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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Why is quantum entanglement considered to be an active link between particles?
From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every ...
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Does the collapse of the wave function happen immediately everywhere?
It is usually taught that when we measure some measurable value the wave function collapses immediately everywhere. This idea sounds like a simplification of some more complicated mechanism.
Are ...
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Understanding the Bloch sphere
It is usually said that the points on the surface of the Bloch sphere represent the pure states of a single 2-level quantum system. A pure state being of the form:
$$
|\psi\rangle = a |0\rangle+b |1\...
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Should it be obvious that independent quantum states are composed by taking the tensor product?
My text introduces multi-quibt quantum states with the example of a state that can be "factored" into two (non-entangled) substates. It then goes on to suggest that it should be obvious1 ...
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Quantum entanglement faster than speed of light? [duplicate]
Recently I was watching a video on quantum computing where the narrators describe that quantum entanglement information travels faster than light!
Is it really possible for anything to move faster ...
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What is spontaneous symmetry breaking in quantum systems?
Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture.
According to the classical picture, spontaneous ...
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How is a quantum superposition different from a mixed state?
According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state.
Now, consider the state
$...
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Differences between pure/mixed/entangled/separable/superposed states
I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum ...
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Quantum information references
I was hoping you guys could recommend reading material on quantum information. I have a good background in quantum mechanics, including in foundational issues, as covered in Ballentine's Quantum ...
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Understanding quantum entanglement.. help me validate this analogy!
I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is:
Let's say I receive two envelopes. ...
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What happens to the quantum information of a particle and an antiparticle when they annihilate?
I understand that the quantum no-deleting theorem dictates that it's impossible to delete quantum information, so what happens to the quantum information of a particle and an antiparticle when they ...
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Why is $\theta \over 2$ used for a Bloch sphere instead of $\theta$?
I'm a beginner in studying quantum info, and I'm a little confused about the representation of a qubit with a Bloch Sphere. Wikipedia says that we can use $$\lvert\Psi\rangle=\cos\frac{\theta}{2} \...
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What's wrong with this experiment showing that either FTL communication is possible or complementarity doesn't hold?
The assumptions are:
Alice and Bob have perfectly synchronized clocks
Alice and Bob have successfully exchanged a pair of entangled photons
The idea is simply to have Alice and Bob perform the ...
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Trouble with operator-sum representation of a quantum operation
I am reading about the operator-sum representation of quantum operations in Nielsen's and Chuang's 10th Anniversary ed of Quantum Computation and Quantum Information (N&C). I have become quite ...
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Is there such a thing as "Action at a distance"?
What ever happened to "action at a distance" in entangled quantum states, i.e. the Einstein-Rosen-Podolsky (EPR) paradox? I thought they argued that in principle one could communicate faster than ...
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How many bits are needed to simulate the universe?
This is not the same as: How many bytes can the observable universe store?
The Bekenstein bound tells us how many bits of data can be stored in a space. Using this value, we can determine the ...
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Is it possible for more than two particles to be entangled in a quantum way?
So I know that two particles can be entangled in a quantum way, but is it possible that more than two particles be entangled in a quantum way? Most descriptions provide with two-particles cases, so I ...
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Prove that the ensemble decompositions of a density operator $\rho$ are related by a unitary operator
In my class it was told that ensemble decompositions of a density operator $\rho$ are not unique, but that the ones that exist are related by a unitary operator. I'm trying to prove this, but I get ...
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These two operators commute...but their eigenvectors aren't all the same. Why?
The Hamiltonian
$$H = \left[ \begin{array}{cccc}
a & 0 & 0 & -b \\
0 & 0 & -b & 0\\
0 & -b & 0 & 0\\
-b & 0 & 0 & -a \end{array} \right] $$
commutes ...
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Is limited computational capacity a fundamental obstacle?
Statistical physics books often motivate the necessity of statistical/thermodynamic description by impossibility of calculating the trajectories of all the molecules (I speak of "trajectories&...
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What is the difference between general measurement and projective measurement?
Nielsen and Chuang mention in Quantum Computation and Information that there are two kinds of measurement : general and projective ( and also POVM but that's not what I'm worried about ).
General ...
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Maximum theoretical data density
Our ability to store data on or in physical media continues to grow, with the maximum amount a data you can store in a given volume increasing exponentially from year to year. Storage devices continue ...
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Is there something behind non-commuting observables?
Consider a quantum system described by the Hilbert space $\mathcal{H}$ and consider $A,B\in \mathcal{L}(\mathcal{H},\mathcal{H})$ to be observables. If those observables do not commute there's no ...
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Examples of density operators $\rho=\sum\limits_n p_n|\phi_n\rangle\langle\phi_n|$ in which the states $\{|\phi_n\rangle\}$ are not orthogonal
The set of quantum states $\{|\phi_n\rangle\}$ in the definition of the density operator $$\rho=\sum\limits_n p_n|\phi_n\rangle\langle\phi_n|$$ need not be orthonormal, and need not form a basis. But ...
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Where is locality used in CHSH/Bell's inequality?
A very similar question is asked here, but I'm still confused :(
From Bell, in a hidden variable model, $A = A(\lambda, a)=\pm 1$ is the observed spin of the first particle around axis $a$, and $B = ...
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What is the $S$ operator in the CHSH inequality $-2\leq S\leq 2$?
