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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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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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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Von Neumann entropy of mixtures of coherent states

I'm trying to calculate the Von Neumann entropy of statistical mixtures of coherent states. The problem is that such states are in general non-Gaussian, so one cannot follow the formalism developed ...
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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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On LOCC operations

I am trying to learn quantum information theory. Suppose we have a bipartite (as well as multi-partite) quantum system $H_A \otimes H_B$. What is a LOCC map $\phi: \mathcal{B}(H_A \otimes H_B) \...
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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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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 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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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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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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51 views

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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74 views

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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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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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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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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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 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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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 $$|\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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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 $\mathrm{...
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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 $\mathrm{Tr}(\...