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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How to efficiently get the largest probabilities / amplitudes of a quantum state stored as an MPS?

Let's say, that we have the following pure, superposition state $$ |\psi \rangle = \frac{1}{\sqrt{2}}|000001 \rangle + \frac{1}{2}|101101 \rangle + \frac{1}{2}|100100 \rangle $$ stored in the MPS form....
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Formalism to go from distinguishable to indistinguishable states in quantum mechanics, and the probability combination rules?

I was wondering how can we go from an analyzed system of particles, where we have considered them to be distinguishable, to results about the same particles where we consider them indistinguishable. ...
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Is the state $|0101\ldots\rangle+|1010\ldots\rangle$ an $N$-particle GHZ state?

We know GHZ state can write as: $$ |\textrm{GHZ}\rangle = \frac{1}{\sqrt{d}}\sum_{i=0}^{d-1} |i\rangle \otimes \ldots \otimes |i\rangle = \frac{1}{\sqrt{d}}\sum_{i=0}^{d-1} (|\textrm{0}\rangle \otimes ...
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How to understand the frequency picking in spin-boson model in the Born-Markov limit?

I have been reading the book Decoherence and the quantum-to-classical transition by Maximilian Schlosshauer, section 5.3.2 A classical example is the spin-boson model which has the following ...
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In quantum mechanics, is there an actual difference between 'observation' and interaction?

I apologize if this is just me misreading into things. So in some cases I've read that observation is simply interaction, only given a name that's somewhat misleading to the laymen. With the observer ...
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Maximally entangled states of a qutrit system [closed]

How do I construct a qutrit system and then a maximally entangled state for a qutrit system?
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Is quantum entanglement an exchange of something between two particle objects? [closed]

I have quite a few questions about quantum entanglement. I did some research, but I really don't know much about it. How can two particles at a distance interact with each other. Maybe they can ...
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Is Banach-Tarski applied to qubits paradoxical? [closed]

Would it be paradoxical to use the Banach-Tarski theorem onto the Bloch sphere? Let me elaborate by asking you: Do you know how to implement the Banach-Tarski paradox onto the solid sphere in $\mathbb{...
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Quantum Physics, Quantum Correlations [closed]

In the paper "On the Einstein Podolsky Rosen Paradox" , 1964 by J. S. Bell, its really hard to comprehend the physics behind the use of hidden variable lambda. If there are any papers ...
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1 answer
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What is the relation between purity and ${\rm Tr}(\rho^2)$, for a density matrix? [duplicate]

I would like to understand the equivalence for a state $\psi$ to be pure and its density matrix $\rho=|\psi\rangle\langle\psi|$ having the property $$\operatorname{trace} \rho^2=1.$$ For this I should ...
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Calculation on the squashed entanglement

The definition of squashed entanglement:link I read a paper on this topic, and found a good result (Fig.2(a)) from it showing that the squashed entropy can indicate topological phase transition of SSH ...
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Operator Systems vs Operator Algebras

I am someone who works in mathematics, works with operators, and tries to interpret things in terms of a "toy" QM that doesn't necessarily have anything to do with actual QM. Two things in ...
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What happens to the information that a photon carries, when it interacts with another body that reflects, transmits, or absorbs it?

When a photon gets absorbed in a body, it transfers all its information to the body(what we call "being absorbed"). Now, it is the body that further processes the information and releases it ...
1 vote
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On the separability definition of mixed states

Consider a mixed quantum state $\rho_{A \cup B}$ acting on the Hilbert space $H=H_A\otimes H_B$. This state is separable if it can be written as a finite convex combination of pure product states (see ...
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Is the composition of two mixing CPTP maps a mixing CPTP map?

A CPTP map $T$ is called mixing if and only if it has a single fixed point $\rho^*\in S(\mathcal{H})$ (where $S(\mathcal{H})$ is the convex subset of density matrix operators) to which it converges ...
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How to obtain the unitary operator to get specific partial trace?

Is there a unitary $U_{AB}$ such that, for any density operator $\rho$, we have $${\rm {Tr}}_A \left[U_{AB} \left(\frac{I_A}{2} \otimes \rho_B\right)U_{AB}^{\dagger}\right]= \frac{\rho_B}{2}+\frac{I_B}...
1 vote
1 answer
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How do I find the exchange energy from the effective Hamiltonian?

