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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Quantum cloning of orthonormal states

If I understand correctly, for two orthonormal states $\left|\psi_1\right\rangle$ and $\left|\psi_2\right\rangle$ in the Hilbert space H, there must exist a unitary transformation $U$, such that: $$U\...
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Undergraduate quantum book treating density operators, mixed states, and entanglement [duplicate]

I'm working on a project on quantum measurement theory - in particular, relating to the quantum Zeno effect - over the summer. Right now, I'm in the process of doing background readings that'd enable ...
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Quantum entanglement and affecting the particles [duplicate]

I am trying to grasp some aspects of the quantum entanglement, but the existing resources (including some of the links here) seem a bit confusing. I am trying to find an answer to the following ...
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Improved gap estimates for quantum adiabatic evolution

In his PhD thesis, Daniel Nagaj mentioned that Deift† et al has tightened the relationship between the adiabatic evolution time $T$ and the energy gap between the ground state and first excited state, ...
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Using open system dynamics to define a quantum state

Background The density matrix of a closed quantum system with Hilbert space $\mathscr H$ evolves according to the von Neumann equation \begin{align*} i\hbar\dot\rho=[H,\rho]. \end{align*} Given a ...
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What is an incoherent state?

I am reading through a recent paper which speaks frequently of "incoherent states" without ever defining what such a state is. I gather from the context of the paper that it has something to do with ...
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Bloch sphere representation of $\sigma_x$ operator on $|1\rangle$

I am trying to visualize a Hamiltonian H=$\hat{\sigma_x}$ $$ \hat{\sigma}_{x} = \left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array} \right) $$ acting on the state $| 1 \rangle$. I can write ...
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Can we perform matrix operations of CNOT on 2 qubit systems? [closed]

I am trying to get started on quantum computing. I find that 2x2 matrices like Pauli X,Y,Z,or gates like H,S can be used to perform operations on single qubits as direct matrix multiplication. For e.g ...
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Teleportation without classical channel

In an article on vixra, there is a statement that teleportation of information can be done without the use of classical communication channel. I know that this is forbidden by the no-communication ...
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Shape of the state space under different tensor products

I am currently studying generalized probabilistic theories. Let me roughly recall how such a theory looks like (you can skip this and go to "My question" if you are familiar with this). Recall: In a ...
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Can every density operator be written as an outer product of two vectors?

I have a feeling this is a very basic question. I apologize if it is. Using Dirac's notation, can every (mixed) density operator $\rho_A$ of system $A$ be written as the ket-bra (outer) product $|a_1 ...
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What is the entropy of a pure state?

Well, zero of course. Because $S = -\text{tr}(\rho \ln \rho)$ and $\rho$ for a pure state gives zero entropy. But... all quantum states are really pure states right? A mixed state just describes ...
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Questions on the Lechner-Hauke-Zoller quantum annealing architecture

The Lechner-Hauke-Zoller quantum annealing architecture was first introduced in A quantum annealing architecture with all-to-all connectivity from local interactions. While going through the paper, I ...
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Why is Quantum Teleportation important in Cryptography?

I think the physical principle is that (Wikipedia): For every qubit teleported, Alice needs to send Bob two classical bits of information. These two classical bits do not carry complete ...
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Probability of measuring a pure qubit state after some unitary rotation [closed]

Suppose I have the prepared state $$|+\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}}$$ and the unitary $Z_{\pi/2}$ which rotates a state in the Bloch sphere by $+\pi/2$ about the $z$-axis. As I ...
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How is the lifetime of a symmetric and antisymmetric state determined by its constituents

In the context of quantum mechanics, there is the concept of so called symmetric and antisymmetric states, which can have multiple constituents. A type of hybridized state, if you will. To keep the ...
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Why can't a classical bit behave like a qubit?

For example i have a 2 qubits which can have 4 possibilities i.e. 00, 01, 10, 11 so this shows that the 2 qubits can contain four bits of information as they are superpositioned but i think 2 ...
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A 'distance' measure that involves 3 quantum states

The following question was asked by my friend Elie Wolfe. Given two quantum (or even classical) states $\rho, \sigma$, there are various measures that say how 'far' these two quantum states are, such ...
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How is CNOT operation realized physically?

