\}$, ...
user avatar
  • 207
4 votes
1 answer
111 views

How do we trace over subregions in a fermionic QFT?

Bosonic Case In a bosonic QFT, the Hilbert space associated to a surface $\Sigma$ is the appropriate space of wavefunctionals on $\Sigma$. Hence, if $\Sigma=\Sigma_1 \sqcup \Sigma_2$, we find that the ...
user avatar

1
2
3 4 5
59