I've just recently started studying noise in singlet-triplet qubits and the exchange interaction (as a function of detuning ${\epsilon}$ and tunnel coupling ${t_c}$) seems fundamental in many studies. ...
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Orthogonal states evolution

I'm a bit little confused about orthogonality in QM. $<a|b>=0$ what does physically mean? Let's suppose that $<a|b>=0$ and for $t=0$ the system is in state a. Is there a possibility to ...
1 vote
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Projection Postulate of Quantum Mechanics. Where does the Projection occur in the detection process?

This question is about a specific instance of the measurement problem. Let's say we excite a single emitter producing a single photon (described by state $ |\psi_{i}>$), which then "travels&...
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What does an effect algebra mean in terms of familiar quantum concepts?

I've heard of this particular representation of quantum theory before and been trying to toy with it for some time: https://en.wikipedia.org/wiki/Effect_algebra but I am not quite sure how to directly ...
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Choi-Jamialkoski Theorem in Phase damping channel [closed]

I am trying to replicate the solution I have to this problem provided by the instructor in the class where I am trying to use the Choi-Jamialkoski theorem to prove that Phase damping channel is ...
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What does $\langle -z|$ mean in this expression $\langle -z|\rho|z\rangle$?

In some formulas of the Wigner function, there is an expression $\langle -z|\rho|z\rangle$ where $|z\rangle$ represents a coherent state. I don't understand what $\langle - z|$ means. Some other ...
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Adiabatic elimination in the presence of single-photon transitions

I am trying to derive an effective Hamiltonian for a system that includes both periodic drives near resonance with certain transitions (that should lead to one-photon transitions) and pairs of drives ...
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Action of Pauli matrices after change of basis

Let $X$, $Y$, and $Z$ be the Pauli matrices represented by $$X=\begin{pmatrix}0&1 \\ 1 & 0\end{pmatrix}, \quad Y=\begin{pmatrix}0&-i \\ i & 0\end{pmatrix}, \quad Z=\begin{pmatrix}1&...
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Energy gap of a Heisenberg model on bipartite lattices

Consider the antiferromagnetic Heisenberg model on some "graph" where each vertex corresponds to a spin-1/2 and the edges represent interaction between the vertices, i.e., \begin{equation} \...
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Possible (Minor) Error in Original Lieb-Robinson Bound Paper

Introduction I was reading through Lieb and Robinson's original paper introducing their eponymous bounds, and I came upon the following statement: The task remains of corroborating our assertions ...
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What happens with the positions in De Broglie–Bohm theory after a filtering mesurement?

According to Quantum Mechanics (QM) after a filtering measurement of an observable $\hat{\text{M}}$ where the result $M_1$ was obtained, the wave function is projected to a Hilbert subspace which is ...
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3 votes
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Calculating entanglement negativity without constructing density matrix

There are two procedures that I know of for finding the von Neumann entanglement entropy of a bipartite system split between $A$ and $B$ - a bad way and a better way. I have in mind computationally ...
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CNOT gate path interference

I have a question on paper "https://doi.org/10.1038/nature02054". In this paper, the CNOT gate is realized using a beam displacer for higher stability. The figure below shows a 1:1 mapping ...
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Projective measurements on composite systems

Let's say we have a single system $A$, with density matrix $\rho_A$, and we perform the projective measurement $\{P_i\}$. The statistics will be given as $p_i = \mathrm{Tr}\{ P_i \rho \}$. Now, say we ...
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Covariance matrix of the complete system when only one mode is heterodyned

Let's say we have a two mode Gaussian state $A + B$ characterized by the covariance matrix $\sigma$ (in block matrix form:): $$\sigma = \begin{pmatrix} \sigma_A & \sigma_{AB} \\ \sigma_{AB}^T &...
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To verify the completely positivity: about conditionally completely positive

I'm reading the paper Assessing Non-Markovian Quantum Dynamics, by M.M. Wolf (PRL 101, 150402 (2008), arXiv:0711.3174). It mentions how to decide whether a generator is a valid Lindbladian generator, ...
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Non Markovain dynamics [duplicate]

What are the examples of the practical implementations of studying the non-Markovian dynamics of such open quantum system (e.g. quantum dot)?
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How does a disentangler disentangle a short ranged entangled (SRE) states in multi-scale entanglement renormalization ansatz (MERA) circuit?

