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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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Mathematics of quantum mechanics for beam splitter

I'm reading a book where quantum interference is explained with a common experiment, where photons are thrown to some apparatus formed by two beam splitters: Describing the problem using linear ...
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How to evaluate the probability when a particle is detected?

Everyone knows the standard probability interpretation of the quantum mechanics. For example, the wave function of some particle at some time $t$ is $\psi (x,t)$. Therefore, if the particle is ...
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Why does the read-out efficiency increase when coupling an atomic ensemble to an optical cavity?

I went through a paper where it mentioned that the read-out efficiency of a quantum memory would be increased by coupling the atomic ensemble with an optical cavity. I think rydberg atoms were used to ...
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How to understand the quantum operators [on hold]

I am reading a research article based on quantum image watermarking, Sang, J., Wang, S. & Li, Q. Quantum Inf Process (2016) 15: 4441. https://doi.org/10.1007/s11128-016-1411-z The authors ...
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Can we recover a state on a composite system from a state on the subsystem?

$\renewcommand{\ket}[1]{\left \lvert #1 \right \rangle}$ $\renewcommand{\bra}[1]{\left \langle #1 \right \rvert}$ I'm wondering if we can recover the state of a composite system from the information ...
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Application of improved compatibility

It's a standard piece of quantum information theory that noise can be helpful in augmenting compatibility of quantum observables. For example given a qubit state $\rho$ and the two Pauli observables $\...
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Where's the Database in Grover's Algorithm

I am a little confused by parts of Quantum Computation and Quantum Information by Nielsen and Chuang on Grover's algorithm: Grover's algorithm searches a number of quantum states for a "marked ...
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How does quantum memory work using atoms? [closed]

My understanding is that two photons are prepared together which are said to be entangled, one of the photons interacts with an atom and the state of the atom changes according to the what state the ...
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Quantum Measurement in Different Basis [duplicate]

How can you make measurements on a qubit that is in a different basis than your measurement qubit? (i.e. You want to measure a single qubit in the $|+\rangle$/$|-\rangle$ basis but you can only make ...
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Say you run qubit $A = (|0⟩ + |1⟩) / √2$ and qubit $B = |0⟩$ through a CNOT gate. What is the state of qubit $B$ afterwards?

I am new to the weeds of quantum computing and this question is probably pretty elementary. Say you run qubit A = (|0⟩ + |1⟩) / √2 and qubit B = |0⟩ through a CNOT gate. What is the state of qubit B ...
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Does taking partial trace commute with local operators?

Suppose we have a big system with two subsystems $H=A\otimes B$. For a unitary $U$ in the Hilbert space $A$ and a state $\rho$ in the Hilbert space $H$. Is the following statement true? $$ \text{Tr}_B ...
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Constructing Lindblad operators

When considering the dynamics of open quantum systems in the markovian approximation, it is known that its master equation must be of the GKSL form $$\dot{\rho}(t) = -i[H(t),\rho(t)]+\sum_k \gamma_k(t)...
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Quantum tunneling requirements

Why does quantum tunneling require a narrow potential barrier? I mean what makes zener diodes so unique is that they dont undergo heating because their potential barrier is very narrow.
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Calculate $x+y$ probabilistically from qbits in state of $\frac{1}{\sqrt{2}}(|x\rangle + |y\rangle)$

Assuming we have $N$ qbits, it is placed in a composite state that correspond to integer $x$ and $y$: $\frac{1}{\sqrt{2}}(|x\rangle + |y\rangle)$. The actual integer $x$ and $y$ being unknown. Is it ...
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Local rotations to make a density matrix visually appealing?

I'm curious if there are general rules for finding the local rotations on a density matrix which make it most visually appealing? I have approached this problem in the past from the perspective of ...
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How can one get the density operator from the characteristic function?

To solve analytically the master equation of two qubits interacting with a cavity mode through their environment we use the charactristic function, $$\chi (\beta)=\operatorname{tr}[\rho D(\beta)],$$ ...
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Pinch points in fidelity per site (quantum phase transitions)

In Sachdev's Quantum Phase Transitions he defines a quantum phase transition in an infinite lattice as the point in which the ground energy as a function of the parameters of the system becomes non-...
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QFT Hilbert space and analysis of quantum black holes

QFT Hilbert space is infinite dimensional and it is known that given a region $A$ and its complement $A^c$ of the spacetime, the QFT Hilbert space $\textbf{does not}$ decompose into $\mathcal{H}_A \...
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Does a polarizer affect both entangled photons or only one?

