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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Some good reference to study for first time the Tavis-Cummings model?

I want to study for the first time the Tavis-Cummings model. Is there some good introductory reference (article, paper, book or whatever) to learn the formalism of the model?
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Is there a common mathematical foundation for quantum and classical computation?

Is there a (natural) formalism that neatly and insightfully includes classical and quantum computation? I have a mostly sound basis in quantum mechanics (as a physics grad), and a much less sound but ...
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Schmidt decomposition where is the number of dimension $n_A < n_B$ encoded in the proof?

I am confused about something in Schmidt decomposition. I remind the theorem then a possible proof for it. Schmidt theorem: Let $H_A$ and $H_B$ be two hilbert spaces of dimension $n_A < n_B$ ...
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18 views

Different definitions of conditional quantum entropy

On Wikipedia, the conditional quantum entropy is defined as follows $$H(A|B)_{\rho_{AB}} = H(\rho_{AB}) - H(\rho_B)\tag{1},$$ where $\rho_B$ is the partial state after tracing out system $A$ and $H(...
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24 views

How physical interaction/processes are connected with the information processing?

It is so hard to simulate few particle systems (to deduce information about the next steps of the particles) but those same particles move without spending any resources or concerns in the right ...
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Transitions between states

In the time dependent perturbation theory, transition between two states requires time dependent hamiltonian, V(t). The question is, why the constant or time independent perturbation does is not ...
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32 views

Interaction (Dirac) picture and time dependent perturbation theory

Why in many, if not all, references that discuss the time dependent perturbation theory, they start the discussion with the interaction (Dirac) picture, although, what we need is only solving the time ...
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36 views

Creation $n$-particle states [closed]

The n-particle states are defined by the creation operators on the vacuum state orthonormalized How we prove that the n particle states are ? How we prove:
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31 views

Generalised measurements and collapse

My reference is Nielsen and Chuang's "Quantum Computation and Quantum Information". When introducing qubits, $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$ the authors state that (*)When we measure ...
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Bit threads as noisy quantum channels

In literature on the holographic duality, recently a new way of looking at the Ryu-Takayanagi formula has been presented, where the minimal surface area has been replaced by the maximum number of "bit-...
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Difference between multiphoton signal and, $n$-photon signal state

I was reading decoy state quantum key distribution article, by Lo et.al. (PRL paper , PRA paper). In this article, authors have discussed the possibility of photon number splitting attack due to ...
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Viewing quantum teleportation as a channel

Suppose Alice has two qubits $A'$ and $A$ and Bob has one qubit $B$. The system is in the state $$\rho_{A'}\otimes \Phi^+_{AB} $$ where $\rho$ is an arbitrary state and $\Phi^+$ is the maximally ...
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What is a non-square density matrix? [closed]

At first glance the idea of a non-square density matrix makes no sense because we cannot normalize it to have unit trace. But we can certainly form an outer product $|a\rangle\langle b|$ with $|a\...
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what we call “erase” in the delayed choice quantum eraser experiment?

im thinking about the quantum eraser experiment and I got some insight that I want to check. Suppose that I have the system of the experiment (S): a closed box with 2 slits, with a 1 bit detector (D)...
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96 views

Coarse-graining and probabilities in quantum theory

What is the origin of probabilities in quantum theory if it is not postulated? I mean, how can we interpret Born's Rule as a probability and how does it enter in quantum theory? More than this, I want ...
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Quantum Entropy Venn diagrams

We know that in classical information theory the Shannon Entropies follow such Venn-Diagram approach to summarize its' relations and inequalities between-marginal,joint and conditional entropies. Is ...
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Experimental Parameters and Unitary in a specific Boson Sampling Experiment

I tried to reproduce the data of one of the four historically first BosonSampling experiments. While they present the information in a very accessible form, unfortunatly I fail to understand some ...
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93 views

Is there any definition for $(\hat{a}^{\dagger} \pm \hat{a})^{n}\hat{S} \left | 0 \right> $

Specifically, I want to apply the following operators $\hat{P}^n = \left( \hat{a}^{\dagger} - \hat{a} \right)^n \tag{1},$ $\hat{X}^n = \left( \hat{a}^{\dagger} + \hat{a} \right)^n \tag{2},$ (...
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35 views

Hamiltonian for 2-qubit system

What is the general form of a Hamiltonian for a 2 qubit system? The Hamiltonian for D-Wave system is: $H = K_1\sigma_x^1 + K_2\sigma_x^2 + H_1\sigma_z^1 + H_2\sigma_z^2 + J_{12}\sigma_z^1\sigma_z^2 ...
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What is the nature of the quantum state that could be assigned to a large solid object, that could describe all it's degrees of freedom?

