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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Second order quantum coherence function

I have one question from the course of quantum optics. In general the second order quantum coherence in time is defined as, $$g^{(2)}(\tau)=\frac{\left\langle E^{(-)}(t)E^{(-)}(t+\tau)E^{(+)}(t+\tau)...
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Tensor product of Hadamard operators

The Hadamard Operator on one qubit is: \begin{align*} H = \tfrac{1}{\sqrt{2}}\left[\,\left(\color{darkgreen}{|0\rangle + |1\rangle}\right)\color{darkblue}{\langle 0|}+\left(\color{darkgreen}{|0\...
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Hamiltonian of a quantum harmonic oscillator

On page 286-287 of Nielsen Chuang's Quantum Information and Quantum Computation (10th edition) book, the Hamiltonian for a quantum harmonic oscillator is approximated as $H=a^\dagger a.$ What are the ...
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Why doesn't the quantum eraser violate the no-deletion theorem?

In the quantum eraser experiment and its variants, you basically have a double slit experiment, where you detect which slit the photon went through, but then forget this information. My question is, ...
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Atomic system satisfying a simple level scheme

I have a simple two level system with an allowed dipole transition between the levels. The top level is also allowed to decay to another third level (looks a bit like a lambda system). Could someone ...
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How do we imagine a Hadamard gate acting on the Bloch Sphere? [closed]

We can rewrite the Hadamard gate as $R_x(-\pi/2)R_z(-\pi/2)R_x(-\pi/2)$. I am trying to visualize the effect of applying the Hadamard gate to $|+\rangle$ on the Bloch sphere. The X gate takes $|+\...
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Can Quantum Measurement Be Detected After The Fact?

My question is simple and has a crude drawing associated with it. I was watching some videos of the quantum erasure experiments and being a computer scientist have researched quantum encryption (...
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Proof of Uhlmann Theorem [closed]

In p228, Chapter 9 of Mark Wilde's text , in the course of proving Uhlmann's theorem for quantum fidelity, it claims $$\sum_{i,j} <i|^R <i|^A (U^R \otimes (\sqrt{\rho}\sqrt{\sigma})^A) |j>^R |...
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Quantum circuit and Witness preserving amplification for QMA

My question is about the witness preserving amplification scheme for QMA proposed by Marriott and Watrous in 2005 (see http://arxiv.org/abs/cs/0506068 and http://www.cims.nyu.edu/~regev/teaching/...
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How to understand the relationship between these two geometrical structures?

During my study of quantum information processing, I occasionally meet two different geometrical structures: (a) The geometry of the Hilbert space of quantum state, where the superposition and ...
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Is it possible to make a state tomography of an entangled state only by measurements on subsystems?

As far as I can understand, to make a state tomography of a composite system, a properly selected set of joint measurements should be carried out on the composite system to estimate the density matrix ...
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How to understand the measurement on entangled state in the following cases? [closed]

Assuming an EPR pair AB, event MA is a measurement on A. My questions are: (1) At MB and MB' (depending on where B is located), if we try to describe the state of B (but not measure B yet), what'...
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What is entanglement entropy? and all those stories about counting [closed]

In Quantum mechanics entanglement is a concept that informs us about nature of states. It is a statement about non-product states, thus correlations. This is my rather foolish view of entanglement(...
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Quantum algorithm for checking if element exists

I am currently having hard times while facing an interesting idea, which could speed up many present quantum algorithms, but I am not sure whether my thought is not misleading, or more precisely, ...
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What's wrong with my Quantum Early Warning System (Thought Experiment) [closed]

I'm a lay physics enthusiast and I came up with a thought experiment that I can't fully wrap my head around: Alice and Bob are worried about an impending attack by the dreaded Xenomorphs, so they ...
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are there known fundamental limits of quantum computer scaling?

Quantum computers provide exponential speedup relative to classical computers. However, it is empirical fact that increasing of number of qubits makes the the computer harder and harder to keep ...
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Deriving a POVM from a projective measurement

I understand how to show that every POVM is equivalent to a projective measurement on a larger Hilbert space, but I don't understand why the converse is true. The vast majority of explanations of ...
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Which information is “destroyed” when a qubit is read?

A quantum bit is a unit vector in $C^2$. That is, a four dimensional unit vector. A computational basis is a pair of orthogonal vectors in $C^2$ that you choose - say, [0, 1] and [1, 0]. So the ...
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What is $\gamma$ in the qutrit?

We know that the qubit is defined as follows $$\lvert\psi\rangle = \alpha\lvert 0\rangle + \beta\lvert 1\rangle$$ where $\alpha, \beta \in \mathbb{C}$. We can also rewrite the state of the qubit using ...
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The black hole paradox

I recently read in the news that Stephen Hawking claims to have solved the Black Hole Information paradox. I researched a bit about the paradox and the research that Stephen Hawking did to solve it. ...
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Is in all 'superluminal signaling' setups, entanglement involved? [closed]

Nonlinear extension of QM may lead to the 'superluminal signaling' so that it seems to violate the finite speed limit. I am wondering if it's true that in all such kind of 'superluminal' setups, ...
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Why can you only measure velocity or location in a particle?

I was talking to a family friend in the field of optics at a quantum scale (not sure the proper name for this) and he was explaining to me why you can only determine either the velocity or location of ...
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183 views

Fermi's Golden Rule

Consider a system with countable quantum states. One can define $J_{ij}$ as the rate of transition of probability from i-th to j-th quantum state. In H-theorem, if one assumes both $$ H:=\sum_{i} p_{i}...
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Is density matrix really a description of 'state'? [closed]

Generally a density matrix is in fact a description of a set of equivalent (experimentally indistinguishable in linear QM) states. So there is no 1-to-1 correspondence between density matrix and '...
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What is the Philosophy Behind Relational Quantum Mechanics?

