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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Product of ground eigen-energy with highest eigen-energy of 3 qubits

Consider a 3-qubit quantum system with ground state $|\psi_0\rangle$ and highest energy state (for the problem at hand, in general there might be higher) $|\psi_{\rm top}\rangle$. The corresponding ...
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Truncated Completely Positive Trace Preserving (CPTP) maps

Let us consider the the Liouville equation of a level $N$-system with density matrix $\rho$ together with its standard properties (positive semi-definite, unit trace, etc). The evolution of the system ...
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Code distance and other questions about Quantum double model as an error correcting code

Kitaev's quantum double model is an error correcting code, see: https://arxiv.org/abs/1908.02829 I am in a class on quantum error correction and the professor commented that a quantum double model for ...
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Is the circuit unitary in Nielsen's method for calculating complexity?

I was trying to learn how to calculate circuit complexity (1707.08570) when I chanced upon a seemingly confusing concept. The "Nielsen method" involves looking at a unitary transformation $U$...
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Displacement measurement in quantum optics

I was following a talk where it was stated that performing a displacement $D(\alpha)$ on an optical mode, followed by a single-photon detection without number resolution, corresponds in the case of no-...
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39 views

On the invariance of $ \rho |\psi \rangle$? (For Wigner and his friend)

Motivation So let's say I shoot circular polarized light which is either right $| R \rangle$ or left $| L \rangle$ polarized. My friend notices that I choose left and right equally $50$% of the time. ...
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Measuring a qubit in the wrong basis

I'm a computer scientist and right now I'm trying to end the research work for my master thesis and a basic problem of quantum mechanics is blocking me. I'm trying to do a probability calculus of the ...
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24 views

Why is Measurement Device Independent (MDI) Quantum Key Distribution (QKD) truly MDI?

I am having a hard time understanding why MDI-QKD is truly measurement device independent. My current vision is that Charlie (the one who performs the Bell state measurements) is simply sampling the ...
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69 views

Why are rotation operators and Pauli rotations defined so that $R_x(\pi)\neq X$?

When applying a Hadamard Gate Wikipedia defines it as $XR_y(\frac{\pi}{2}) = H$. The effect of a Pauli Gate $X$ is defined as a Rotation of $\pi$ radians about the x-Axis on the Bloch sphere. The ...
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78 views

Gaussian envelope operator applied to an arbitrary wave function

I am studying the reference given in [1]. In that, the authors define the non-unitary "Gaussian envelope" quantum operator $\mathcal{\hat{M}}$ (see Eq. 4 in reference [1]): $$\mathcal{\hat{...
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Is a room-temperature & pressure single-photon sensor theoretically possible?

In the realm of photonic quantum computing, single-photon sensors are required for determining the outputs of each chip. Unlike most forms of QC, photonic chips themselves may be run at room ...
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XOR/CNOT on 2 qubits in superposition - Deutsch [closed]

In an attempt to understand the design and to show that the Deutsch algorithm works with and only with sets of perpendicular qubits, my head got stock on this. What is $(|0⟩ - |1⟩) ⊕ (|0⟩ + |1⟩) = ? $ ...
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Proof that joint-measurability means commutativity

For $i=1,2$, two measurements $m_{i}:\mathcal{X}_{i}\to\mathcal{L}(\mathcal{H})$, from alphabet $\mathcal{X}_{i}$ to set of bounded linear operators on Hilbert space $\mathcal{H}$, are compatible or ...
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LOCC distinguishability of a mixture of Bell states

Consider the Bell states \begin{align} |\psi^0\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle),& \quad |\psi^1\rangle = \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle), \\ |\phi^0\rangle = \frac{...
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What's the big deal with information being lost in a black hole?

In the video here: https://www.youtube.com/watch?v=d_XuFkVdAYU (10:57), it is said that the loss of information when matter falls into a black hole is a paradox. He gives an example of throwing a ...
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Time evolution of $\pi/2$ pulses

This is the topic Ramsey interferometry. I want to do this without referencing the Bloch sphere, just with the Hamiltonian (given on Wikipedia and below) and Time-Dependent Schrodinger Equation. A $\...
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What is the relation between joint measurability and common refinement (pure state decomposition) of density operators?

