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.

learn more… | top users | synonyms (1)

3
votes
1answer
118 views

How can I derive Fusion-Rules for Anyons?

I am reading Pachos "Introduction to Topological Quantum Computation". Pachos writes that a model for anyons consists of a list of all anyons and a fusion rule for them. Given a model with anyonic ...
2
votes
2answers
275 views

How could memory be organized in quantum computers?

A classical computer has a memory made up of bits, where each bit represents either a one or a zero and its implemented by two-state transistor logic. However, a quantum computer maintains a sequence ...
1
vote
1answer
129 views

Separability of density operators on tensor product spaces

Consider a composite system $\mathcal{H}=\mathcal{H}_{A}\otimes\mathcal{H}_{B}$ where $\mathcal{H}_{A}$ and $\mathcal{H}_{B}$ are Hilbert spaces of constituent components (say two qubits). Let ...
1
vote
1answer
146 views

Book question positive square root on quantum operator

On p.86 Section 2.2.4 of the Quantum computation and quantum information book by Nielsen, $M_{o}$ is defined as the positive square root of the positive operator. Is the "positive square root" ...
1
vote
1answer
80 views

Purity of a maximally mixed quantum state

The trace of the square of a density matrix(which is also called the Purity of the quantum state) is (lower)bounded by the inverse of the dimension of the Hilbert space and (upper) bounded by 1. I ...
0
votes
1answer
68 views

Quantum probability [duplicate]

I would like to get an idea of what "quantum probability" means and how it differs from classical frequentist or Bayesian probability. Can anyone enlighten me in non-too-technical terms?
2
votes
1answer
88 views

Purification of Gaussian states

Let us consider an $n$-mode Gaussian state $\rho_g$ (mixed state) in the Bosonic Fock space $\Gamma(\mathbb{C}^n)$. My question is, can we have a purification of $\rho_g$ which is itself Gaussian? ...
2
votes
0answers
38 views

dependence of braiding matrix element on the fusion product of anyons

In the case of Majorana fermions (MFs), one knows that if one braids MF $a$ with MF $b$, then braiding matrix element $R^{c}_{ab}$ depends on the state $c$ which is the fusion outcome of $a$ and $b$. ...
0
votes
1answer
64 views

Discrimination of Bell states on unkown qubits

Consider the scenario where Alice is given three qubits, and promised two of them are maximally entangled Bell state $\in_R \{\frac{|00+11>}{\sqrt{2}}, \frac{|00-11>}{\sqrt{2}}\}$ and one of ...
-1
votes
1answer
52 views

Does quantum teleportation lead to a change of quantum states?

Particles A and B are entangled, quantum information of particle A is transmitted to particle B via quantum teleportation, does particle B's quantum state change? What happens to particle A's quantum ...
2
votes
1answer
92 views

Eigenvalues of density operator under quantum channel

Consider a 2x2 density operator $\rho$ with eigenvalues $\lambda_{1},\lambda_{2}$ (where $\lambda_{1}\geq\lambda_{2}$) evolving into a 4x4 density operator $\rho'$ (with eigenvalues ...
7
votes
1answer
285 views

Quantum and classical scaling of memory

In the literature of Quantum Computation (QC), when discussing the simulation of quantum systems, one usually comes across comparisons with the classical digital analog such as: "Classically the size ...
1
vote
2answers
199 views

Why can you only measure velocity or location in a particle?

I was talking to a family friend in the field of optics at a quantum scale (not sure the proper name for this) and he was explaining to me why you can only determine either the velocity or location of ...
2
votes
2answers
276 views

How many parameters are needed to specify a quantum state?

We have a spin state \begin{align} \ |{\Psi}\rangle=a_u|{U}\rangle+a_d|{D}\rangle \end{align} where $|U\rangle$ and $|D\rangle$ are $up$ and $down$ basis vectors, and $a_u$,$a_d$ are their complex ...
2
votes
0answers
53 views

Ordering of eigenstates in the quantum adiabatic theorem

Suppose we have an 'initial' Hamiltonian $H_{i}$ whose eigenvalues are all non-degenerate, which we order as follows: $ E^{0}_{i} < E^{1}_{i} < \dots < E^{N-2}_{i} < E^{N-1}_{i}$ Suppose ...
0
votes
0answers
30 views

Entanglement entropy for stabilizer states

A stabilizer state for a stabilizer set S for a system of qubits can be written as $\rho=\frac{1}{2^{n}}\sum_{g\epsilon S}g$ . If we take a bipartition A-B of our system and partial trace over A, ...
0
votes
1answer
65 views

The simulation hypothesis and the halting problem [closed]

I have a basic knowledge of classical and quantum information which isn't remotely enough to make me an expert on the subject. That being said, reading some questions about the simulation hypothesis ...
1
vote
2answers
71 views

Photons have a property from the matter they interact with?