Consider a metallic object. To study it's electrical and thermal properties, we could construct the band structure arising from the Bloch wave vectors of individual electrons in periodic potential. ...
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47 views

Mean value of a discrete operator

Given an orthonormal basis $\{|i\rangle\}$, I am dealing with an operator that looks like this: $$L=\sum_{j=1}^N|j\rangle\langle j|+\sum_{j\ne k}|j\rangle\langle k|.$$ I would like to calculate its ...
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54 views

When does the identity $\|\mathrm{Tr}_B UXU^\dagger\|_1=\|\mathrm{Tr}_B X\|_1$, with $U$ unitary, hold?

Let $\mathcal{H}_{AB}$ be a bipartite, complex Euclidean space, and let $U\colon\mathcal{H}_{AB}\to\mathcal{H}_{AB}$ be a unitary operator. Define the trace norm as $$ \lVert X\rVert_1 = \text{Tr}(\...
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Can any bipartite state be written as $\rho_{AB}=\sum_{ij} p_{ij}\rho_A^i\otimes \rho_B^j$?

I'm having a silly doubt. If $\rho_{AB}$ is separable then we can write it as $$ \rho_{AB}=\sum_i p_i\rho_A^i\otimes \rho_B^i$$ but can we write a general (maybe entangled) state as $$ \rho_{AB}=\sum_{...
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What's the meaning of a new quantum state vector obtained from an operator acting on original quantum state vector

Let's say we have a single photon state vector, i.e., $\left|1\right>$. We know that the state vector is normalized since $\left<1\right|\left.1\right>=1$. If we are taking a creation ...
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Partial trace of matrix product state

I have come accross a formula that puzzles me a bit in the proof of lemma 23 (page 32) of this paper. The authors start from a (translationally-invariant) matrix product state: $$\lvert\psi\rangle := ...
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85 views

Understanding the density matrix for pure states vs. mixed states

So, there's a question in my textbook that explains the following scenario: A physicist runs two experiments A and B to prepare quantum systems in a variety of initial states. In experiment A he ...
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82 views

How to determine the purity and nature of a composite system?

So for the combined state of a pair of two-level atoms, A and B, with a density matrix $$\rho =\frac{1}{2}\lvert g_A, g_B \rangle\langle g_A, g_B \rvert + \frac{1}{2}\lvert g_A, e_B \rangle\langle ...
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461 views

In layman terms: Why can't Quantum Entanglement be used to achieve FTL Communication? [duplicate]

I've found a lot of questions that try to answer this, but I can't quite understand the answers so far. If you can make two particles be entangled, why can't you force one of them into a pattern that ...
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1answer
52 views

Why is the diamond norm called like that?

The diamond norm is a measure of the distance between two quantum channels. If $\mathcal{E}_1$ and $\mathcal{E}_2$ are two channels, then the diamond norm is defined as $$ \delta^{\diamond}(\mathcal{...
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Which spin-1/2 photon states can be used in the context of Bell's inequality violations?

In textbooks, the violation of Bell's inequality is usually demonstrated for spin-1/2 systems in the state $$| \psi \rangle = \frac{1}{\sqrt{2}} \left( | +- \rangle - | -+ \rangle \right).$$ Most ...
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Is it possible to use Bayesian method in improving the measuring conditions and accuracy of an electron's (or photon) momentum and position?

for you who need a definition for what a "Bayesian method" is, and as per wiki's easy definition. it's a method of statistical inference in which Bayes' theorem is used to update the probability for a ...
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Can we create “asymmetric” EPR pairs in experiments?

