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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Intuition on positive-operator valued measures (POVM)

I'm having a little trouble understanding what positive-operator valued measure (POVM) are- in particular why/how they are non-negative. For instance, if they just represent measurements, what about ...
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Split property for type III algebras entails practical separability

I am reading Halvorson's thesis (http://philsci-archive.pitt.edu/346/1/main-new.pdf), however I don't understand a proof at p.50 where he tries to explain why the split property allows a local agent ...
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Eigenvalue of the adiabatic Hamiltonian of Farhi's three qubit 2-SAT problem

I was trying to reproduce example 3.3 of Quantum Computation by Adiabatic Evolution by Edward Farhi et. al. This is an adiabatic algorithm to solve an instance of three qubits 2-SAT problem. I think ...
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Dimension of separable state

Please can you help me to understand how the dimension of the set of separable states is $\dim \cal H_1 + \dim \cal H_2$? This is the relevant passage: So far, we have assumed implicitly that the ...
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What are the “other” Hadamard matrices?

The Pauli matrices $$ X = \begin{pmatrix}0&1\\1&0\end{pmatrix}, Y=\begin{pmatrix}0&-i\\i &0\end{pmatrix},\,\text{and}\, Z=\begin{pmatrix}1&0\\0&-1\end{pmatrix} $$ can be used ...
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Information retrieval from a database

Consider a database $\cal D$ containing $N$ entries $A_0, A_1, ... A_{N-1}$, which are some fixed and unknown strings of $k$ bits; you can access this database sending a coherent superposition of ...
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142 views

What is a good book for quantum mechanics and quantum computation? [duplicate]

I am looking for a book in quantum computers for self-learning.The kind of book that teaches quantum-mechanics + quantum-computation. I have basic understanding in calculus , linear-algebra (like ...
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264 views

Dicke states, spin squeezing and quantum metrology

Dicke states are by definition simultaneous eigenstates of the $J_z$ and $J^2$ operator. What is the difference between these states and Dicke squeezed (DS) states? I know that these are "entangled" ...
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If distant observers never see a black hole form in finite time how can the information paradox be a problem?

So, at least as reported in the media, the physics community is still struggling with the problem of resolving the impossibility of retrieving information from beyond the event horizon of a black hole ...
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characterization of non-entangling gates

I suspect the following is true and "well-known" but I cannot find any reference for it. Can anyone help? Let $U$ be a unitary quantum gate acting on a pair of $d$-dimensional qudits. Suppose $U$ is ...
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If two quantum two-party states have the same entanglement, can they be transformed into each other by local unitary operation?

We know that local unitary operations will not change entanglement. But if two party state have the same entanglement in some measure, can they be related with local unitary operation?
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Is this theory about Universe and information true?

I recently saw this video about information and randomness. At some point, it states that a completely predictable universe would infringe the second law of thermodynamics, because it would imply that ...
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169 views

Simple Mach-Zehnder Interferometer with Polarizing Beam Splitters

I am wondering which state leaves the simple interferometer below. The beam splitters are polarizing beam splitters (PBS) which transmit vertical polarization and reflect horizontal polarization. Say ...
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Density matrix formalism and group representation

The postulates of quantum theory can be given in the density matrix formalism. States correspond to positive trace class operators with trace 1 on a Hilbert space $\mathcal{H}$. Composition is defined ...
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338 views

Measuring non-commuting observable at once

Given an Hilbert space $H$ (finite dimensional for sake of clarity), and two non-commuting operators $$A = \sum_a a |a\rangle\langle a|$$ and $$B=\sum_a b |b\rangle\langle b|,$$ is it possible to find ...
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Reduce density matrix for given eigenfunction [closed]

My question is about how to find reduce density matrix for partition of given eigenfunction. Full question is just in image.
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Can quantum vacuum carry entropy?

So, we know that the state of quantum vacuum does carry energy, as it was measured in the Casimir effect. This energy comes from particles almost instantaneous creation and annihilation. Even if they ...
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How to calculate resources taken up in quantum computation

Suppose I have $n$ qubits namely $\{|\psi_{1}\rangle,|\psi_{2}\rangle.....|\psi_{n}\rangle\}$. I apply a series of unitary operations $U_{1},U_{2}...U_{n}$ (applied in order) to these qubits. Each ...
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Time and particles [closed]

What it is in basic particles that make them propagate themselves through time or, basically, what brings that property known as Duration in a particle (wave)? I sense that this is somehow is based ...
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What kind of transformation can be applied to qubits?

I have a doubt on what kind of transformations can be applied to qubits. I understand that the transformations need to be reversible , but they also have to preserve the norm: that's why the ...
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QM interpretations

I don't fully appreciate what the discovery of the decoherence phenomenon adds to the Copenaghen interpretation of QM. I will be more precise: the Copenaghen interpretation, if I am not wrong, is ...
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1answer
123 views

How can I solve an equation involving partial trace?

I am unable to find the solution to the following equation: Tr$_{2}[U(|\psi\rangle \langle\psi|\otimes \rho)U^{\dagger}]=\rho$ Here $\psi$ is state vector representing a qubit and $\rho$ state of ...
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Proof involving tensor product

I am trying to prove when the following holds: $$|a\rangle |b\rangle \langle c|\langle d| = |a\rangle \langle c| \otimes |b\rangle \langle d|$$ where $\otimes$ stands for tensor product and the ...
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Can an arrangement of particles be duplicated precisly?

Is it possible to teleport or clone someone or something? After watching this TED talk by Max Tegmark - https://www.youtube.com/watch?v=GzCvlFRISIM I find myself wondering if it is then possible to ...
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Is the spin and charge of an atom a quantum or classical concept?

