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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Are there any specific examples of the application of Lewis-Riesenfeld procedure to time dependent Hamiltonians in QM?

Lewis-Riesenfeld invariant theory is a theory applicable to solve time-dependent Schrodinger equations. I have always encountered the theory related to the procedure, however never encountered any ...
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Production of entangled photons by spontaneous down conversion

I have found that the conditional uncertainty product of position and momentum of any one photon produced in the spontaneous parametric down conversion process using a gaussian pump beam decreases ...
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Two definitions of the density matrix?

There seems to be two different definitions of definitions of density matrices in Physics. In Quantum Information we define a the density matrix associated with a wave function $ | \psi \rangle$ as ...
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What processes create or destroy information?

From a classical standpoint, it seems pretty clear that information can be easily lost. If you knock over a bookshelf and the books fall out, it seems like their initial order on the shelf cannot be ...
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Complexity of quantum simulation

Richard Feynman showed that Quantum simulation on a Turing machine will have an exponential slowdown. If that is so, does this put quantum simulation outside of P (complexity class)? I thought quantum ...
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CNOT Gate for quantum systems [on hold]

A you know the CNOT gate is 4 by 4 matrix, is there any way to show it by a 2*2 matrix? if yes what will be the elements?
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Exact solution of Qubit Decoherence using Transfer Matrix

I'm going through a particular paper on decoherence: Exact Solution of Qubit Decoherence models by a transfer matrix method I'm having trouble understanding a particular step in the mathematics ...
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How is the lifetime of a symmetric and antisymmetric state determined by its constituents

In the context of quantum information, there is the concept of so called symmetric and antisymmetric states, bright and dark, or superradiant and subradiant depending on the source you are using. The ...
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A seemingly paradox for Eigenstate Thermalization Hypothesis (ETH)

ETH states that for a system, all of its eigenstates thermalize. To be more specific, consider an energy eigenstate of the full system $H|n\rangle=E_n|n\rangle$. If the full system is in this ...
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If we can't clone quantum states, then how does stimulated emission work? [duplicate]

So we know we cannot fully copy a quantum state. But doesn't stimulated emission does just that? Say, a photon in a particular qubit state $|\psi\rangle = \alpha |0\rangle + \beta |1\rangle$ passes ...
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What is the qualitative difference between quantum superpostion and mixed states? [duplicate]

As I understand it, if one has a complete knowledge of the state of a quantum system (insofar as one knows the statistical distributions of all the observables associated with the state) then one can ...
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Collective angular momentum , Dicke states and indistinguishable particles

During course of quantum mechanics we dealt with addition of angular momenta. If we have two particles with spin $j_1$ and $j_2$ we can introduce total spin operator: $$\mathbf{J} = \mathbf{j}^{(1)} ...
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how do you find a schmidt basis and how can the schmidt decomposition be used for operators?

There's a System in the state $|\Psi\rangle=\frac{1}{2}\left(|00\rangle+|01\rangle+|10\rangle+|11\rangle\right)$. I know that that's not an entangled state, since ...
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Measurement on two Qubits

Assuming I have two Qubits, i.e. a four-dim. Hilbert space. In the following, I choose the basis {|11>,|10>,|01>,|00>}. I want to have a look on the non-diagonal part <11|$\rho$|00>. How can I ...
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Is there a quantum computing model accounting for uncertainty of a qubit state?

Any physical quantum computer would have a limit on the fidelity with which it can create qubit superposition states. If we're trying to create $|\Psi\rangle = c_0|0\rangle + c_1|1\rangle$, the ...
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Trace of an observable [closed]

If $X$ and $Y$ are two observables and $\rho$ is a density operator, is it true that for every complex number $z$ the quantity $$ \mathrm{tr}[\rho (X+zY)^*(X+zY)] $$ is non-negative?
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Holevo Information and Quantum Mutual Information

This question is about the difference between Quantum Mutual Information and Holevo Information of quantum channels. From http://arxiv.org/pdf/1004.2495.pdf equation 7 we know that the sum of quantum ...
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What do operations on single Qubits of Unfactorable Superpositions Do?

So suppose I have the following Quantum Circuit: A ---- |Control| -----|Hadamard|---- B ---- |xxxxxxx|------------------------ Which is a 2 input Controlled Gate (applying some gate of two choices ...
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Measuring qubit as the presence or absence of a particle [closed]

My background is not physics so forgive the confusion. If we use photon polarization as qubits, I can understand that the angle is in a superposition between 0 and 90 degrees. But we can also use ...
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Can a non-entangled qubit be teleported by entangling it?

Let's say I have a qubit that is not entangled in state $\psi$. I want to teleport this qubit by entangling it with another qubit but still getting $\psi$ back in the end. Is this possible, or would ...
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What exactly does No cloning mean, in the context of Quantum Computing?

I am trying to get an intuitive idea of how the No-Cloning theorem affects Quantum computation. My understanding is that given a qubit $Q$ in superposition $Q_0 \left| 0 \right> + Q_1 \left| 1 ...
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Is QC with Superpositioned Quantum Gates any different than normal Quantum Computation?

This might be more appropriate for theoretical CS stackexchange, but it feels sufficiently low level to be relevant here. Consider the following thought experiment: I have a Quantum FPGA, it is a ...
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Approximate cloning of a quantum state, informed by past measurements

Suppose I give you a state $|\psi\rangle$, and tell you a sequence of measurements that have been performed on it. The measurements are not guaranteed to be orthogonal to each other, or to cover the ...
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If all the particles of a Bose-Einstein condensate become entangled with each other,does the system still remain a Bose-Einstein condensate?

I know that an entangled system is found in a single entangled state and that when you try to observe the individual state of a particle from an entangled system using a reduced density matrix, you ...
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If I pass one member of an entangled pair through a polarizer, does the other member assume a correlated polarization?

