Questions tagged [quantum-information]

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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109 views

Set of unitary operators such that $U|0\rangle = |\psi\rangle$

In quantum computing, one of the central areas of study is to determine efficient quantum circuits - described by unitaries - to prepare a state $|\psi\rangle$ from the initial computational basis ...
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Method of Moments for an operator in quantum random walk [migrated]

I was reading a paper by Grimmett, Janson, and Scudo, see here for arxiv version of the paper, where they show that for all positive integers $$\lim_{n \to \infty}E[(X_{n}/n)^{r}] =\int_{\Omega} h^{r} ...
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106 views

Integration with respect to Haar measure and reduced density matrix [closed]

Consider a bipartite system $\mathcal{H}_A \otimes \mathcal{H}_B$, with $|A|,|B|>>1$ and not necceserly $|A|=|B|$. Following Jerusalem Lectures on Black Holes and Quantum Information (eq. 5.8) ...
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Is the sum of two gaussian density matrices also gaussian?

Gaussian density matricies are nice because they are fully characterised by its 2-point correlation function. Consider a free fermionic theory with creation/annihilation ops $c_i,c^{\dagger}_i$, the 2-...
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Weak measurement and distinguishability

Suppose you can perform any weak measurement of your choice on an ensemble of particles composed of two equally sized sub-ensembles, but you can't use any other source of information about which ...
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Expected value in usual quantum mechanics vs quantum information

In standard Quantum Mechanics, one computes the expected value of an operator $A$ (arbitrary state $|\Psi\rangle$) as $$ \langle\Psi|A|\Psi\rangle. $$ This has the virtue that we can compute for ...
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What would an interference pattern at relativistic speeds look like?

What would happen to a dual slit experiment's interference pattern if one observer was moving at relativistic speeds and another wasn't? For example if an observer performs a double slit experiment on ...
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is room temperature quantum (qubit) nuclear magnetic resonance possible?

I know it is possible to do room temperature NMR. Not just that but one can also use the earth's magnetic field for the nuclei to precess about. If done this way, one gets precession at about the KHz ...
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What is the theoretical upper limit, if any, to the quantity of information bits that can be encoded within a given volume of space? [duplicate]

By encoding I mean representing bits of information as some form of mass-energy that can be, at some time in the future, decoded back into the original information bits without loss. This does not ...
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1answer
78 views

How is many world interpretation of quantum mechanics compatible with no cloning theorem?

In many worlds interpretation of the quantum mechanics all possible outcomes of a measurement are realized, however, in different universes. Everytime a measurement occurs we register one outcome and ...
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Does entanglement mean that information travels faster than light? [duplicate]

Every time in physics (in popsci) I hear that it is not possible to travel faster than light, as this would cause many problems that I do not understand. On the other side, in Quantum Computing (in ...
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Leakage of superconducting qubit: why it occurs with short driving pulses and not as well with long ones

My question in very short: Short pulses on superconducting qubit usually induce leakage. But a long pulse can be seen as a sequence of short pulses (imagine all of the short pulse as square pulses: ...
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1answer
113 views

Solution to the time-independent Schrödinger's equation for systems with spin

I'm currently taking a course on quantum computing and we've just introduced the concept of spin in a not so very formal way and I'm no physicist, so please be gentle. Apparently, the solution to the ...
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Why is the identity not considered when expanding a $2 \times 2$ matrix in the Pauli basis? [closed]

I am aware of the expansion of a two dimensional matrix $M$ in Pauli basis given by $$ M = \sum_{\mu=0,1,2,3} c_\mu \sigma_\mu$$ with $\sigma_0 = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$...
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How do $|1⟩$ and $-|1⟩$ represent the same state?

I am a newbie to quantum mechanics (I come from more of an engineering/CS background), and today my quantum computing professor stated that $\def\ket#1{\left|#1\right\rangle}\ket{1}$ and $-\ket{1}$ ...
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Are violations of realism the same thing as contextuality?

I am basically looking for a counter-example where we'd get contextuality but not violations of realism (and vice-versa). If no such counter-examples exist, then it seems to me that they're really one ...
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Does a von Neumann algebra correspond to a quantum system?

We usually associate a quantum system with a Hilbert space $\mathcal{H}$ and consider the set of bounded operators on $\mathcal{B}(\mathcal{H})$. Especially the set of unit-trace and positive (semi-...
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Why real quantum mechanics fails in multipartite systems?

