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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Quantum computing, NP complexity [closed]

Hi I have a very limited knowledge of quantum physics and its bothering me trying to understand quantum computing. I want understand how a qubit can return usable data faster then a regular bit, how ...
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Quantum computing with biological matter? [closed]

As a biologist with physics background I wonder whether there is a way to use biological matter to create quantum computers or at least to advance the field somewhat. Usually, my first feeling would ...
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Understanding the delayed choice quantum eraser from a quantum information stand point

A continuation of Understanding the quantum eraser from a quantum information stand point What quantum circuit would correspond to delayed choice? In particular, the decision of whether to not to ...
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Entanglement, superposition, and propositional logic [duplicate]

From what I am understanding, there is entanglement in a system if there is a correlation between elements of that system. For an example that I found, If you have only two cards and know that one is ...
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Understanding the quantum eraser from a quantum information stand point

Is there a way to understand the quantum eraser experiment in terms of quantum information? In particular, is there a quantum circuit that would function as a quantum eraser experiment? The issue I'm ...
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Approximate cloning of a qubit, given multiple starting copies

Suppose I'm given several clones of a qubit in a pure unentangled state. That is to say, I'm given the state $(a \left|0\right\rangle + b \left|1\right\rangle)^{\otimes n}$. My goal is to make $d$ ...
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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 ...
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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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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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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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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 ...
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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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A question about the universal quantum cloning machine (UQCM)

In the recent paper Replicating the benefits of Deutschian closed timelike curves without breaking causality, a quantum state cloner based on open timelike curve (OTC) was mentioned. There to clone ...
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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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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 ...
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293 views

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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92 views

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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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), ...
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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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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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164 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} ...
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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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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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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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are locally unique pure quantum states also ground states of some local hamiltonian?

Let $H=\sum_i H_i$ be some k-local hamiltonian with a unique ground state $|\psi>$. Then it is easily shown that $|\psi>$ is k-locally distinguishable from any other state $|\psi'>$. Is the ...
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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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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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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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The minimal knowledge required for theoretical research in Quantum computing & AMO physics

I'm a senior undergraduate student and I have chosen my future Ph.D research area in {Quantum Computing}$\bigcap${AMO physics} (e.g. design a new experimental realization of QC or propose a new way to ...
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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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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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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: ...
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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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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 ...
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Difference between DMRG (density matrix renomalization group) and MPS (matrix product states)?

I am learning DMRG recently. I noticed there are many papers both in the DMRG approach and MPS (such as variational matrix product state (VMPS) by F.Verstraete and J.I.Cirac) approach. In my eyes, ...
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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 } ...
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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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Bloch sphere for more than 1 qubit [closed]

Of course in general the Bloch sphere is a representation for one qubit, but what if it's a higher-dimensional system which has only two eigenvectors with non-zero eigenvalues? You should be able to ...
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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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What do quantum theory and general relativity have in common? [closed]

What areas of commonality are there between quantum theory and general relativity? Is it even possible to use the the two when calculating the same physical behaviour? Is there a correlation between ...
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How does one compute the state of a quantum system following imperfect measurement?

Suppose I have a quantum system $S$ ("system") with Hamiltonian $H_S$ and initial density matrix $\rho_S(0)$. I allow $S$ to interact with another system $P$ ("probe"), which has Hamiltonian $H_P$ and ...
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Which is a good and short book for foundations of quantum mechanics? [duplicate]

I am looking for a book that has stuff on quantum states, entanglement, etc. I am aware of the book, Geometry of Quantum States. I have read Ballentine's book, Quantum Mechanics: A modern development ...
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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 ...