Asymmetric here is just for lack of a better word. What I am looking for are experiments that can create a simple EPR pair but without 50% 50% chance of each state. As I understand from standard ...
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Irreversibility as an artificial concept and relationship with quantum mechanics

In my statistical physics classes we are following the book Statistical physics of particles - by Mehren Kardar and we were viewing the derivation of the boltzmann equation and irreversibility . ...
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In the many worlds interpretation, where does the energy come from to create branching universes? [duplicate]

In the many worlds interpretation, where does the energy come from to 'create' the new universes at all the branching points? Is it being taken from some infinitely energy-replete background universe? ...
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51 views

Does the principle of superposition hold for open quantum systems?

In closed systems, the dynamical equation is the Schrödinger equation, for which the principle of superposition holds. In open quantum systems, does the principle of superposition hold?
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47 views

Partial trace over continuous degrees of freedom

Let us suppose we have some quantum system whose Hilbert space admits a bipartition $\mathscr{H}\simeq \mathscr{H}_A\otimes \mathscr{H}_B$. Let $|n\rangle_A$ be a basis of $\mathscr{H}_A$ and $|m\...
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Relative entropy of complementary channel

Given a channel $N: A \rightarrow B$, assume there exist two quantum states $\rho, \sigma \in \mathcal{D}(A)$ (where $\mathcal{D}(A)$ refers to positive semidefinite operators with trace 1) that ...
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110 views

Negative-result Measurement interpretation and the Quantum Zeno effect

I'm trying to wrap my head around negative-result, or "interaction-free" measurements that seem to provide very real, actionable information about a system. Such measurements are described in the ...
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47 views

Entanglement swapping proves there are no time paradoxes?

I am trying to make sense of the Delayed Choice Entanglement Swapping: In the entanglement swapping procedure, two pairs of entangled photons are produced, and one photon from each pair is sent ...
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1answer
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Computing flux modulation of the energy spectrum in a DC SQUID

I've been reading some work by Y. Chen et al's paper on tunable couplers for transmon qubits (you can find the work at https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.113.220502) and wanted to ...
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Can one construct a non-zero (conditional) probability in this situation?

Background Inspired by this video I'd like to ask the following question: I'm not an expert at QED or optics. But this is my $2$ cents on the problem: "Do we see the light or the object?" Problem ...
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47 views

Is there a geometrical representation of classical bits, like that of the Bloch Sphere for quantum bits?

Consider only a single qubit. We know that it can be accurately described using the so called Bloch Sphere. Is there a similar geometric construction used to describe classical bits?
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Classical-quantum channel and entropy of output state

The setting: Consider a channel $N$ defined by measuring its input state in some basis $B$ and outputting a density matrix $\tau_i$ for the $i^{th}$ outcome. $$N(\rho) = \sum_i \langle i\vert \rho \...
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How does EPR pair shows simultaneously two defined values?

In the paper "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete ?", it implies that with an entangled state it is possible to know two physical quantities simultaneously. ...
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29 views

How to left-normalize a Matrix Product State

If you are reading this, you should probably have some background in Tensor Networks or Matrix Products States or this will be insufficient information. So when putting a MPS into left (or right) ...
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146 views

Conditional probability between time parameter and operator in quantum mechanics?

Question and Background So I came across a question on conditional probability in quantum mechanics: How is conditional probability handled in quantum mechanics? There's an interesting comment which ...
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82 views

Why do the degrees of freedom of a density operator not match up with the degrees of freedom of a state vector? [duplicate]

The density operator $\rho$ of a mixed 2-qubit system has $4^2-1=15$ degrees of freedom. We can require Tr[$\rho^2$] $ =1$ so that the system is in a pure state. Now we have 14 degrees of freedom. If ...
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84 views

What Prevents Delayed Choice Quantum Eraser Experiment from Being Used to Predict the Future?

Reading about the DCQE experiment commentary by Ross Rhodes. My question is: why can't information about the future state of the idler photon (the one that heads toward the Glen-Thompson prism) be ...
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50 views

What observable(s) does a mirror operate on?

I'm reading this introduction to the Mach-Zehnder interferometer, and I'm confused about what the mirrors are doing. Suppose we're describing the path (upper / lower) and polarization (vertical / ...
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66 views

Kraus operators of a classical quantum channel

Consider a channel $\mathcal{E}: A\rightarrow B$ that maps quantum states $\rho_A\in A$ to $$\mathcal{E}(\rho_A) = \sum_i \langle i\vert \rho_A\vert i\rangle\tau_i\ ,\tag{1}$$ where $\tau_i\in B$ ...