I was reading this paper "Quantum physics needs complex numbers" by Renou et al. In the paper, they propose the standard entanglement swapping scenario and use CHSH3 inequality to show that ...
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Is limited computational capacity a fundamental obstacle?

Statistical physics books often motivate the necessity of statistical/thermodynamic description by impossibility of calculating the trajectories of all the molecules (I speak of "trajectories&...
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Why Do Thermal Operations Form a Semigroup?

Given a fixed "background temperature" $T$ and an $n$-dimensional system, the set of thermal operations is usually defined to be $$ \bigcup_{m\in\mathbb N}\Big\{ \operatorname{tr}_B\Big(U\...
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Entropy of the Universe and Quantum Information [closed]

From what I have understand, heat death of the universe requires a positive cosmological constant. And so when the universe achieves thermodynamic equilibrium, it shall have maximum entropy. Now I ...
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How do ladder operators and number states act on multimode states?

The ladder operators for number states, $\alpha_{\ell}^{\dagger}$, and $\alpha_{\ell}$ have the following properties when working on mode $\ell$: $$\begin{array}{l} \hat{\alpha}_{\ell}\left|n_{\ell}\...
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What is the status on quantum information (processing, communication…) in infinite-dimensional Hilbert spaces?

In canonical references for learning quantum information, such as Nielsen's Quantum Computation and Quantum Information and Preskill's lecture notes, the focus seems to be on systems with finite-...
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Why is classical simulation of 1d quantum systems effective?

There is a basic argument for why the quantum systems are generically hard to simulate classically. Namely, the dimension of the state space grows exponentially with the number of degrees of freedom. ...
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Is it possible to find the most probable pure state from a mixed state?

Since a mixed state is a normal statistical combination of many pure states, is it possible to find the list of pure state that makes up the mixed state? I realise there are many different pure states ...
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How to measure average value of qubits?

Recently I have been studying quantum mechanics in The Theoretical Minimum by Susskind. In his experiment, when the apparatus rotated by an arbitrary angle within the $x{–}z$ plane, the average ...
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Can the Hamiltonian be upscaled to speed up quantum gates?

In quantum computing, gates are performed unitarily, i.e. $|\psi\rangle \mapsto U|\psi\rangle$, driven by some Hamiltonian, i.e. $U = \exp(-iHt)$. Consider $H$ as time independent, if it is ...
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Decomposition of a 2 qubit gate into standard quantum gates

In here it is claimed that any entangling two qubit gate of the form $$ U =e^{-iH}, $$ where $H = h_x \sigma_x\otimes \sigma_x + h_y \sigma_y\otimes \sigma_y + h_z \sigma_z\otimes \sigma_z$ can be ...
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4answers
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Do all wavefunction collapses have to be evident in some way?

All wavefunction collapses are events which reveal some kind of classical information or thermodynamically visible 'event'. Is this true? In that case, what is the evidence of a 'not' collapse. A 'not'...
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Does the collapse of the wave function happen immediately everywhere?

It is usually taught that when we measure some measurable value the wave function collapses immediately everywhere. This idea sounds like a simplification of some more complicated mechanism. Are ...
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CNOT over a $|+\rangle$ qubit

I want to use the CNOT gate over a qubit $|0+\rangle$, but the definition says that CNOT flips the second qubit if a $1$ is found in the first one (i.e. 0 to 1, and 1 to 0). However, what is is to ...
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Why does the Hadamard act as $H^{\otimes n}|x\rangle = \frac{1}{\sqrt{2^n}}\sum_{y\ \in\{0,1\}^n}(-1)^{x_1y_1+···+x_ny_n}|y\rangle $? [duplicate]

In quantum-information, we have been told that the Hadamard gate over $n$-qubits can be defined as: $$H^{\otimes n}|x\rangle = \frac{1}{\sqrt{2^n}}\sum_{y\ \in\{0,1\}^n}(-1)^{x_1y_1+···+x_ny_n}|y\...
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67 views

Wavefunctions as Inner Product

In the following expression, n and m belong to the number basis and x is the position: $$ \langle n|m \rangle = \int_x n^*(x) m(x) dx = \int_x \langle n|x \rangle \langle x|m \rangle dx $$ I ...
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Bounding the value of a function for separable spin states

