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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Mapping a given density matrix to the generalized 2-qubit state

The generalized 2-qubit state is given as: $$ \rho = \frac{1}{4}[ I\otimes I + (m_x\sigma_x + m_y\sigma_y + m_z\sigma_z)\otimes I + I \otimes (n_x\sigma_x + n_y\sigma_y + n_z\sigma_z) + ...
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Quantum Computation

Is there any rule or technique so that one can design quantum gate operator from matrix operator? Suppose, what will be the quantum gate operator for this matrix operator : $$ \left( \begin{array}{c ...
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QFT in Quantum Computing and Control Theory?

Is QFT being applied to quantum computing and control theory? I took yesteryear a basic course on quantum computing and if I remember correctly we didn't touch on any QFT (though I think that if it ...
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379 views

Two Qubit problem

A two-qubit system was originally in the state $ \frac{3}{4}|00\rangle-\frac{\sqrt{5}}{4}|01\rangle+\frac{1}{4}|10\rangle-\frac{1}{4}|11\rangle $ , and then we measured the first qubit to ...
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508 views

How is a Qubit in two states under Superposition?

I have read a little about Quantum computing. From what I understand, Quantum Superposition is when a qubit is in a state $\alpha|0\rangle$ + $\beta|1\rangle$, where $\alpha$ and $\beta$ are ...
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How is it that Quantum entanglement does not let you transmit infomation?

when I was first introduced to entanglement I was told that "it is a phenomena that allows information to be transmitted faster than light", however, as I kept reading up on it, this seemed to be an ...
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87 views

why non orthogonal states are indistinguishable?

I want to know what does it mean by distinguishable quantum state from Mathematics perspective I mean mathematically. As a non physics background student could any one explain me why non orthogonal ...
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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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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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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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111 views

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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196 views

Thermodynamics for Dummies: Entropy and temperature

I do not study physics and I have never had a course in thermodynamics. I have no idea what it is about, but I am currently taking a course where we had something about entropy. Would be great if ...
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100 views

How to derive quantum Fourier transform from discrete Fourier transform (DFT)?

I am interested in Shor's algorithm, and I am reading several papers that related to the quantum Fourier transform (QFT). I know the there is a difference between the output of QFT and DFT (DFT). ...
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135 views

Do generalized Pauli Operators generate SU(n)?

A commonly used generalization of Pauli Operators is the "clock" and "shift" operators summarized here: http://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices Pauli Operators are generators ...
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Physical Interpretation of the Bloch vector

In the expression of the density matrix of a (Electron-Spin) Qubit $$ \rho=\frac{1}{2}(I + x \sigma_x + y \sigma_y + z \sigma_z) $$ where $\tau=(x,y,z)$ is unit vector in the Bloch sphere, which is ...
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Writing down an entanglement in bra-ket notation

I have a relatively complex (for me anyhow) situation which I would like to capture in bra-ket notation, rather than in words. However, I've not been able to find a source which will help me ...
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What does “decompositions of a mixed state” mean?

I came across an expression for Entanglement of formation for a mixed state $$E_F(\rho_{AB}) = \text{min}\sum_i p_i S(\rho^i_B)\leq S(\rho_B)$$ where minimum is taken over all the decompositions of ...
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Practical example of stabilizer codes

Given the Steane code $$ \left|0\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|0000000\right\rangle + \left|1010101\right\rangle + \left|0110011\right\rangle + \left|1100110\right\rangle + ...
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Confusion about a lemma on the time constraint of an adiabatic evolution (arXiv:quant-ph/0604077)

I am going through the paper Quantum adiabatic evolutions that can't be used to design efficient algorithms by Zhaohui Wei and Mingsheng Ying. On the second page they prove a lemma. The statement goes ...
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What are some examples of infinite state quantum mechanical systems that do not involve free particles?

That is, the quanta are in bound states where there are least upper bounds and greatest lower bounds to their energy states but there are at least a countably infinite many energy levels they can ...
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221 views

Why does this state have a Schmidt rank of 1?

A system is entangled if and only if the Schmidt rank is greater than 1. Why does this ...
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407 views

Ising spin vs Pauli spin matrices

Are Ising spins scalar or operators? I am not a condensed matter physicist hence having some confusion. I have learnt about Ising models from adiabatic quantum algorithm papers. For example this ...
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Purpose of Grover's algorithm?

How is the output of Grover's algorithm useful if the result is required to use the oracle? If we already know the desired state, what's the point of using the algorithm? So can you give me a ...
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154 views

Which similar properties must objects have to sustain quantum entanglement?

