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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Unitarity of integral transformation from kernel properties

Given a continuous set of bosonic modes $a(x)$, consider an integral transformation of the form $$U a^\dagger(x) U^\dagger = \int dy \ G(x,y)a^\dagger(y). $$ Suppose also that the integral kernel is ...
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Two parameter differential equation solution

I am working on the paper titled "Energetic and entropic effects of bath-induced coherences" (https://arxiv.org/abs/1905.02013)and there is a two parameter differential equation for ...
Meysam Azizi's user avatar
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Why do some scientists think information can be destroyed?

Why is information indestructible?. This article soothed my initial questionings on why information is touted as indestructible, especially when things like black holes are agreed to seem to destroy ...
Detinoy's user avatar
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Inverting an integral relation involving a set of continuous modes

Consider a continuous system of bosonic modes $a(x)$, and the transformation $$U a^\dagger(x) U^\dagger = \int A(x,y)a^\dagger(y) \ dy. $$ My goal is to find $U^\dagger a^\dagger(x) U$ in terms of a ...
Phil K.'s user avatar
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Can an isolated quantum system thermalize in the sense that the time dependent density matrix of the state approaches the micro-cannonical ensemble?

Usually people are interested in ETH, or if subsystems of the closed system thermalizes, or in a restricted set of observables or arguments of cannonical typicality or quantum chaotic systems which ...
Fibonacci M's user avatar
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Partial trace on a two-mode continuous-variable quantum state

I have the following continuous-variable entangled state $$ \left|\psi\right\rangle_{1,2}= \int_{-\infty}^{+\infty} dq_{1} dq_{2}~\psi(q_{1}) f_{G}(q_{2})e^{\frac{i}{2} q_{1}q_{2}}\left|q_{1}\right\...
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Shannon entropy and shortening messages of n bits using a block code [migrated]

This semester I'm taking a course on quantum information and quantum computing. Since I'm very new to information theory I have a problem with understanding a paragraph in my lecture notes. The ...
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How do I show separability/entanglement of a tripartite state?

I am studying for an exam in quantum information and I was experimenting with prooving entanglement/separability of multi-dimensional systems but unfortunately I got stuck. I took the following state $...
DyrusCompany's user avatar
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Definition of the single-particle density matrix

The single-particle density matrix is defined as $$\rho_{ij } = \langle \psi | a_j^\dagger a_i |\psi \rangle . $$ I am curious about the order of the indices. Why is it not $$ \rho_{ij } = \langle \...
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What is the difference between a Lindbladian and a Liouvillian in open quantum systems?

As far as I know, when we try to write the Lindbladian equation in a generalized nice operator basis we get Liouvillian. Is this correct? What are the differences between them?
Rishwi Thimmaraju's user avatar
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How to prove that all extensions of a pure state are product states? [closed]

I tried using the $\rho$ operator for this, and I got nothing. I approached it assuming I have two subsystems $A$ and $B$, both inside their own Hilbert space $H_A$ and $H_B$. And even defined $\rho = ...
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How many base measurements are there? [closed]

Base understanding: Given an n-dimension array a(x1, x2 ... xn), where each given dimension x is an 1-dimensional array in the set R. The data populating x must be non-redundant measurement of reality....
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How many base dimensions are there? [closed]

Let's imagine we have a 1-dimensional line. (This means a flat, straight line). There are electromagnets lying on it. They are like special rocks that can stick to each other and some metals. How ...
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Decomposing (potentially) symplectic transformations

Background Beam splitters Let $\hat{\mathbf r}=(x_1,p_1,x_2,p_2)^T$ be the vector of canonical operators for a two-mode bosonic system. A lossless beam splitter parametrized by an angle $\theta$ ...
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Is stochasticity totally incompatible with current theories of conservation of information in quantum physics?

Most physicists accept the unitarity principle of the universe, according to which the state of a system at any given time must determine its state at any other time (information is never lost, ...
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How do non-local correlations occur in QM without a cause? [closed]

The Copenhagen interpretation of QM ultimately amounts to asserting that non-local correlations occur without a cause since that cause would involve propagation of information faster than the speed ...
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Conceiving an entangling measurement on copies of a two-mode Fock state

Consider two copies of a general pure two-mode Fock state with a definite number of photons $N$ as follows. $|\psi\rangle^{\mathrm{TMFS}}=\sum_{n=0}^{N} c_{n}|n\rangle_{a}|N-n\rangle_{b}$ where $c_n$ ...
JayanthJ's user avatar
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Production spin density matrix $R$ in particle physics and quantum state tomography

