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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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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Interaction Hamiltonian coupling question

System is composed of two qubits and the bath is one bath qubit. The interaction Hamiltonian is: $$\sigma_1^x\otimes B_1 + \sigma_2^x\otimes B_2$$ where $B_i$ is a 2 by 2 matrix. I try to interpret ...
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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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Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...
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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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39 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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65 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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36 views

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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56 views

Relating purity of reduced density matrix to concurrence [closed]

Given the initial quantum state: $$ |\psi\rangle=\alpha|0\rangle+\beta|1\rangle $$ If I perform the CNOT operation: I get the two cubit state: $$|\Psi'\rangle=\alpha|00\rangle+\beta|11\rangle \ ...
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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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1answer
168 views

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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62 views

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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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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24 views

Production of entangled photons by spontaneous down conversion [closed]

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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34 views

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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50 views

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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59 views

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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1answer
41 views

CNOT Gate for quantum systems [closed]

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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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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2answers
78 views

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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1answer
42 views

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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39 views

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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47 views

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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53 views

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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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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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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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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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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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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How are the field operator and quantum state after a beam splitter and a polarizing beam splitter individually?

How are the field operator $\hat{a}$, $\hat{a}^\dagger$ and the quantum state (like coherent state $|\alpha>$, Fock state $|n>$) changed after a beam splitter and a polarizing beam splitter ...
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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 ...
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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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are locally unique pure quantum states also ground states of some local hamiltonian?

Let $H=\sum_i H_i$ be some k-local hamiltonian with a unique ground state $|\psi>$. Then it is easily shown that $|\psi>$ is k-locally distinguishable from any other state $|\psi'>$. Is 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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Heisenberg XXX time evolution operator for three qubits

I've a problem to reproduce the result in equation (4) on page three of this paper: http://arxiv.org/abs/0802.2588. So far I've understood that they apply a Heisenberg XXX interaction between ...
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84 views

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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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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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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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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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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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 ...