I encounter a problem in understanding the role of disentanglers in Multi-scale entanglement renormalization ansatz (MERA). I do understand that without disentanglers, some short ranged entangled (SRE)...
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Informations about non-Markovianity? [closed]

What are the examples of the practical implementations of studying the non-Markovian dynamics of such open quantum system (e.g. quantum dot)?
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1 answer
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Quantum dots applications [closed]

I wanna find some interesting project for my master thesis concerning quantum dots, meanwhile I'm learning open quantum dynamics (Markovian & non-Markovain). Is there some ideas to combine these ...
3 votes
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Derivation of Nielsen and Chuang's Eq. (8.127) and (8.128) [closed]

In subsection 8.3.6 "Phase damping" of Nielsen and Chuang (2010), the Hamiltonian is given as $$ H = \chi a^\dagger a(b+b^\dagger) \tag{8.126}\label{8.126} $$ and $U = \exp(-iH\Delta t)$, ...
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Looking for reference material in quantum algebra

I want to reconstruct some problems to take my study further deeper that are closely aligned with information retrieval in the form of quantum algebra. but I wonder if there are very limited books ...
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Post-measurement state after homodyne measurements of part of the system

Let us have an $N$ mode Gaussian state and B denote the last mode (for simplicity I just consider a two-modes state) It is said in articles (and for example How to find the covariance matrix after a ...
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Is there a physical intuition behind the disentanglement of Werner states and the sudden death of entanglement?

It is possible to write two-qubit Werner states in terms of a mixture between a Bell state and the maximally mixed state: \begin{equation} \rho_W = \lambda |\Psi_-\rangle \langle\Psi_-| + \frac{1-\...
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Is my simplistic understanding of a Qubit, Superposition and Entanglement correct? [closed]

I've gone through a number of Lenny Susskind's lectures on entanglement (both just for the joy of it and to better understand quantum mechanics) where he delves into the idea of a qubit. For the sake ...
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Nielsen and Chuang give 4 nomenclatures / definitions for projective measurements - are they equal?

What this question is about (the 4 nomenclatures in short): Nielsen, M.A. and Chuang, I.L. state in their famous book (see http://dx.doi.org/10.1017/CBO9780511976667, p. 87 ff.) that there are 4 ...
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How many apparent horizons could the universe have?

I was reading a paper written by Nobel laureate George Smoot, Go with the Flow, Average Holographic Universe, which assumes the holographic principle as true and conjectures that our universe would be ...
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Applying law of the unconscious statistician (LOTUS) to wavefunction

I have a wavefunction $\psi(x)$ given by the points-spread function of a spatial invariant aperture. I define the wavefunction of an arbitrary photon incident on the aperture as $\psi_s(x) = \psi(x-...
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Why does nobody try to calculate the possibility to implement quantum computer with math and physics principle? [closed]

UPDATED: Classic computer can be easily implemented in many ways just in different computing velocities, But we have not found any easy way to construct quantum computer scalable by using quantum ...
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Counterfactual Quantum Computation is Really Weird

In this video https://www.youtube.com/watch?v=dQIfSrRBEgw a high level 'popular' introduction to Counterfactual Quantum Computation is provided. The only part that seemed to 'come out of the blue' was ...
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How to quantify the one-way flow of information in Markovian dynamics

It is said that in the Born-Markovian dynamics (Master equation), the information flow is one way, i.e. from the system to the environment. How to understand this sentence? Is there a quantity of the ...
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Why do Liquid-state NMR qubit only work with fermionic nuclei?

"The ideal picture of liquid state NMR (LSNMR) quantum information processing (QIP) is based on a molecule in which some of its atom's nuclei behave as spin-½ systems." https://en.wikipedia....
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To what extent does Hardy recover quantum mechanics?

In his 2001 paper, Hardy claims to recover quantum mechanics from five reasonable axioms. I am a mathematician and honestly admit that I don't understand the paper. I would like to understand exactly ...
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Can quantum information conservation verified in this specific situation?

Consider a projective measurement of a superposition of states: $$\frac{1}{\sqrt{2}} |\Psi_1\rangle + \frac{1}{\sqrt{2}} |\Psi_2\rangle \xrightarrow[measurement]{projective} |\Psi_1\rangle, \qquad (|\...
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