Consider $N$ spin-1/2, for which we can define the collective spin operator $\vec{S}=\sum_i \frac{\vec{\sigma}^{(i)}}{2}$. My question is, what is the upper bound $U$ on $$ f(\rho) = \text{Var}[ S_z ] ...
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Topological order and volume-law entanglement

Topological order is a property traditionally most associated with ground states of gapped Hamiltonians. However, using the notion that topological order is fundamentally about a form of "long-...
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2answers
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Hadamard gate over 2 qubits [closed]

Let H be the Hadamard gate: $$(\frac{1}{\sqrt{2}})\begin{pmatrix}\begin{array}{rrrrrrrr} 1 & 1 \\ 1 & -1 \end{array}\end{pmatrix}$$ I would like to write down the matrix associated to the ...
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1answer
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Need help in finding the sources to read some formulas related to information theory [closed]

I am reading an article. I have not read information information theory before. Can some one please tell which results are used in equation $(34)$ and what result is used to arrive at the conclusion ...
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Hong-Ou-Mandel in Fock Space for Arbitrary Polarization and Number Inputs

I would like to input an state: $$|\psi\rangle_{in}=\frac{1}{\sqrt{n_H!n_V!m_H!m_V!}}(a_{H}^{\dagger})^{n_H}(a_{V}^{\dagger})^{n_V}(b_{H}^{\dagger})^{m_H}(b_{V}^{\dagger})^{m_V}|0000\rangle_{...
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A question on mutual quantum information

As I have seen, the usual definition of mutual quantum information concerns with bipartite systems, which makes perfect sense to me. However, I was wondering if it makes any sense to speak about the ...
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1answer
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Does uncopying an information requires a copy of the same program in this scheme? If so, how?

In the paper Information is Physical by Rolf Landauer (reference), it is claimed that Uncopying is not equivalent to erasure and, just like copying, can be done with a dissipation per step ...
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Zero capacity quantum channels

All the currently known examples of quantum channels with zero quantum capacity are either anti-degradable or PPT. These notions can be conveniently defined in terms of the Choi matrix of the given ...
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Theoretical description of a two-mode squeezed state with continuous modes

Given two distinguishable modes $a$ and $b$ with $[a,a^\dagger]=1$ and $[b,b^\dagger]=1$ and $[a,b^\dagger]=0$, the two-mode squeezed vacuum state is given by \begin{equation} \exp (\zeta^* a b - \...
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Are there sub-exponential local complex partition functions?

Consider an arbitrary local, translation-invariant, classical statistical lattice model such as the Ising or Potts model. The partition function $Z$ is a sum over products of local Boltzmann weights, ...
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What gate combinations create entangled two-qubit states?

I know that in order to make a two qubit entangled state, this quantum circuit is used: But I was wondering if there are any other gate combinations which also create entangled two quit states. If ...
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Do correlations in local quantum spin systems always decay exponentially or algebraically?

Consider translation-invariant quantum spin systems, that is qu-d-its on a lattice with a geometrically local Hamiltonian. Usually, such models are either gapped (in an ordered/disordered phase) or ...
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Computing state overlap from the expectation value of the Ctrl-Z operator

I am trying to understand an algorithm for computing the overlap between two single qubit states, $\left |\psi\right>$ and $\left |\phi\right>$: $$ \left| \left< \psi | \phi \right> \right|...
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“Secular” approximation in the Lindblad equation for an open quantum system

Some context: I am deriving the Lindblad equation following “The Theory of Open Quantum Systems” by Breuer and Petruccione (somebody transcribed the section I am reading in this link). My question: I ...
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What is the invariant associated with constant (quantum) information?

(PhysOrg.com) -- In the classical world, information can be copied and deleted at will. In the quantum world, however, the conservation of quantum information means that information cannot be created ...
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Doubt about the Gaussian state

I am reading an article that makes an application using the Gaussian state. The author of the article writes the Gaussian state as follows: $$\psi(q) = [2\pi(\Delta q)^2]^{-\frac{1}{4}}e^{-\frac{q^2}{...
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Memory effects in open quantum systems: Markovian approximation question

Setting: Quantum system $S$ composed of a subsystem of interest $A$ and a subsystem acting as the environment $B$ such that $S=A\cup B$. System $S$ is described by density matrix $\rho$ whereas ...

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