When a photon leaves its source and hits our eye, our brain sees the source of the photon (Like a lightbulb or a star). When a photon is ejected from its source and bounces off of an object we see the ...
2
votes
2answers
132 views

Superposition in Quantum Mechanics

First of all, let $V$ be a vector space over the field $\mathbb{F}$. It is possible then to show, by Zorn's Lemma that there is a basis for $V$. The main point is that although basis are quite ...
29
votes
7answers
5k views

What is Quantum Mechanics really about?

This question might sound very silly, so I'm sorry if that's the case. I'll try my best to make my point clear here. Before explaining, just to make clear, I'm not confused because of the Math ...
4
votes
0answers
63 views

What quantum measurement formalism is easiest to implement physically?

As part of my studies and research, I have learned to work with three different measurement formalism which I define to avoid any ambiguity with the nomenclature: General measurements, which are ...
1
vote
0answers
37 views

What is special about quantum entanglement? [duplicate]

Get two pieces of paper. In secret write the same number on both papers. Transfer one paper to the Moon. Look to the paper which is left at the Earth. Voila! We know what is on the Moon paper. The ...
2
votes
2answers
202 views

The black hole paradox

I recently read in the news that Stephen Hawking claims to have solved the Black Hole Information paradox. I researched a bit about the paradox and the research that Stephen Hawking did to solve it. ...
0
votes
0answers
30 views

Are the produced entangled photons in type II SPDC always in phase?

Are the produced entangled photons in type II SPDC (spontaneous parametric down conversion) always in phase? In Kim's delayed choice quantum eraser, two entangled photons are produced by a BBQ ...
1
vote
1answer
65 views

Can one detect a single photon through measuring its impulse/momentum on a mirror?

Can one detect a single photon through measuring its impulse/momentum on a mirror? If the answer if YES or theoretically possible, photon path and interference fringes can be detected simultaneously ...
0
votes
1answer
84 views

Relationship between Toffoli gate and Deutsch gate

I am reading a book called "Quantum Computing for computer scientists" and stuck at this exercise for a day. Bellow is the description of Deutsch gate: And here is the description of Toffoli ...
2
votes
1answer
81 views

Can someone explain why this QM FTL communication setup is wrong?

So I thought I understood the double-slit experiment and EPR paradox until this setup occured to me. It combines EPR entanglement with "which-way" double slit setups. I know it must be wrong, but I ...
0
votes
2answers
67 views

Light (Laser) operated optical switch

I have searched the web and found that optical switches are activated either through mechanical or electro/magnetics. Making them sort of Optomechanical or optoelectronic switches. Lets exclude ...
2
votes
1answer
91 views

How to understand the three state descriptions from 3 observers of such a system?

Assuming an EPR pair $\psi_{AB}=|00>+|11>$ and three observers Alice, Bob and Charlie, who can communicate with each other but they do not do it for the time being. Alice with a qubit $|0>$ ...
0
votes
2answers
66 views

Why these quantum information processing protocols have a similar structure?

I noticed for some quantum information processing protocols such as teleportation, entanglement distillation, bound entanglement activation, entanglement catalysis, the protocols seem to have a ...
2
votes
1answer
67 views

finding generic Quantum circuits for k-local hamiltonians

Let $P_n$ denote the Pauli group on $n$ qubits (think of n as a large number). Let $G=\left<g_1,...,g_n\right> < P_n$ be some abelian subgroup such that each $g_i$ acts on at most $k\ll n$ ...
0
votes
0answers
57 views

Is the entanglement of mixed states meaningful?

For mixed 2-partite states, the entanglement of formation (EoF) is defined by the convex roof of all its possible decompositions. Since density matrix is not a complete description of a mixed state, ...
1
vote
1answer
105 views

Approximation of an unitary operator by simple operators

For quantum computation, it's well known that any unitary operator can be approximated with an arbitrary accuracy by simple operators, for example to approximate an unitary operator on n qubits by no ...
2
votes
0answers
50 views

Diameter of the space of unitary operation manifold for quantum computation?