I think I understood very well how operations on one qubit are done - if qubit is electron, we just apply magnetic field in direction we want to make spin precess (unitary operations on single qubit). ...
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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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What's Bob's state after this quantum circuit? [closed]

As shown in the picture, we know Alice's state will be intact after this circuit, but what about Bob's state, will it be $|0\rangle$ or $(|0\rangle+|1\rangle)/\sqrt{2}$ and why? I think it will be $(|...
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Why probability of detection by performing unambiguous quantum measurement is less than random guess in mesoscopic quantum regime?

In mesoscopic quantum regime (mean photon number 10000) and non-orthogonal coherent state(number of non-orthogonal coherent state 2000), why probability of detection by performing quantum unambiguous ...
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Why probability of detection of optimum unambiguous discrimination between linearly independent symmetric states is less than random guess? [duplicate]

Considering the analysis and result of this paper, http://arxiv.org/pdf/quant-ph/9807023v1.pdf, I have used equation (3.15) and (4.3) to calculate the optimum probability of success for mean photon ...
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Does the Observer Effect define quantum behavior regardless of conscious observation?

I read the Wikipedia article about the Observer effect and I was a bit confused by the wording of the introductory section. Does the method of observation collapse the wave function (or define the ...
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Interference experiment and entanglement with apparatus

Consider a single photon in a Mach-Zehnder interferometer. Considering the photon only, the output state is the sum over both paths $$\vert 1 \rangle + \vert 2 \rangle=\vert \psi \rangle + e^{i\...
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Transition rate of two level system subjected to noise

(this question is simpler than its length implies. I did this on purpose to provide a nice complete development for future readers) The setup Suppose we have a two-level quantum system with ...
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Gaining intuition over Hamiltonian for qubit systems

A typical Hamiltonian for a two state system with some driving field can be written as $$H=J(t)\sigma_z+h\sigma_x$$ This represents a qubit system driven along a single axis. On the other hand we ...
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How does quantum superposition make calculation faster?

In every description of a quantum computer I've seen (that isn't extremely technical), they've been described as computers that use qubits, that use a superposition of 1 and 0 to make processing ...
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Heisenberg Representation of Quantum Computers explain observable transformations

The Heisenberg Representation of Quantum Computers (Daniel Gottesman) http://arxiv.org/abs/quant-ph/9807006 Suppose we have a quantum computer in the state $|\psi\rangle$, and we apply 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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What is the use of a Universal-NOT gate?

The universal-NOT gate in quantum computing is an operation which maps every point on the Bloch sphere to its antipodal point (see Buzek et al, Phys. Rev. A 60, R2626–R2629). In general, a single ...
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quantum clone of orthogonal quantum states

I am a little bit confused about the no-cloning theorem for two orthogonal quantum states. In Nielson&Chuang page 24-25, it states that an unknown state $|\phi\rangle$ cannot be copied since $|\...
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What gives a particle its identity?

A lot of very smart people have stitched together the standard model, and I accept it. I don't understand it, but I assume there should be a mechanism of sorts that gives a particle some fundamental ...
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Constructing a POVM to discriminate $m$ quantum states. What if they're linearly dependent?

I've come across this problem in Nielsen & Chuang's Quantum Information book (problem 2.64) Suppose Bob is given a quantum state chosen from a set $|ψ_1 \rangle, . . . , |ψ_m\rangle$ of linearly ...
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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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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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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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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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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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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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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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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 $$|\Psi\rangle=\frac{1}{\sqrt(2)}(|...
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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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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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What is coherence in quantum mechanics?

What are coherence and quantum entanglement? Does it mean that two particles are the same? I read this in a book called Physics of the Impossible by Michio Kaku. He says that two particles behave in ...
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Did Leggett and Caldeira solve the measurement problem?

In 1983 Leggett and Caldeira published a paper (see also here) that shows the evolution of the density matrix in a dissipative system. Follow-up work by Zurek and others shows the relevance to ...