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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Master equation with a coherent bath

When we consider an oscillator $a$ acting with a bath of oscillators $b_i$ with the interaction Hamiltonian reads $$H_{int}=\sum_{i}g_ia b_i^{\dagger}+g_i^*a^{\dagger}b_i,$$ with the free Hamiltonian: ...
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CNOT Gate in Pauli Basis

The CNOT gate is usually written as $|0\rangle\langle0|\otimes I + |1\rangle\langle1|\otimes X$ (with $X,Y,Z$ beign the Pauli Basis and $I$ the Identity). I have yet to stumble across the ...
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Is quantum entanglement the only true quantum phenomenon? [closed]

I once heard that in essence, the only truly unique quantum effect is, or is due to, quantum entanglement. Is that statement true? If true, how can I convince myself of it? If false, what are the ...
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Complex Coupling Strength in Light-Matter Interaction Hamiltonian

The quantised electric field operator is given by : $$ \hat{\mathbf{E}}(\mathbf{r},t) = i\sum_{\xi}E_{\xi}\left(\mathbf{u}_{\xi}(\mathbf{r})a_{\xi}-\mathbf{u}^*(\mathbf{r})a_{\xi}^{†}\right) $$ where ...
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What is the difference between "cluster states" and "graph states"?

I wonder about the difference between the cluster state and the graph state. I guess the only difference is the graph of the cluster state is limited to a two-dimensional square lattice The concept of ...
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What is the measure of decoherence?

Assume we have a qubit, and it is interacting with the environment. I know that people say that when the qubit is in $$\begin{pmatrix}\frac{1}{2}&\frac{1}{2}\\ \frac{1}{2}&\frac{1}{2} \end{...
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How is the Big Bang compatible with the preservation of quantum information?

As detailed at https://en.wikipedia.org/wiki/No-hiding_theorem , in the quantum world, information cannot be created or destroyed. The Bekenstein bound limits the amount of information that can be ...
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Why an energy constraint gives the canonical ensemble (NVT) when we maximize von Neumann entropy, when energy is not conserved in NVT?

In Sakurai and Napolitano's Modern Quantum Mechanics 2nd Edition, I'm learning Section 3.4, page 188 where they derive the canonical ensemble by maximizing von Neumann entropy with energy constraint. ...
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Degenerate quantum error correction code

I have been reading this to understand quantum error correction a bit. On page 13, there are paragraphs about degenerate QEC. It says, if $E_{1}E_{2} \in H $, $E_1 $ and $E_2$ will have the same ...
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Why can we distinguish two electrons in different experiments?

Electrons are indistinguishable particles, however, when I set up two independent experiments (at two positions), I can talk about "the electrons in Experiment x". What's going on here? I ...
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Coherence and superposition principle - equivalent properties?

I'd like to revisit a question I posted earlier. While I now know what coherence means (and how it can be defined) I still struggle to give an intuitive explanation that goes along with the word "...
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A variation of a Bekenstein's thought experiment

Consider a glass of water with mass $m$ and temperature $T_w$ released very close to the black hole horizon. The black hole being at temperature $T_{b} = \frac{1}{8\pi G M}$. Now, the final state is a ...
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Entanglement across a bi-partition of a many particle system

Alice and Bob each have two qubits labelled $A', A$ and $B, B'$ respectively. The density operator of the total system is $\rho_{A'ABB' } \in \mathcal{L}(\mathcal{H}^2 \otimes \mathcal{H}^2 \otimes \...
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Directly get tangent vector of Bloch sphere from quantum state (qubit)?

We know that Bloch sphere is a good way to represent a qubit(two energy quantum systems). Now I want to know the tangent vector in Bloch sphere, e.g. for states $\frac{1}{\sqrt{2}}\left( \begin{array}{...
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Forming an upper bound [duplicate]

\begin{eqnarray*} \|\left(E_{i} \otimes I_{d}\right)|\psi\rangle-\left(I_{d} \otimes F_{i}\right)|\psi\rangle \|^2&=&\|\left(E_{i} \otimes I_{d}\right)|\psi\rangle\|^2-2\langle\psi|E_i\otimes ...
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Under what conditions is a POVM a von Neumann measurement?

I want to know a definition of a von Neumann measurement. Because I can't find this concept referenced correctly in internet, and what differentiates it from a POVM, that by definition is the ...
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Do there already exists solutions to quantum gravity which are mathematically consistent and consistent with PRESENT observations? [closed]

This question is inspired by a recent video by Sabine Hossenfelder on the topic of black hole information loss. At about 8:23 the makes the claim that "...there are many possible solutions to the ...
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Are qubits just analog, continuous classical bits?

Topologically, classical bits (cbits) are essentially special cases of qubits restricted to the poles of the Bloch sphere. However, this restriction doesn't seem to be classical per se, but is simply ...
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Has the possibility of time travel been proven or demonstrated? [duplicate]

This study by Lesovik et al., 2019 seems to claim they have either sent information or an electron back in time. What is the current status of the idea of time travel (at least on the scale of ...
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How to model a Josephson junction as a two-level atom?