I want to perform quantum state tomography. For that, I need to construct a production spin density matrix $R$ . But I am unable to write it. I can write the matrix element for the process eg. $\tau^+ ...
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First excited states of the Heisenberg model on a bipartite lattice/graph

In the antiferromagnetic quantum Heisenberg model \begin{equation} H=J\sum_{\langle i,j\rangle} X_i X_j + Y_i Y_j +Z_i Z_j, ~~~(J>0) \end{equation} if the underlying interaction is biparitite, i.e....
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Bayesian update approach for quantum phase estimation query

Bayesian Estimation Approach for Quantum Phase Estimation: I am interested if my understanding of the iterative method for Bayesian quantum phase estimation is correct before producing computational ...
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What is the oracle in every quantum algorithm? [closed]

I hope this question won't be closed. There is a machine called oracle which appears in a lot of algorithms of quantum computing, such as Deutsch's algorithm and QFT period-finding. This oracle ...
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How does a heat bath measure a system?

In the information theoretic treatment of say, the canonical ensemble, one must maximise the Shannon entropy $$ S =-\sum_i p_i \ln p_i$$ where $p_i$ is the subjective probability for occupying state $\...
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Swap operation in a Radiative Random Unitary Circuit

In ref PhysRevLett.131.220404, the author have studied the scrambling in a Radiative Random Unitary Circuit (RUC) -- a RUC that exchanges qubits with an environment at a rate $p$. It might perhaps be ...
Young Kindaichi's user avatar
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Bit structure in Adiabatic Quantum Computing [closed]

https://arxiv.org/pdf/quant-ph/0007071.pdf In Chapter 6 in the paper "A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability”, by Edward Farhi, Jeffrey ...
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Can Fock states be teleported using conventional boson-based platforms in continuous variables? [closed]

Is it possible to teleport Fock states using conventional bosons-based platforms in continuous variables? Usually with bosons-based platforms people perform two-mode squeezing, beam splitter, and EPR (...
Camilo160's user avatar
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Displacement operator and phase space

I read a paper on open quantum system, it's about non-Markovian process with memory effects. They describe a generic model of two qubits interacting with correlated multimode field. They describe the ...
Yohay Halfon's user avatar
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What are the implications of the EPR bridge information metric being invariant under all conditions, including distance in this universe?

What if the reason why instantaneous state information is able be transmitted between entangled particles through an EPR bridge is that the metric that this is conveyed in is invariant under all ...
Odysseus Ithaca's user avatar
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Encoding information on photon qubit

I study QKD which relies on the single photon as a qubit, on which information is encoded. There are many protocols which mainly differ on how information (bit) is encoded on the qubit : polarization ...
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What is the computational complexity of adding two matrix product states?

I am relatively new to matrix product states (MPS) and I'm interested in the computational complexity of performing an operation of the form A|a> + B|b> where A, B are scalar coefficients and |a&...
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Generator of two-qubit quantum gate

I would like to know how to derive the explicit form of the GENERATOR of a general two-qubit gate (also here), e.g., controlled-rotation Y. From the definition: $$\exp(-i\theta G) \ ,$$ I see it is: $$...
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Decoherence model of two qubits interacting with correlated multimode fields - open quantum system

I read paper on open quantum system, that talk about non-Markovian process and memory effects. they described the system as a generic decoherence model of two qubits interacting with correlated ...
Yohay Halfon's user avatar
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Measurement unit of a tensor product combinations of quantum states in Pusey-Barrett-Rudolph (PBR) theorem proof

I'm dealing with the Pusey-Barrett-Rudolph (PBR) theorem proof, in which we are using a basis built of linear combinations with tensor products. I'm trying to figure out whether measuring those linear ...
Wojciech Szyszka's user avatar
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2 answers
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What can we say about the eigendecomposition of quantum channels?

It is known that quantum channels, being CPTP maps, map density operators to density operators. And thus, they can be seen as superoperators. Similar to operators, where eigenstates and eigenvalues ...
ironmanaudi's user avatar
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Phase-covariant unitaries

A quantum channel $\Phi$ acting on an $n$-mode bosonic space is called phase-covariant if it commutes with the phase-shift operator, i.e. if $U_{\phi}\Phi(\rho)U_{\phi}^\dagger=\Phi(\rho)$ for any $\...
Phil K.'s user avatar
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Can I use a delayed choice quantum eraser to see into the future? [closed]

From what I understand about the delayed choice quantum eraser is that (per the diagram below), an interference pattern will be seen on D0 if a photon hits the last detectors D1 and D2 where they are ...
Alexander Kleinhans's user avatar
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Unitary evolution of the displacement operator in terms of positions and momenta

