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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Partial measurement (destructive) collapses |1> to |0>

In the following QScript program: ...
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How to prove that the ground state of the Hubbard model is not a Slater determinant?

Of course it is expected. But how to prove it analytically? Slater determinant is mentioned in almost every quantum mechanics textbook. But it is necessary to warn the undergraduate students that not ...
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Can the new results (about photonic time travel) make quantum computers feasible?

New results published about photonic time travel, reference here make quantum computers a reality in the near future? These results seem to indicate that there can be qubits that can exhibit nonlinear ...
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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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Subgroups of the Clifford Group

We recall the definition of a Clifford group (over $n$ qubits) is the set of unitary transformations: $$\{U: UPU^\dagger\in\mathcal{P}\}$$ where $\mathcal{P}$ denotes the corresponding Pauli group (...
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316 views

Can we use quantum entanglement as a way to send information or data? [duplicate]

Can we use entangled particles to transmit information or data such as TCP/UDP packets? If so why hasn't this been done yet? Surely the costs of bringing this to market are much cheaper than laying ...
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Bloch Sphere and $SU(2) \to SO(3)$ map

For any matrix $U \in SU(2)$ there is an associated map from $S^2$ (the surface of a 3-disk) to itself defined by $\pi \circ U$, where $\pi$ is the projection map from $\mathbb{C}^2$ to $CP(1)$, that ...
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I would like to ask any interested reader about “Quantum Bidding in Bridge”

see http://journals.aps.org/prx/pdf/10.1103/PhysRevX.4.021047 I would like to see how specific examples are worked out. Specifically, details on how the quantum protocol in figure 1. of the above ...
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203 views

Number of Parameters Required to Specify n-Qubit States and Quantum Operations

How many parameters are required to specify the density matrix of a $n$-qubit system, and how many parameters are required to specify a quantum operation (completely positive maps between states) on ...
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Universality of Quantum Operations

Does an analog of the Solovay-Kitaev theorem exist for quantum operations, a generalization of quantum gates that also includes all completely positive maps?
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Most natural tensor structure for a quantum field

A quantum field is described by a Hilbert space. In many instances, the chosen tensor structure on this Hilbert space corresponds to that of space-like separated regions of space-time. The ...
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Thermodynamics of binary symmetric channels

I am reading this very interesting paper: http://m.iopscience.iop.org/1751-8121/41/40/402002/pdf/1751-8121_41_40_402002.pdf about thermodynamics of channels in information theory. More generally, ...
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What are the requirements on conditional unitaries for overcomplete bases?

On way to describe "pure" decoherence (that is, decoherence with respect to a basis that doesn't involve transitions between basis states) between a system $\mathcal{S}$ and an environment $\mathcal{E}...
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Coarse-graining on a second channel decreases mutual information?

Let $X_1,B_1,X_2,B_2$ and $Y_1,A_1,Y_2,A_2$ and $C_1$ and $C_2$ be binary random variables. Suppose: $I(X_2:B_2|C_2=0)+I(Y_2:A_2|C_2=1) \leq 1$. This can be thought of as a bound on the capacity ...
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69 views

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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312 views

Stimulated emission and No cloning theorem

I have a little trouble with the simulated emission. I know of the no-cloning theorem which states that it is not possible to duplicate any state. One the other hand, I know about the stimulated ...
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What are the prerequisites to study topological quantum computation/topological phases of the matter? [closed]

I am an undergraduate student and I would like to approach the subject of topological order with focus on topological quantum computation, I know (very) little QFT and basic algebraic topology (if ...
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Solution of dynamics of density matrix

Given the dynamics of the density matrix: $ \frac{d}{d t}\begin{pmatrix} \rho_{00} & \rho_{01} \\ \rho_{10} & \rho_{11} \end{pmatrix} = \begin{pmatrix} \lambda i(\rho_{10}-\rho_{01})+\lambda^...
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Alice sends random states in a channel, what Bob receives?

Suppose Alice prepares $\rho_x$ with probabilities $p_x$ and sends it to Bob. I would say this is the same thing as "Alice prepares $\rho = \sum_x p_x \rho_x$ and sends it to Bob", but Preskill's ...
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Meaning of the Reduced Density Operator

I am confused about what it is exactly that a reduced density operator describes. To illustrate, I came across the following seemingly paradoxical argument. Consider a bipartite system $AB$, ...
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101 views

Continuous Variable Entanglement Measure for the Statistically Mixed State

Can anybody tell me, which is the best entanglement measure for the Continuous Variable Entanglement of a Statistically Mixed State ? I have read that Schmidt decomposition is not valid in this ...
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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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If the discretized $x$ and $p$ are conjugate variables, why are there two $U$s in $U_{FFT}xU_{FFT}^{\dagger}=p $?

While studying some quantum mechanics from Nielsen's book on quantum computing, specifically the simulation of the single-particle Schrödinger equation using a quantum computer, I came across ...
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Density matrix as a simple state

I computed eigenvalues and eigenvectors of a density matrix for state $a|0\rangle+b|1\rangle$. For eigenvalue $0$ for example, I obtain an eigenvector $(-b^*/a^*, 1)$ before normalization. Now I would ...
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Entangled event horizons

Assuming it is possible in principle to entangle the degrees of freedom of the event horizons of two black holes, and that this is something that can be done, either after the black hole is formed, or ...
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Does squeezing a vacuum state produces photons?