Quantum entanglement occurs when particles such as photons, electrons, molecules as large as buckyballs, and even small diamonds interact physically and then become separated; the type of ...
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Question on the preservation of information via mapping to free field states

In Hawking's paper, "Breakdown of predictability in gravitational collapse", the crux of Hawking's argument is as follows: ...,one can extend the principle to treatments in which the gravitational ...
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At what time exactly does decoherence happen? and retrodating

Take a qubit initialized to $|0\rangle$. Apply a Hadamard transform to it. Measure it with an apparatus along the $|0\rangle,\, |1\rangle$ basis. If zero, spare a living cat. If 1, kill the cat. ...
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Number of conditions for a two-particle state to be decomposable

Suppose we have a general two-particle state $ \Phi (x_1, x_2 ) = \sum_{n_1,n_2} \phi_{n_1,n_2}(x_1,x_2)|n_1,n_2> $, where $n_1$ can be any of $n$ possible states, and $n_2$ can be any of $m$ ...
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fermions and quantum gates

Say that I have 2 qubits - 2 spin half fermions. my initial condition is $|00\rangle$ in the spin-wave function and some anti-symmetrical spacial wave function. I'm wondering about what happens when ...
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50 views

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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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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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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Maximum density that we can store information

I was informed that: There is a maximum density at which we can store information. For a sphere with surface area A, the maximum information that can be contained within is equivalent to the ...
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Jump Method and the Lindblad Equation

I am studying the time evolution of a density matrix using the Lindblad equation. My initial density matrix is $\rho(0)=|\alpha\rangle\langle\alpha|$, where $|\alpha\rangle$ is a coherent state. Then ...
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Design a quantum circuit from a matrix

I have unitary matrix and I would find the quantum circuit associated. There are 3 qubits input so it's a 8x8 matrix but it's not a simple operation. The number of gates is not specified. Is there a ...
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Quantum Key Distribution (QKD) Upper and Lower Bounds

Many papers on Quantum Key Distribution protocols discuss the protocols upper and lower bounds (on quantum bit error rate QBER). For example, BB84 has a lower bound of 11% and an upper bound of ...
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Info request on studying QIT/QIS or QM with a Computer Science background [closed]

I've been considering a career change for a long time and recently discovered the Two-Slit Experiment, which, to put it frankly, blew my mind. I then started some hefty reading and investigation into ...
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CNOT gate broken in 2 different quantum simulators? Or am I wrong?

My understanding is that the control qubit in a controlled-not gate remains unchanged after the controlled-not operation is performed on a target-qubit (so the Pauli-X gate is performed only on the ...
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Grover algorithm $R_D$ Circuit

I need sketch two circuits to understand Grover algorithm. The first is the operator $R_f$ and another is the operator $R_D = H^{\otimes n}(2|0\rangle\langle0|-I)H^{\otimes n}$. I get the first ...
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160 views

2 following gates, permutation matrix

I have a circuit that has 4 wires and 2 following each other Toffoli gates. I have permutation matrix for each Toffoli gate (A and B). Do I have to multiply that 2 matrices to get the entire ...
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Quantum Circuit, example of the Bernstein-Vazirani problem

This question is regarding the quantum circuit in the picture below. Suppose we have the set up below, where U performs the operation $U:\mid x \rangle \mid y \rangle \rightarrow \mid x \rangle\mid y ...
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Using wavepackets instead of photons in quantum computer

Why does a photonic quantum computer require photons? Why wouldn't wave packets work just as well, better in fact since it would get away from the use of fragile single photons? (Article)
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OAM states for wireless communications

Can someone give me an overview of how OAM states are used in communications? Using Orbital Angular Momentum States seems like a hot topic for communications. I read a few articles about the basic ...
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Can double entanglement preserve correlations?

We have 2 EPR experiments running in parallel, with Alice having one leg of each (a1,a2) and Bob the other leg of each (b1,b2). Thus (a1,b1) are anticorrelated, as are (a2,b2). Thus also (a1,a2) are ...
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What is the difference between quantum cryptography and quantum teleportation?

Generate two entangled photons, send one to a message sender and the other to the intended receiver. Both the sender and the receiver recover the same piece of quantum information from the photons, ...
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How to deterministically distinguish the following quantum states?

(1) How to deterministically distinguish the following quantum states: $$\frac{1}{\sqrt{2}}[|+0\rangle|0\rangle+|-1\rangle|1\rangle$$, $$\frac{1}{\sqrt{2}}|-0\rangle|0\rangle+|+1\rangle|1\rangle$$, ...
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Entanglement and conservation

Is the following assertion sufficiently unique to merit a paper? Every absolute conservation law implies a corresponding form of entanglement, not just spin (angular momentum). Linear momentum ...
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Quantum Coin Flipping Protocol

$\newcommand{\ket}[1]{\left|#1\right>}$ I have the next protocol: $A$ tosses a fair coin $a\in \{0,1\}$, if $a=0$, $A$ sends to $B$ $\ket{\psi_0}=\ket0$, if $a=1$ $A$ sends to $B$, ...
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Second Qubit Not Flipped in Hadamard Gate

I'm very new to QM and Quantum Computing and I have a likely simple question, It may simply stem from my lack of knowledge of vector calculus. We have a 2-qubit quantum state: $$ \mid\psi\rangle = ...
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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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Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...