What exactly does $S$ represent in the CHSH inequality
$$-2~~\leq ~S~\leq ~2?$$
Sorry I've been reading for a couple days and I can't figure out what exactly $S$ is and the math is a bit over my ...
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Where does deleted information go?
I've heard that, in classical and quantum mechanics, the law of conservation of information holds.
I always wonder where my deleted files and folders have gone on my computer. It must be somewhere I ...
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Are coherent states of light 'classical' or 'quantum'?
Coherent states of light, defined as
$$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle
$$
for a given complex number $\alpha$ and where $|n\rangle$ is a ...
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Characterisation of the generalised Bloch space in spherical coordinates
I'm so confused by the following definition in the "Quantum Error Correction" by Lidar and Brun that not even sure how to formulate the question properly.
Let $\mathbf n$ denote a unit vector, i.e.,...
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Importance of Kronecker product in quantum computation
To get product state of two states $|\phi \rangle$ and $|\psi \rangle$, we use Kronecker product $|\phi \rangle \otimes |\psi \rangle$. Instead of Kronecker product $\otimes$, can we use Cartesian ...
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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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Is there a symmetry associated to the conservation of information?
Conservation of information seems to be a deep physical principle.
For instance, Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory.
We may wonder if there is an underlying ...
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What can the D-Wave quantum computer do?
The media are reporting the commercially sold 128-bit quantum computer from D-Wave
http://news.google.com/news?ned=us&hl=us&q=d-wave+quantum&cf=all&scoring=n
which of course sounds ...
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Canonical examples of quantum channels
I have a conjecture about quantum channels. On which examples should I test it before I try to prove it, ask it on StackExchange, or write a paper about it?
(Note: This is meant to be a reference ...
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What is Quantum Mechanics really about? [duplicate]
This question might sound very silly, so I'm sorry if that's the case. I'll try my best to make my point clear here. Before explaining, just to make clear, I'm not confused because of the Math ...
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Is purification physically meaningful?
Consider a quantum system with Hilbert space $\mathscr{H}$ and suppose the quantum state is specified by a density operator $\rho$. Since it is Hermitian, it has a spectral decomposition: $$\rho = \...
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How are qubits better than classical bit if they collapse to a classical state after measurement?
Classical computers store information in bits, which can either be $0$ or $1$, but, in a quantum computer, the qubit can store $0$, $1$ or a state that is the superposition of these two states. Now, ...
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What is coherence in quantum mechanics?
What are coherence and quantum entanglement? Does it mean that two particles are the same?
I read this in a book called Physics of the Impossible by Michio Kaku. He says that two particles behave in ...
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What is the Wigner function of $|n\rangle\langle m|$?
I have been searching in the literature for the Wigner function of $|n \rangle \langle m|$. For $n=m$ it can be found in page 120 of Barnett and Radmore's Methods in Theoretical Quantum Optics and it ...
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How is CNOT operation realized physically?
I think I understood very well how operations on one qubit are done - if qubit is electron, we just apply magnetic field in direction we want to make spin precess (unitary operations on single qubit).
...
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Seemingly a paradox on the eigenstate thermalization hypothesis (ETH)
In the research field of Many-body Localization (MBL), people are always talking about the eigenstate thermalization hypothesis (ETH). ETH asserts that for a isolated quantum system, all many-body ...
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How to connect these two formulations regarding the need for a density matrix in quantum mechanics?
I found these two formulations:
The density matrix is:
1) "needed if we consider a system that is part of a larger closed system."
2) "needed for a system to be in a statistical ensemble of ...
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What is the relation between linear purity and von Neumann entropy of a state?
Given a density matrix $\rho$, its linear purity is $\mathrm{Tr} \rho^2$, its von Neumann entropy is $-\mathrm{Tr} \rho \log \rho$. Knowing one how do I calculate the other?
Edit:
My thought is ...
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Delayed Choice Quantum Eraser without retrocausality?
After reviewing the more than half dozen questions on the DCQE here, this doesn't seem to have been asked or answered directly - if I've missed this piece in one of the other questions or answers ...
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What's the intuition behind the Choi-Jamiolkowski isomorphism?
What is the intuition behind the Choi-Jamiolkowski isomorphism? It says that with every superoperator $\mathbb{E}$ we can associate a state given by a density matrix
$$ J(\mathbb{E}) = (\mathbb{E} \...
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How do we know quantum entanglement works no matter the distance?
It is said quantum entanglement works regardless of distance. 2 particles can be entangled and information is shared instantaneously, even if they are lightyears away from each other.
But how do we ...
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Ignorance in statistical mechanics
Consider this penny on my desc. It is a particular piece of metal,
well described by statistical mechanics, which assigns to it a state,
namely the density matrix $\rho_0=\frac{1}{Z}e^{-\beta H}$ (...
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What is a completely positive map *physically*?
This can be considered as a continuation of this question.
What does it mean to be a completely positive map, from a Physics point of view?
A positive map $h:\mathcal{B(H)}\rightarrow\mathcal{B(K)}$ ...
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Do Category Theory and/or Quantum Logic add value in physics?
I know they have their adherents, but do more or less esoteric branches of mathematics such as Category Theory and/or Quantum Logic provide powerful tools for new theory development or are they just ...
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How is conditional probability handled in quantum mechanics?
In ordinary probability theory the conditional probability/likelihood is defined in terms of the joint and marginal likelihoods. Specifically, if the joint probability of two variables is $\mathcal{L}(...
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