I have no idea whether these properties of an atom fall under quantum or classical physics, or perhaps both. Some clarification would be helpful.
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A question on partial trace and density matrix computation

Consider a Pure state of a two dimensional system $|\psi\rangle={1\over\sqrt{2}}(|e_1\rangle|e_1\rangle+|e_2\rangle|e_2\rangle)$ where $\{|e_i\rangle\}$ is an orthonormal basis. Could any one just ...
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A machine which copies any object with 100% accuracy?

Does physics allow for a machine that copies an object with 100% accuracy?
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Is there a way to obtain an RG flow equation for Quantum spin systems using MERA

We restrict ourselves to ground states of translationally invariant 1d quantum systems. I understand that there is the scale invariant MERA(multiscale entanglement renormalization ansatz) which ...
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Does quantum collapse involve a loss of information? Does it require energy as suggested by the Landauer Limit?

I read in the context of quantum computing or of the minimal energy required for computation that there has to be a minimum possible amount of energy required to change one bit of information, called ...
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Projection of Quantum State onto Bell State

I am very interested by this paper on entanglement swapping and timelike entanglement. The one thing I get really tripped up with is the whole idea of a projection onto a bell basis. I understand ...
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Computer game with quantum optics/ information

Is there a computer game using principles of quantum optics or quantum information? By game I don't mean just a simulation or an interactive course, but something that can be played in an enjoyable ...
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Why is optical orbital angular momentum (OAM) called “topological charge”?

The terminology "topological charge" is frequent in lots of research papers related to optical vortex or optical OAM, it is used to represent the optical OAM. Why? How to comprehend it?
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Joint-measure of POVM's

I feel disturbed by this question: Suppose $A$ and $B$ are POVM's with respective $\sigma$-algebras $\mathcal{F}_A$ and $\mathcal{F}_B$ and outcome spaces $\Omega_A$ and $\Omega_B$. Then why can't I ...
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What would happen when a material with Inhomogeneously broadened profile interacts with a light beam?

I have something which I am sure that I understand it correctly. Would you please told me if I explain this correctly or not. Sorry in advance for my English. When a light beam interacts with an ...
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How many states are there in the observable universe

If we took a single instant and considered all possible states of all energy and matter do we have any bounds on how much that would be? Would that number be related to information?
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Compatibility of effects implies compatibility of POVM's?

Let $A = \{A_1 ,\ldots , A_n\}$ and $B = \{B_1 \ldots , B_n\}$ be two POVM's. Suppose every pair $(A_1, B_1)$ is jointly measurable as a couple of effects. Does this imply the joint-measurability of ...
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Does all information in the universe come from the observer?

In absence of the observer any system undergoes unitary evolution, that is reversible evolution without entropy change. It is believed that the initial state of the universe had very low entropy, ...
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Numerical Computation of Linbald Equation [closed]

Can anybody suggest me a good algorithm for the time evolution of the reduced density matrix using Linbald equation. My Hamiltonian is time dependent. I am aware about Qotoolbox and Qutip. I have ...
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Why can't classical information be transmitted through quantum entanglement by measuring time between change events? [duplicate]

If the effect of measurement in quantum entanglement occurs instantaneously why can't it be used to transmit classical information faster than light? I'm based my question off this seemingly well ...
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Quantum Entanglement and BB84 protocol

Can Quantum entanglement can be used to strengthen the security or increase the efficiency of communication via the BB84 protocol? If so, how?
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Why does quantum cryptography give us uncrackable codes?

Why does quantum cryptography give us uncrackable codes? What makes it 'uncrackable'? Articles in for example pop science magazines always claim QC produces uncrackable coded, however I highly doubt ...
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Increase path length for a photon with two mirrors vs optical fiber

Is it possible to build two mirrors in vacuum such that a light pulse (single photon) gets refleted many times in order to increase the distance it travels? For example like that? Say I want the ...
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Inner products containing the tensor product of two operators

The book Nielsen & Chuang "Quantum Computation and Quantum Information" presents the concept of tensor products as follows. Suppose we have the vectors $|v\rangle$ and $|w\rangle$ which exist in ...
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Quantum computing and ambiguity

I do a bit of hobby programming and I often search the internet for little oddities that are fun to ponder over. I have read a few passages that try to explain quantum computing to the layman like ...
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How can I actually use the BB84 protocol?

I have read how the BB84 protocol could work. However, I couldn't see a way to implement it in the laboratory, so that I could make a demonstration in the university's quantum optics laboratory. ...
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Is the subadditivity of quantum entropy valid in the infinite-dimensional case?

Does the subadditivity (and strong subadditivity) of quantum entropy hold for infinite dimensional quantum systems as well? Unfortunately the books in my hand give proof for finite dimensional cases ...
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Entanglement in single particle state

Is it possible that we have entanglement in different degrees of freedom of a singe particle. like spin and linear momentum .
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Detect missing frequencies in a frequency distribution

I have photons with a frequency distribution where one frequency is completly cut out. For example a frequency distribution like that: My question is: How precise can the position (frequency) of ...
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Finding the stabilizer group given a state

Consider general pure state $|\psi\rangle$ in some hilbert space $\mathcal{H}$ (which could be a tensor product of other Hilbert spaces) I would like to know whether there is a way to ...
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The DLCZ Protocol

I have been reading the article review for Optical Quantum Memory (http://arxiv.org/abs/1002.4659) when I came across this section about DLCZ protocol. I don't understand about Beam splitter. For what ...