I watched this video on Relational Quantum Mechanics yesterday and my brain has been trying to comprehend it since. The interpretation I currently have is this: If an observer O measures the state S ...
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How to understand the instant state collapse in all references?

When a subsystem A of an EPR pair AB is measured, it's usually said that the state of B collapse instantly, and also this is true for all observers according to relativistic quantum information. ...
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About quantum measurement problem, proper or improper mixture?

Generally a quantum measurement is regarded as resulting in a definite outcome due to "state collapse" and the post-measurement state is described as a proper mixture with the ignorance of the ...
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Quantum Error Correction: Surface code vs. color code

Recently, two groups working on quantum computers published results on quantum error correction. The first was Rainer Blatt's group, who used trapped ions to perform a topologically encoded qubit ...
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Superposition State in Coin Toss

I was reading the following lines from Quantum Computation and Quantum Information by Nielsen and Chuang on page 278 of chapter 7. A coin has two states and makes a good bit but a poor qubit ...
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What does it mean that quantum teleportation can be classically simulated?

Quoting here from Quantum Computation by Nielsen and Chuang : (Gottesman–Knill theorem) Suppose a quantum computation is performed which involves only the following elements: state preparations ...
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How to define a 'clone' of a mixed state?

State clone of a pure state is clear. But how to define a clone of a mixed state? For example, for a proper mixed state A, $\tfrac12(|0\rangle\langle 0|+|1\rangle\langle 1|)$, if there is a clone of ...
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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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In a universe with four spatial dimensions would there be elementary particles with intrinsic isoclinic spin?

Elementary particles have an intrinsic property called spin which is different from classical spin as it does not involve actual rotation and the magnitude of spin cannot be changed but particles with ...
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How much can we compute with one single qubit?

This might be a little stupid question, but I was just talking with some friends who are working in neuroscience and I tried to explain them quantum computing. When I explained them the bloch sphere ...
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Quantum entanglement and superdense encoding etc

Is the following a somewhat correct analogy for what these phenomenae are? Imagine a box of thousands of apples where exactly half of each apple is red and the other half is green. Each apple is ...
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Infinite bits to describe a qubit

In the Quantum Computation book by Nielsen and Chuang, the authors write in the context of quantum teleportation "Even if she (Alice) did know the state |w> , describing it precisely takes an ...
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The role of context in information theory

Consider Hofstaedter’s jukebox analogy: A jukebox that contains only one record, but many different record players, each of which interprets that one record in a different way to produce an entirely ...
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Quantum computing records (entangled qubits)

What is the current record number of entagled qubits and how has this number been increased? The latest result on stack exchange, which is 3 years old, reports 14 via this post: How many stabilised ...
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Quantum information references

I was hoping you guys could recommend reading material on quantum information. First off, here's my background. Personally, I started reading Ballentine's Quantum Mechanics and I found it be a very ...
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Improper integral of the product of exponential function and Laguerre polynomial

I saw this integral in the book [Gerry C.C.,Knight P.L.] Introductory quantum optics: $$\frac{1}{\pi^2}\int_{-\infty}^{\infty}L_n(\lvert\lambda\rvert^2)e^{\lambda^*\alpha-\lambda\alpha^*-\frac{1}{2}\...
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How long does it take to a local perturbation to propagate along a quantum system?

Imagine to have a one-dimensional system in its ground state, and to apply a local perturbation at one edge of the system. How does the system evolve after being perturbed? More specifically, how ...
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What determines the anyon fusion outcome (if several are possible)?

Given the fusion rule (for anyons) "A x B = 1 + C" it is possible for the anyons A and B to fuse to the vacuum "1" or to fuse to the anyon C. What determines what will happen if they fuse? Is the ...
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How to write a noisy state as a separable operator

Bipartite operators close enough to the identity are separable. But how does one compute the product operator terms of the separable expansion? In particular, if $\left| \Phi \right> = m^{-1/2} \...
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The entanglement of a two dimensional particle and the one of two one dimensional particles

Case 1: Usually, entanglement is a correlation between more than one particles. For example, the momentum $p_1$ of the particle $1$ and the one $p_2$ of the particle $2$ have the relation that $p_1 +...
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Quantum Mechanics and Causality

Causality coupled with special relativity states that no particle can travel faster than light. Interpreting in terms of quantum mechanics, it means that dirac delta wave-function at x=a, can't ...
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The minimum time for a quantum state to evolve to an orthogonal state

I'm reading this paper by Margolus and Levitin The maximum speed of dynamical evolution: http://arxiv.org/abs/quant-ph/9710043 about the so called Margolus-Levitin theorem. For the main result, ...
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Is there a theory of reference and formal truth in quantum information theory? [closed]

Is there a theory of reference and formal truth in quantum information theory? I.e. a "quantization" of Frege Tarski or the Typographical Number Theory (TNT) system in "Gödel Escher Bach". Status ...
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How Quantum Fourier Transform equal to Hadamard Transform on 4-by-4 matrix?

I just don't understand why $QFT_4$ become the same as Hadamard Transform $H_4$ The Hadamard matrix is as follwoing, $$ H_2 = \frac12 \begin{pmatrix} 1 & 1 & 1 & 1 \\ 1 & -1 & ...
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How do we take the limit of this quantum operation?

I am wondering how to take the following limit: \begin{align} L= \lim_{\tau \to \infty} \frac{1}{\tau} \int_{-\tau/2}^{\tau/2} dy \, \left(1 - \frac{1}{\sqrt{ \pi} \sigma } \int_{-\tau/2}^{\tau/2}...