Suppose you have two polarization-entangled photons A and B in the following state: \begin{equation} \Phi=\frac{1}{\sqrt{2}}\bigl(\left|H_{A},H_{B}\right\rangle + \left| V_{A},V_{B}\right\rangle\bigr)...
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Calculating the probability of one particle being in a certain state in two-particle system

Let's say I have the two-particle state $$|\psi\rangle=\frac{|H\rangle_a|H\rangle_b+|V\rangle_a|V\rangle_b}{\sqrt{2}}$$ where $H$ is horizontally polarized and $V$ is vertically polarized. And I ...
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The maximally mixed state is at the center of all quantum states

The set of quantum states $\rho$ in $d$ dimensions is the set of positive semidefinite operators living in a Hilbert space of dimension $d$. Let us denote this set by $\text{Pos}(X)$ and note that ...
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Closest separable/ closest PPT state given an arbitrary state?

After searching for results, the closest result I found was https://aip.scitation.org/doi/pdf/10.1063/1.3591132?class=pdf. The summary of that paper is: Given an arbitrary seperable/PPT quantum state ...
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AD and PD channels

The well-known Amplitude Damping (AD) and Phase Damping (PD) channels are characterized, respectively, by the following Kraus operators: \begin{equation}\label{KrausAD} O^{AD}_0 = \begin{pmatrix} ...
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Quantum logic gates (2-inputs 1-output)

Is there a quantum logic gate (or any sequence of QLGs) that takes as input two Qubits and outputs one Qubit? If yes, could you please write it down in the simple example? If no, could you explain ...
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Verifying the “quantum teleportation identity” in $\mathbb{C}^2 \otimes \mathbb{C}^2$ (Bell basis)

$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}$ Let $\{\psi_{i,j} : i, j = 0,1\}$ be the Bell basis of $\...
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Can we write the Quantum Fidelity between two density operators in terms of Quasi-Probability Distributions: $P$, $Q$ and $W$?

Quantum Fidelity between two density operators, $\hat{\rho}$ and $\hat{\sigma}$, is given by $F(\hat{\rho},\hat{\sigma})=\left(Tr\sqrt{\sqrt{\hat{\rho}}\hat{\sigma}\sqrt{\hat{\rho}}}\right)^2$, where $...
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Does adiabatic quantum computation require the initial and final ground states to be non-orthogonal?

Background At a recent talk, I was told by the speaker that it is not possible to adiabatically transfer from one ground state $|\psi_0 \rangle$ to another $|\psi_1 \rangle$ if these states are ...
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Could a non-unitary time evolution violate the no-cloning theorem?

It is written in some places that the unitarity of time evolution is what prevents quantum cloning. However, consider the typical definition of a cloning operator $A$. For all $\left|\psi\right>$ ...
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What is the difference between coherent states and the entangled states used in quantum illumination?

I've been reading about utilising quantum illumination systems to out perform classical microwave radars, but I've gotten confused over a point they're making regarding the distinction between the ...
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What do the area laws for mutual information and correlations actually state? [closed]

I am trying to understand what are the key points of this paper: Area laws in quantum systems: mutual information and correlations. If I understand correctly the law states that the information flux ...
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What is “Rotational Invariance” in the context of qubits

In this question the state, $\frac{1}{\sqrt{3}}\left|00\right\rangle +\frac{1}{\sqrt{3}}\left|01\right\rangle +\frac{1}{\sqrt{3}}\left|11\right\rangle$, has been said in the answers to not be able to ...
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PEPS expression of Toric Code ground state

It is well known that the ground state of 2D Toric Code system can be represented by $D=2$ PEPS (Projected Entangled Pair States, i.e. the tensors in the 2D network are connected by 2-dimensional ...
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Definition of the fully depolarizing quantum channel

The fully depolarizing quantum channel in a $d$ dimensional Hilbert space is defined by $$ \mathcal N^D (\rho) = \text{Tr}[\rho]\frac I d $$ I've seen that definition in several places but I don't ...
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“Interaction-Free” measurement involving statistical mixtures

What happens in the standard "interaction free measurement" when the detector connected to a bomb is replaced with attenuation (where light is lost through a semi-transparent medium)? Consider the ...
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Is the disposition of $1$s and $0$s when writing orthogonal ket vectors purely conventional?