Does that mean I have influenced the measurement result of one member of the entangled pair by acting on the other? Can information be sent this way using entanglement?
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When will a useable universal quantum computer first be realised? [closed]

Ideally with the reference to the type of technology, when do experts predict a small universal quantum computer of a couple hundred qubits will be developed? From my reading the leading techology is ...
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Can a system be PERFECTLY simulated by a quantum (and classical) computer? [closed]

This is a thought experiment, and as such will assume some crazy things. Let's say I decide to perfectly simulate my university as it is right now. I use a magic machine to instantly scan the entire ...
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the probability amplitude of a photon

In one of Richard Feynman's lecture, he says that the angle of amplitude of a given path depends on what time the photon is emitted from the source. How does the angle of amplitude depend on time ...
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C2(U) Unitary Matrix Representation

Above is my work for the unitary matrix representation of a C2(U) gate. However, this does not agree with a link I found online for what it should look like. Below my work, I have written the ...
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what is the analog of electronics for quarks or protons?

Is there an equivalent field for quarks or for protons as there is electronics for electrons where you can build engineer and mess around with things? May be even hack ?
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Chance of distinguishing between many pure states

Helstrom has demonstrated that the maximum probability of any process correctly distinguishing between two pure states $|\psi_0\rangle$ and $|\psi_1\rangle$ is determined by their trace distance: ...
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Physical meaning of $Tr(\rho ^2)$

If $\rho$ is the density matrix of a system then $Tr(\rho ^2) \leq 1$. If the equality holds the system is in a pure state and it is in a mixed state otherwise. But, what is the physical meaning of ...
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On $k$-extendability of bipartite states

Definition of $k$-extendability can be given as follows. Let $k\in \mathbb{N}$. A state $\rho_{AB}$ on a bipartite Hilbert space $\mathrm{A}\otimes\mathrm{B}$ is $k$-extendible with respect to ...
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Unitarity of quantum evolution

In this paper by Charles Bennett, he says on page 25, I understand why U(XOR) gives the result it does but why is that a consequence of its unitary property? Thanks
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Completely positive maps and symmetric states

Let $\mathcal{N}$ be a completetely positive trace preserving map (aka a quantum channel) acting on a finite dimensional system $\mathrm{A}$, and let $\pi$ denote the maximally mixed state on ...
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Probability distribution of a pretty-good measurement

Let $\rho_{XE}$ be a classical-quantum state. That is, $$ \rho_{XE} = \sum_{x}\Pr[X=x] \cdot |x\rangle \langle x | \otimes \rho_{x} $$ where every $\rho_{x}$ is a density matrix with ...
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Rotations in Bloch Sphere about an arbitrary axis

I am trying to understand the following statement. "Suppose a single qubit has a state represented by the Bloch vector $\vec{\lambda}$. Then the effect of the rotation $R_{\hat{n}}(\theta)$ on the ...
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What does it mean to find a particle in a range at a given value?

Find the probability of finding the electron in the range $\Delta r = 0.02a_0$ at (a) $r = a_0$ and (b) $r = 2a_0$ for the state $n = 2$, $l = 0$, $m = 0$ in hydrogen. I don't understand the ...
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What is the easiest way to prepare a Glauber coherent state? [closed]

Without using a laser source. Can you, for example, create a coherent state by filtering another light source (incandescent light bulb, LED, etc)?
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What is the current big question or motivation in quantum information? [closed]

As an prospective student, I am facing a crossing as many people did. I would love to know what is the current big question or motivation in the quantum information society? If anyone knows the answer ...
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How many states does a qubit have? [closed]

There is something I am trying to understand about qubits. If a qubit can exist in an infinite (is that even correct?) number of states prior to the measurement, then why can it only be measured in ...
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Reference request: QFT and AdS/CFT for information theorists

There is a lot of buzz recently about connections between quantum information theory and quantum field theory/string theory. I would like to understand in particular how quantum information methods ...
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Questions regarding reversible processes, entanglement, and time reversal symmetry [closed]

Can we, a priori, state that a physical state is entangled with its environment? Its hard for me to come up with a reason for why we can't. For my next question, consider a physical state: ...
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Is Thermalization of a subsystem simply the result of Decoherence of its state?

I would appreciate answers that explain both the concepts in short to underline if there are any key differences between the two. Also, how does a localized state survive decoherence?
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How is the range of $x\cdot s$ in Simon's algorithm restricted to $\{0,1\}$?

The final critical step of Simon's algorithm (before setting up a simpler system of equations to solve) involves taking advantage of the fact that $$x\cdot s \in\{0,1 \}$$ but for $x,s \in ...
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Can a qubit have an imaginary component?

My knowledge of linear algebra is limited and my physics knowledge mostly comes from high school and Youtube so please bear with me. In the equation $$|x\rangle = a|0\rangle+b|1\rangle,$$ I read that ...
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Numerically finding the energy diagram of the hamiltonian

I'm looking at a collection of three two level systems (qubits) coupled to each other (with known bare state energies and couplings). The hamiltonian is given by ...
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What is the difference between the atomic resonance frequency and the Rabi frequency?

I've been trying to work my way through the solution to the optical bloch equations for a two-level atom system which is being driven by a laser. One thing that has been confusing me is the difference ...
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Understanding the Mathematics of Wigner function [duplicate]

I fully understand that Wigner function provides the complete information of a state of a quantum system, i.e. quantum phase space, while not violating Uncertainty principle. But can anyone tell me ...
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How can all information be localized if local realism is dead?

I'm confused about whether quantum mechanics is local or not. The authors of a recent, much publicized experiment argue that their results "imply statistically significant rejection of the ...