Consider a set of $M$ signal modes described by the creation operators $\mathbf a^\dagger = (a_1^\dagger,...,a_M^\dagger)$, and let $\Phi_U$ be the channel defined by the conjugation $\Phi_U(\cdot)=U(\...
Phil K.'s user avatar
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Characteristic function of composite channels

For single-mode Gaussian channels $\mathcal C$, it holds that $\mathcal C = \mathcal A_G\circ L_\eta$, where $A_G$ is an amplifier channel described by the action $$\chi_{\rho'}(\xi)=\chi_\rho(\sqrt G\...
Phil K.'s user avatar
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2 answers
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Photon and qubit representation

The photon spin-1 has two states, $\pm\hbar$, just like the spin qubit ($\pm\frac{\hbar}{2}$). From a quantum information point of view, they can encode the same amount of data. However, I am confused ...
deb2014's user avatar
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Multimode unitary channel in terms of action on characteristic function

Consider a set of $M$ signal modes described by the creation operators $\mathbf a^\dagger = (a_1^\dagger,...,a_M^\dagger)$, and let $\Phi_U$ be the channel defined by the conjugation $\Phi_U(\cdot)=U(\...
Phil K.'s user avatar
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Where is my mistake in using a measurement operator instead of Born’s rule to calculate the probability of detecting photons at an arbitrary angle?

As I asked in this question: https://quantumcomputing.stackexchange.com/questions/36998/how-can-i-calculate-the-measuring-probabilities-of-a-two-qubit-state-along-a-cer/37000#37000 From here I know ...
Alex1111's user avatar
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1 answer
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Can we project into Pauli size sectors efficiently?

Suppose that we have a system of $L$ qubits and some Hermitian operator $\mathcal{O}$ acting on the system. We can expand $\mathcal{O}$ in Pauli strings $P_{n}$: $$\mathcal{O} = \sum_{n=0}^{4^{L}}c_{n}...
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On properties of open quantum dynamics and Lindbladians

It is well known that the open quantum dynamics is governed by the Lindblad master equation $$\partial_t{\rho}=\mathbb{L}(\rho)=-\frac{i}{\hbar}[H, \rho]+\sum_i \gamma_i\left(L_i \rho L_i^{\dagger}-\...
ironmanaudi's user avatar
2 votes
1 answer
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Measure of connectivity in Graph States

Given $G = (V,E)$, with the set of vertices $V$ and the set of edges $E$, the corresponding graph state is defined as $$|G\rangle = \prod_{(a,b)\in E} U^{\{a,b\}} |+\rangle ^{\otimes V}$$ where the ...
Young Kindaichi's user avatar
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Is Quantum State Tomography (QST) an inherently supervised or unsupervised problem in Machine Learning?

I am studying how to apply neural networks to the problem of Quantum State Tomography (QST) and I got confused when it comes to decide if this is a supervised or unsupervised learning problem. At ...
Dimitri's user avatar
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Effects of measurement on the entropy in quantum mechanics

How does measurement in quantum mechanics (QM) impact the system's entropy? The measurement process in QM is considered time-irreversible. Are there principles akin to the second law of thermodynamics ...
Omid's user avatar
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Tightly-focusing a single photon

I'm curious about the feasibility, both theoretically and experimentally, of tightly focusing (or spatially trapping) a single photon to guarantee its precise targeting. If it’s possible, isn’t it ...
Omid's user avatar
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Lindblad evolution as continuum limit of a discrete process coupling system and environment

I have trouble understanding the derivation of the Lindblad evolution in terms of the time evolution under a Hamiltonian $H$ in a system-environment Hilbert space $H_S\otimes H_E$, where we trace out ...
Andi Bauer's user avatar
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Does the density matrix still holds for infinite subsytems?

Consider a maximally mixed state composed of $n$ equal qubits. Its density matrix is then:$$\hat{\rho}^{(n)}=\hat{\rho}^{\otimes n}.$$ The eignevalues of such a matrix, $\lambda$ will all be equal (...
Oscarcillo's user avatar
1 vote
2 answers
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Why does the Lamb-Dicke parameter decrease with the number of ions in an ion chain

I would like to understand (ideally with a nice pedagogic reference), why the fidelity of quantum gates in long ion chain decreases with the number of ions in the chain. In this reference, it is ...
StarBucK's user avatar
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Why we cannot transfer information using a spin entangled singlet? [duplicate]

In QM and QE effects an entangled particle pair is called also a singlet with some properties of the two particles like spin, non-locally correlated. However, there is no transfer of information ...
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