I have seen people saying that under certain condition, the dynamics in the Josephson junction can be simplified to that of a two-level system, governed by a the following Hamiltonian which ...
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Particle number conservation in matrix product state

I've been trying to understand how particle number conservation is enforced in matrix product state algorithms. As far as I understand, if the Hamiltonian commutes with the number operator, you can ...
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Commutator of positive semidefinite Hamiltonians

I have the following questions about the commutator of positive semidefinite Hamiltonians. Under what condition, the commutator will be positive semidefinite? Under what condition, the commutator ...
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Coupled and uncoupled qubits - Hilbert space representation

Suppose I have two situations: one where two qubits, $q_A$ and $q_B$, exist independently (on separate sides of the quantum chip, maybe), and one where they exist with some coupling between them. And ...
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Why is it easier to construct 2-qubit gates than 3-qubit gates?

In Quantum Computer Science, by Mermin, it is stated that $1$- and $2$-qubit gates are more feasible to construct than $3$-qubit gates or more. Given a fixed collection of qubits, are there any ...
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Deutsch-Jozsa algorithm

Quantum queries We just apply the boolean function to the computational basis labels. X is an n-bit string representing an n-qubit state, then we can try $|x\rangle$ to $f(x)$. but if $f(x)$ is ...
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If 2 electrons are entangled $[a] [b]$. if we throw a photon at $-[a]$ will it come out of $[b]-$? [closed]

i was confused as to what will happen when two electrons which are entangled and then if one is exposed to light. will the absorption and emission theory still work and if so how will it work in this ...
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Unmeasurable observables in quantum mechanics

Let's consider a single particle in 1D harmonic oscillator for definiteness. In standard QM, we say that any Hermitian operator on the Hilbert space is an "observable". It seems that (in ...
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How to compute the Schmidt decomposition of a two-qubit state?

Trying a to do the Schmidt decomposition of $|\Psi\rangle = \frac{1}{2}(|00\rangle+|01\rangle+|10\rangle+e^{i\phi}|11\rangle)$. The solutions I'm looking at do it by first finding the partial density ...
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What do Paz and Zurek mean by "one-bit" measurement in Heiss' Fundamentals of Quantum Information?

In Heiss' Fundamentals of Quantum Information (2002, p. 90) Paz and Zurek look at a "One-Bit Environment for a Bit-by-Bit Measurement". At the end they say, that decoherence because of "...
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Finding $\theta$ and $\phi$ when qubit state is $\frac{1}{\sqrt 2}[i ,1]^T$

Because we know the state of a qubit can be described as: $$ |q\rangle=\cos{\frac{\theta}{2}}|0\rangle+e^{i\phi}\sin{\frac{\theta}{2}}|1\rangle\\\ \\ \theta, \phi \in \mathbb{R} $$ How do I find the ...
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Definition of internal energy for quantum systems

In the last days I questioned my self on the definition of internal energy in quantum systems. Let consider a bipartite system with hamiltonian $H^{AB} = H^A + H^B + V^{AB}$ for instance. Then, if the ...
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Scalability of quantum optimal control

I'm curious to know how scalable in general the quantum optimal control method is to qubit systems. I've looked through many resources and it seems like it only has been applied to small system sizes (...
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Degrees of freedom of a $d$ level system and the dimension of its Bloch manifold

A qubit is described by two independent degrees of freedom that parametrize the Bloch sphere. Question: For a level $d$ level system, i.e., a qu$d$it, what are the corresponding degrees of freedom? ...
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Partial trace of local operators applied to maximally entangled states

I was looking at a problem where two invertible local operators were applied to a maximally entangled state, and didn't quite understand how some of it works out. We have local operators $A \otimes \...
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What is local about the hidden variable in Bell's theorem?

A pion decays to a singlet electron/positron state. We will measure the component of the electron's spin in the $\vec a$ direction and positron's spin in the $\vec b$ direction. If there exists a ...
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Is a highly entangled quantum system synonymous with a strongly correlated system?

Is a highly entangled quantum system synonymous with a strongly correlated system? From wikipedia a key characteristic of a strongly correlated system is that "the behavior of their electrons or ...
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Definition of tensor product in Nielsen & Chuang "Quantum Computation and Quantum Information"

Nielsen and Chuang (Quantum Computation and Quantum Information, 2010) define the tensor product of linear operators acting on vector spaces on page 73. Therefore the tensor product used in the ...
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What is the idea behind quantum speed limits?

Could someone please explain to me how the very basic idea behind existence of a quantum speed limit arises? I think I understand (if it's correct) how it arises naturally between two pure states ...
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How do I visualize a stepwise rotation on the Bloch Sphere using $SO(3)$ and $SU(2)$?

Searching for an implementation (that helps me to understand how $SO(3)$ and $SU(2)$ relate to each other) I came across this interesting question Visual interpretation, on the Bloch sphere, when ...
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The Equivalence Principle necessitates a mixed state description for the exterior of a black hole?

I am going through this review paper on the black hole information paradox. In section 2.2 page 10, the author argues the following: One of the basic tenet of general relativity is the Equivalence ...
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How does non-commutativity of observables lead to quantum speedup in solving algorithms in quantum computing?

The question might be misleading, but I'd like to understand a thing. By reading this really interesting question, one realises that the relevant thing in quantum mechanics and not reproducible in ...
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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?
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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 ...
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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 $$\rho := \alpha\, \sigma_0 + \sum\limits_{i=1}^3 \beta_i\, \sigma_i \quad , \tag{1}$$ ...
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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. ...
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How to prove that every mixed one-qubit state admits a Bloch-sphere representation? [duplicate]

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