Here page 13, the author states "...just as two quantum observables are often not jointly measurable, two decompositions of mixed states often have no common refinement (Actually, in the ...
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Why do $\pi/2$ pulses make a $\pi$ pulse?

This is the topic Ramsey interferometry. I want to do this without referencing the Bloch sphere, just with the Hamiltonian (given on wikipedia) and Time-Dependent Schrodinger Equation. A pi/2 pulse in ...
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52 views

Are all physically realistic Hamiltonians local?

My understanding of modern physics is that physicists think that, fundamentally, physical laws are local. For system A to interact with system B, they either need to be very close to each other or ...
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Indistinguishability and different pure state decompositions of mixed states in non-simplex convex set of states in Quantum Statistics

In statistical physics (mechanics), the transition from Maxwell-Boltzmann statistics to Bose-Einstein and Fermi-Dirac statistics was motivated by classically inexplicable phenomena such as Bose-...
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72 views

When is the Liouvillian superoperator not diagonalisable?

An $n \times n$ matrix, $L$, is diagonalisable if it has $n$ linearly independent eigenvectors. I've recently been working with open quantum systems and come across the non-hermitian, Liouvillian ...
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41 views

Mixed state in single mode Light? [closed]

Most quantum optical textbooks introduce thermal light (blackbody radiation) as an example of a mixed state. And those states covered in most of the textbook represents a Fock state, the state of the ...
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How to derive the theorem about CHSH inequality in the $\mathbb{C}^2\otimes\mathbb{C}^2$ space in (Horodecki, 1995)?

In the $\mathbb{C}^2\otimes\mathbb{C}^2$ space, a state can be represented as: \begin{equation} \rho=\frac{1}{4}(\mathbb{I}\otimes\mathbb{I}+\mathbf{r}\cdot\mathbf{\sigma}\otimes\mathbb{I}+\mathbb{I}\...
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56 views

Can the Hermitian operator be related to state space to describe physical phenomena?

Can space-time, in which phenomena occur, and the space of states in which phenomena are described by means of the Hermitian operator be related? I suspect it is because the hermetic operator is built ...
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Why does applying the PPT criterion to the Werner state result in an inequality?

The so called partial transpose criterion (PPT), https://en.wikipedia.org/wiki/Peres%E2%80%93Horodecki_criterion, tells us that is the partial transpose of a density matrix has a negative eigenvalue, ...
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More general quantum measurements than Nielsen and Chuang's general measurement

Background Nielsen and Chuang give a postulate for "general measurements" on quantum systems (which are provably equivalent to unitary time evolution + projective measurements on ancillas) ...
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Existence of informationally complete POVM on infinite dimensional Hilbert space

Do there exist informationally complete POVM (in this sense) on infinite dimensional separable Hilbert spaces? It is known that these exist in finite dimensions (I believe they were used in the proof ...
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65 views

Confusion about interpretation of expectation values in quantum mechanics

Given a state $|\psi \rangle$ one can form the expectation value of an observable $O$ as: $$ \langle \psi|O|\psi \rangle. $$ For the case $O = H$, where $H$ is the Hamiltonian of the quantum system, ...
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64 views

Why is high energy required if we want to send a message in a short amount of time?

I am somewhat puzzled by the following statement "If Alice, after crossing the horizon, has less than a Planck time to communicate with Bob about the status of her qubits, then she is required to ...
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49 views

What exactly is quantum entanglement in simple words?

What exactly is quantum entanglement in simple words? Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and ...
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60 views

Basis representation of hamiltonian

I do not understand this representation of a Hamiltonian involving the basis projection operator and Identity matrix. $$\begin{align} \hat{H}_0&= \sum_{n_1,l_1,j_1,m_{j1} }E_{n_1 l_1 j_1}\left|...
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Applying CNOT in series to ancilla qubit

$\renewcommand{ket}[1]{\left| #1 \right\rangle}$ $\renewcommand{bra}[1]{\left\langle #1 \right|}$Suppose we have to qubits both in the state $\ket{+ }= \frac{1}{\sqrt{2}}(\ket{0}+\ket{1})$, and we ...
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How the probabilities are calculated: Shannon's noiseless coding theorem?