If I want to define the basis in the form of $4$-vectors, how do I proceed to make sure they are orthonormal with one $1$ and three $0$ in each vector? Is it just by convention? Does it matter if I ...
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Why does $\max\{S(\rho_A)-\sum_i p_i S(\rho_A^i)\}$ measure classical correlations, and not full (classical + quantum) correlation?

Let a quantum system be given which has two subsystems $A$ and $B$ so that the Hilbert space decomposes $\mathscr{H}\simeq \mathscr{H}_A\otimes \mathscr{H}_B$. If the state of the system is $\rho$, ...
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Perfectly distinguishable states are mutually orthogonal

$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}$ Let $H$ be a Hilbert space. We call states $\ket{\psi_1}, \...
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Quantum teleportation with moving Alice and Bob

I have questions regarding quantum teleportation, which keep confusing me. Suppose Alice and Bob are in the same inertial frame K, and at time t (in K) Alice teleports a quantum state to Bob. What I ...
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Fidelity and approximately unentangled states

It is well known that fidelity distributes over product states, i.e. $$F(\rho \otimes \rho, \tau \otimes \tau) = F(\rho, \tau) \cdot F(\rho, \tau),$$ and more generally, $$F(\rho^{\otimes N}, \tau^{...
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So is quantum entanglement actually FTL “communication” or is it mundane pre-determination?

I have to say right off the bat, I'm a little frustrated that there seem to be very contradictory answers about this, at least to a layman like me. If two particles are entangled and you separate them ...
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Photon encoding and computational limit of the universe

The amount of information or entropy that can be contained in a region of space is given by the Bekenstein Bound: $I \leq \frac{2\pi RE} {hc \ln2}$ However, recent publications have shown ...
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Photon qubits - does photon entanglement hold for detecting polarizations?

Suppose we produce two entangled photons with perpendicular polarizations. If we place a polarizer followed by a detector for the direction of the one photon, and that detector some instant of time "...
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Is it true that I can construct all expectation values using only tensor products of local Pauli operators?

I understand that the Pauli operators and the identity matrix span the space of complex 2x2 matrices. Let's say you have two qubits and you can perform projective meausurements. So you can measure ...
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How unique is the Schmidt decomposition?

I read the Schmidt basis is unique "up to a phase" or as stated here in answer given by Norbert Schuch "modulo degeneracies". If I choose a Bell state $|\psi\rangle = \frac{1}{\sqrt{2}}\left(|0\...
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Constructing a staggered translation operator

Consider a matrix as a function of position $x$ $$C=\begin{bmatrix} 0 & A(x) \\ B(x) & 0 \end{bmatrix} .$$ Is it possible to construct a matrix $S$ that translates $A$ and $B$ oppositely? $$...
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What is a definition of the trace norm?

I have found that (one?) definition of the trace norm is $$\mid\mid A\mid\mid = \sqrt{A^*A} \tag{1}$$ but now I am reading this paper where (on page 4) it says In particular, we will restrict ...
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Notation in a question on probabilities and particle counting

I'm working through Stephen Barnett's book on quantum information and have come across the following question (1.5, for anyone keeping track at home) A particle counter records counts with an ...
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Possible to write $N$-partite W state as sum of less than $N$ product states?

The $N$-qubit W state is $|W\rangle = \sum_{n=1}^N |n\rangle$ where $$|n\rangle \equiv |0\rangle_1\cdots|0\rangle_{n-1}|1\rangle_n |0\rangle_{n+1} \cdots |0\rangle_{N}$$ is the product state with the ...
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Constructing two-qubit density matrix given expectation values of all products of Pauli operators

I think my question breaks down into two parts. Let's say you have a two qubit system and you can perform projective measurements. Each round of measurements will consist of results looking like ...
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parity oscillation in trapped ions

I am trying to understand this trapped ion paper. More specifically, I am trying to understand what they are exactly varying, when they are varying 'the phase'to obtain the oscillation of the parity....