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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About Shor's error correcting algorithm

In this paper, http://arxiv.org/abs/1301.4504 in equation 4.1 in what sense are the two states a "9-qubit state"? I did not understand this counting. Can someone explain what are the different $X_i$ ...
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What is “code” in “toric code”?

When I first heard people talking about using Kitaev's toric code to do topological quantum computation, I was thinking how many lines does the toric code have. Then I was told that the "code" really ...
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Thought experiment using quantum entanglement in position and its effects

Consider we have two atoms $a$ and $b$. They are entangled with each other in position and momentum, with some wavefuction describing them in position space that is $\Psi(x_a, x_b)$. This ...
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Is this theory about Universe 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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About the Hayden-Preskill circuit

Can someone summarize as to what are the problems and/or the open questions with the Hayden-Preskill circuit? (in the context of understanding black-holes or as a computer science question)It gives a ...
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What is the current state of research about the Hayden-Preskill circuit? [duplicate]

Can someone summarize as to what are the problems and/or the open questions with the Hayden-Preskill circuit? (in the context of understanding black-holes or as a computer science question)It gives a ...
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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 is Getting in the Way of Testing D-Wave?

I know there are other questions i.e. Do quantum computers manufactured by D-Wave Systems, Inc. work? , What can the D-Wave quantum computer do? , etc. But I can't seem to find my answer. What is ...
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Ising formulation of the graph isomorphism problem

Context I have been going through Ising formulations of many NP problems by Andrew Lucas. In section 9 on page 22, the author gave an Ising formulation of the graph isomorphism problem. Here I ...
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Can you read and write a quantum state to a particle without collapsing its probability field?

I know the main problem with a quantum computer is that you can't read and write data from it until after it has run though all of its calculations. But would reading and writing quantum data to ...
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Ultrafast photon detectors

Are there already photon detectors that can resolve the shape of photons in the time domaine if it looks like below where the two humps are separated by a time of the order of femtoseconds? What I ...
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If I have created a polarization-entangled photon source, would I be able to create a qubit?

In my laboratory, I have already obtained a polarization-entangled photon source. It was created via the Spontaneous Parametric Downconversion process of 2 BBO crystals. The next question is that ...
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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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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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preparing qutrit mixed state

I have a problem: Ok so I want to create a superposition qutrit state, like this: $$ |\Psi\rangle=\frac{1}{\sqrt{3}}(|0\rangle+|1\rangle+|-1\rangle) $$ is it possible to go there, starting with an ...
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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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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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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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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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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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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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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 ...
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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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Is there any problem a quantum finite state machine can do faster than a classical finite state machine?

All of the quantum algorithms I've seen so far require a turing-complete quantum computer, at least as far as I can tell. Are there any quantum algorithms that require only a quantum finite automaton? ...
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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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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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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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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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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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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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Quantum Bit Commitment, restricting ourselves to pure states

I have been going through the Preskill lecture notes on quantum computation, and there is a question on Quantum Bit Commitment: Alice wants to make a prediction, either $0$ or $1$, before an ...
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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 biparte system $AB$, described ...
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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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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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Mach-Zehnder with PBS = Bit-Flip?

Is it true that a Mach-Zehnder interferometer with two polarizing beam splitters (PBS) is nothing but a bit flip for the polarisation degree of freedom? Say the PBSs reflect vertical polarized light ...
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Natural units of information

In physics entropy is usually measured in nats. I wonder is there a possible model of a physical system which has entropy of discrete number of nats? How particles and degrees of freedom should be ...
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Quantum Simulation of Schrodinger's equation

While studying some quantum mechanics from Neilsen's book on quantum computing and came across following because x and p are conjugate variables related by a quantum Fourier transform: $ ...
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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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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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What's wrong with this faster-than-light gedankenexperiment?

It is common wisdom - and mathematically proven - that quantum entanglement cannot be used to bypass the relativistic speed limit and transfer information faster than light. So there must be something ...
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On Bell inequality and bound entangled states

I have recently seen some presentation slides of Michał Horodecki (slide number 77) in which he discussed the following conjecture. Bound entangled states satisfy all Bell inequalities The ...
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Entanglement: Is it possible to prepare and reset probabilities to send information?

I'm pretty certain that the answer to the question in the title is a no, but I don't understand why. I have some basic misunderstanding of quantum processes that I’d like clarified in the form of ...
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Can I parameterize the state of a quantum system given reduced density matrices describing its subparts?

As the simplest example, consider a set of two qubits where the reduced density matrix of each qubit is known. If the two qubits are not entangled, the overall state would be given by the tensor ...
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Exhaustive list of assumptions for the Clauser-Horne-Shimony-Holt inequality

I am trying to create an exhaustive list of all assumptions which work as the base of the CHSH inequality. Locality - this means an object can be influenced only by its surroundings. So, the events ...
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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> + ...