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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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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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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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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Numerical Computation of Linbald Equation

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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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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193 views

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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114 views

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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29 views

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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366 views

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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152 views

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> + ...
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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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Is there a handwavy way to explain what quantum correlation means?

Is there a simple way to explain the difference between a classical and truly quantum correlation to a non-quantum person who has basic understanding classical correlation? I mean without invoking ...
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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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Is the universe a quantum computer - is light speed barrier a computational constraint

There is currently a debate ongoing on leading maths blog Gödel’s Lost Letter, between Gil Kalai and Aram Harrow, with the former arguing that building a quantum computer may not be possible due to ...
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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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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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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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Mixed state after measurement

I'm looking at Section 2.4.1 of Nielsen and Chuang's Quantum Computation and Quantum Information were they derive the density operator versions of the evolution and measurement postulates of quantum ...
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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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What is the Reduced Density Matrix?

The difference between pure and mixed states is the difference in their density matrix structure. For density matrix $\rho$ of mixed state the trace of $\rho^{2}$ should be less than 1. For pure ...
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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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Composition of squeeze operators?

I'm wondering if it exists a composition law for the squeezing operation ? I guess so for geometric reason, since they are (generalized, and the phase is annoying of course) hyperbolic rotations of ...
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What is the probability of quantum tunneling occurring in this CPU?

You may have noticed over the last few years that Moore's law is no longer applying to the real world. This observation states that over the history of computing hardware, the number of transistors on ...
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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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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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How much is quantum computation changing the interpretation of quantum theory, and, if at all, how?

At the beginning of quantum computation, David Deutsch made a strong claim that the Many Worlds interpretation of quantum theory was at the foundation of his ability to do what he did. There was a lot ...
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What are the practical applications of quantum foundations?

Many quantum foundation researchers keep emphasizing that For All Practical Purposes (FAPP), quantum foundations are irrelevant. They even invented an acronym for it! Does that mean that quantum ...
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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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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? ).
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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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A good book for Quantum Cryptography

I am interested in Quantum Information and Cryptography in particular. I have gone through Neilson's text and Preskill's notes . Can someone suggest me some good text for Quantum Cryptography ? I ...
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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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Is the reduction map completely positive? [duplicate]

I am struggling with proving the complete positivity of a general map ( granted it is CP ). The reduction map is defined as $$ \rho \rightarrow \mathrm{Tr}(\rho)I - \rho $$ It is a trivial job to ...