This question refers to the section 13.1.2 of the book: Quantum Information, Computation and Communication by JONATHAN A. JONES AND DIETER JAKSCH The text goes as following: " We choose to encode ...
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How to experimentally orient the rotation axis in the Bloch sphere during Rabi oscillations?

Rabi oscillations are well known in the field of quantum physics. I have seen plots of experimental realizations of Rabi oscillations. However, I do not understand how to manipulate the rotation axis ...
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Information travel in the universe

I was wondering how information travels in the universe? I know that information cannot travel faster than the velocity of light, but how exactly does this transfer happen? Like is there any physical ...
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What is the relationship between "quantum coherence" and "coherent states"?

What is the relationship between Quantum coherence and Coherent States? I (almost) get the concept of Quantum Coherence when i think about it in the framework of density matrices. I also get the ...
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67 views

Availability of dataset from "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres"?

I am looking for the most-raw data from the (in)famous Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres experiment. I would like to try repeating their ...
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Matrix multiplication in Feynman's paper on quantum mechanical computers

In a paper by Feynman, on how to embed a Turning machine in the ground state of a many-body quantum system, a product of two matrices is defined (equation 1). This product does not appear to have the ...
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Is an orthonormal eigenbase of an observable Hamel or Schauder?

Suppose $\mathcal{H}$ is an infinite-dimensional Hilbert space, and let $A$ be an observable. The quantum system is prepared in a state $\vert \Psi \rangle$. After measuring the observable the state $\...
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Can the P-Gate be written in terms of pauli matrices?

The P-Gate is an operation which maps $a|0\rangle+b|1\rangle$ to $a|0\rangle+be^{-i\phi}|1\rangle$ by means of a phase shift and can be written as \begin{pmatrix}1& 0 \\ 0 & e^{-i\phi}\end{...
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Computers, quantum information and computational complexity in Kerr-AdS black hole backgrounds

A Kerr-AdS black hole is eternal, never evaporates and has a Malament-Hogarth metric. Bob, a universally programmable reversible classical computer with a fixed maximum memory who only outputs one ...
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Proof that you can't disentangle two parties if you only operate on one

Let $A$ and $B$ be two entangled systems. Can someone prove or sketch a proof of why you cant unentangle $A$ and $B$ by only acting on $A$ or $B$ alone? i.e. by only applying $\mathbb{I}_A\otimes U_B$,...
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Can the degree of entanglement be an order parameter in a phase transition?

In most continuous phase transitions, there is a well-defined order parameter $\langle \psi \rangle$ of some observable that is zero above the transition temperature, and continously grows below the ...
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42 views

General Qutrit Computational Basis with $U(3)$ transformation

I am interested in constructing a general qutrit computational basis $\{|0\rangle,|1\rangle,|2\rangle\}_{(\theta,\varphi,\phi,\psi)}$, that is, writing the most general $U(3)$ transformation matrix (...
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What is the canonical basis in quantum mechanics?

In a paper from 2018, Johannes Bausch et al refers to a classical state of a many-body quantum system to be a product state in the canonical basis. I was wondering what this “canonical basis” is ...
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The deriviation of displacement operator in Quantum Optics?

I've been studying coherent state, then I meet some problem. My teacher told me, one can derive displacement operator via complexify the parameter $\alpha$ in this formula: $$|\alpha\rangle=e^{\alpha( ...
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35 views

Translation or permutation operator on a kronecker product

Let's say that I have an initial state given by { $| i_1\rangle \otimes | i_2 \rangle \otimes \dots \otimes | i_l \rangle $} can I find an operator $\mathbb{T}$ that shifts the state such that: $\...
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68 views

Intuition behind why density operator contains complete information about the system?

I have read this and I want to know why is that the case, and why not simply write two (or more) particles with their 'pure' states, because the latter is much more straightforward?
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83 views

What is the mathematical setting of the Jordan-Wigner transformation?

If I have a system of $N$ fermions, and a system of $N$ qubits/spin-$1/2$ particles, the Jordan-Wigner transformation allows me to represent the fermionic operators $a_i, a_i^\dagger$ in terms of ...
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Do all entangled states violate some Bell inequality?

Suppose I have a multipartite pure entangled two-level system. Is it always possible to form a bell-inequality based on this state such that the observed correlations cannot be reproduced classically? ...

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