A squeezed vacuum state is produced by applying a squeezing operator $S$ on the vacuum state $|0 \rangle$: \begin{eqnarray} S | 0 \rangle = \sum_n C_n |n \rangle \end{eqnarray} My question is, from $...
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Estimating quantum efficiency of gated avalanche photodiode

I have a photon counting system that uses a gated avalanche diode to detect single photons. The repetition frequency of the gates is $f_1$ and the temporal gate width is $\tau_1$ (so the duty cycle is ...
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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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Heisenberg XXX time evolution operator for three qubits

I've a problem to reproduce the result in equation (4) on page three of this paper: http://arxiv.org/abs/0802.2588. So far I've understood that they apply a Heisenberg XXX interaction between 2&4,...
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330 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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269 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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Why do we need non-trivial fibrations?

I am currently reading this paper. I understand how the Bloch sphere $S^2$ is presented as a geometric representation of the observables of a two-state system: $$ \alpha |0\rangle + \beta |1\rangle \...
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Can matter be converted to information?

I know that matter can be converted to energy through E=mc^2. I also know that engery can be and has been converted to information through Landauer's principle (with Maxwell's demons). Does this ...
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How do I simulate this simple quantum circuit in MATLAB

I want to simulate a circuit similar to the one below in MATLAB. If you have a state matrix describing the state of 3 qubits, I understand that you could apply a CNOT matrix tensored with and identity ...
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Why is this entangled?

I am studying a book of quantum computing and the author gives an example of a four qubits separable! He writes: Let $\left|ψ\right> = \frac 1 2(\left|00\right> + \left|11\right> + \...
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Off-diagonal terms of the Husimi $Q$ function?

The Husimi $Q$ function of a quantum state $\rho $ is defined as $ Q (\alpha)=\langle \alpha \vert \rho \vert \alpha \rangle $, where $\alpha = (x, p) $ is a phase space coordinate and $\vert \alpha \...
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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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Entropy of Reeh-Schlieder correlations

Any state analytic in energy (which includes most physical states since they have bounded energy) contains non-local correlations described by the Reeh-Schlieder theorem in AQFT. It is further shown ...
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Proving two forms of atom-field interaction perturbation Hamiltonian are equivalent

In the presence of an electromagnetic field in the dipole-approximation (${\boldsymbol A} = {\boldsymbol A}(0,t)$) we have the two forms $$H_{{\boldsymbol d}\cdot {\boldsymbol E}} = - q {\boldsymbol ...
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Projection operators and their subspaces (of Hilbert space)

I've been watching Susskind's lectures on Quantum Entanglement, and something he said regarding (non-)commuting projection operators confused me. Consider two subspaces {$|a>$} and {$|b>$} of ...
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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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Significance of 'chiral' form for a qubit?

Say I have a qubit with probability amplitude divided evenly among $|0\rangle$ and $|1\rangle$ $$\frac{1}{\sqrt 2}|0\rangle + \frac{1}{\sqrt 2}|1\rangle$$ So it seems that we have a, loosely speaking,...
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Trace in non-orthogonal basis?

Physicists define the trace of an operator $\rho$ as the follows, $Tr(\rho)=\sum\limits_{|s\rangle \in B} \langle s| \rho |s\rangle$ where B is some orthonormal basis, and this quantity is ...
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Quantum Fourier Transform and Entropy

QFT is a nonlocal unitary transformation and so can generate entanglement in a system. It means a separable pure state can be converted into an entangled pure state. Now since the presence of ...
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Understanding of measurement in quantum mechanics?

I have a computer science background with basically zero physics background. I am trying to gain a 'high-level' understanding of quantum mechanics to aid me in some computer science work. Is my ...
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Entanglement entropy and area law

I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: In one dimension, for local gapped models, we have an area law ...
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Bragg's diffraction and Simon's problem

In Preskill's notes, John Preskill goes as If we scatter a photon off of a periodic array of needles , the photon is likely to be scattered in one of a set of preferred directions , where the ...
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Deriving Rabi rotation matrix

I want to understand where the matrix: $$ \left|\psi(t)\right> = \binom{a(t)}{b(t)} = \begin{bmatrix} cos(\Omega t/2)&-ie^{i\phi_L t}sin(\Omega t/2) \\ -ie^{-i\phi_L t}sin(\Omega t/2) & ...
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Advantage of taking qutrits in place of qubits

In general, all the quantum algorithms which I have read so far use qubits (so the space is $\mathbb{C}^2$) and the tensor products of the qubit spaces (space is ${\mathbb{C}^2}^{\otimes n}$). So my ...
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Physically realizable quantum circuits

How do we decide whether a quantum circuit can be realized physically or not ? I was wondering for physical realization of Shor's factoring algorithm using NMR ( I mean can we do it? ).