I am considering the unitary operation manifold for quantum computation. In order to examine the computational complexity of an algorithm using n qubits, we need to define the complexity of a certain ...
0
votes
0answers
23 views

Construct bivariate symmetric (polynomial) Hilbert-Schmidt two-qubit volume functions over the unit square with certain properties

Construct bivariate symmetric polynomials (two-qubit volume functions) f(r,R) = f(R,r) >= 0 over [0,1]^2, with f(1,R) = f(r,1)=0, such that the univariate marginal (integrating over r or R) ...
1
vote
0answers
55 views

How is this circuit equivalent to a Bell measurement?

The circuit elements are : CNOT gate, first qubit is the control bit Hadamard gate (H) The dials represent measurements made in the computational basis Therefore, the circuit (without the ...
0
votes
0answers
36 views

How to find a single coefficient of quantum Fourier transform reliably

Quantum Fourier transform transform $X \in \mathbb{C}^{2^n}$ to $Y \in \mathbb{C}^{2^n}$. Suppose one wishes to find $y_0$, the first coefficient of "vector" $Y$. However, as this is quantum process, ...
0
votes
1answer
68 views

Can a classical 50/50 probability be distinguished from a quantum superposition with a single measurement?

$\renewcommand{\ket}[1]{|#1\rangle}$ A "false" (equally superimposed qubit) is created by mechanically firing with 50/50 probability a resonance photon at a Hydrogen atom qubit in the ground state. ...
0
votes
1answer
96 views

How to construct the operator and the physical experiment needed to perform an arbitrary 'measurement in a basis'?

I have taken an introductory level course in QM and have covered some advanced topics by myself and don't really understand what it means to 'measure in a particular basis'. A projective measurement ...
0
votes
1answer
53 views

two qubits measurment [closed]

Let $$\text{qubit} = \sqrt{\frac{1}{6}} (i∣00\rangle + ∣10\rangle − 2 ∣11\rangle) \, .$$ I need to calculate the probability for each state while measuring both qubits in the standard basis. I did : ...
1
vote
1answer
95 views

Positive Partial Transposition in Fano form

Cite from "Geometry of Quantum States: An Introduction to Quantum Entanglement 1st Edition by Ingemar Bengtsson (Author), Karol Zyczkowski (Author)": "Partial transposition applied on a density ...
1
vote
1answer
64 views

What degrees of freedom (other than polarization) of a photon can be used to store quantum information? [duplicate]

Usually in quantum optics, one uses the polarization degree of freedom of the photon to create and manipulate photonic qubits. This, using various linear optics devices, can be coupled with the 'path ...
4
votes
1answer
143 views

How is classical information put into and retrieved from a quantum computer?

How, if you had to find the factors of say a 256 digit number, would you go about inputting the data and how do the proper answers "drop out" of a quantum computer. Other than terms such as qubits, ...
1
vote
0answers
52 views

Weyl's (and others') Unitary Basis

Galitski's Exploring Quantum Mechanics says (on p.29) 'the number of (linearly) independent unitary ($N$-dimensional) matirces is also $N^2$'. Since the set of unitary matrices does not form a vector ...
0
votes
2answers
58 views

Stern-Gerlach: Why is it probability 1/2 for cooked up silver atoms?

Why does cooking up silver atoms in an oven give them equal probability spin up and spin down?
1
vote
1answer
86 views

The GHZ-State in conflict with local realism

Consider three, with respect to their polarisation, entangled particles in the following state: $|\psi\rangle = \frac{1}{\sqrt2}(|H\rangle_1|H\rangle_2|H\rangle_3 + ...
0
votes
0answers
40 views

The Longest Storage Time of Electromagnetically-Induced-Transparency-Based Quantum Memory

Do anyone know any paper that demonstrate the longest storage time of quantum memories protocol based on EIT achieved experimentally? I have tried to look for it on Google but find nothing.
-1
votes
1answer
61 views

Derivation of minimum uncertainty from Squeezed Coherent State [closed]

I'm studying a book in which I stopped by this point. I don't know how to derive the inequality from $$tr(\rho A^{*}A )?$$
2
votes
0answers
73 views

Topological order and entanglement in quantum quench problem

I would like to ask about useful reviews, must-read papers on the study of topological order and entanglement in quantum quench problems that give a good introduction to the topic.
0
votes
0answers
24 views

How much computation can be performed in given time using given energy inside a ball of given volume?

Landauer principle asserts that there are physical limits on computation given finite free energy (although there are ways around it). $E=hc/\lambda$ provides a lower limit on the amount of energy ...