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.

525 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
27
votes
0answers
611 views

Bell polytopes with nontrivial symmetries

Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, v_i}$, possibly in a nondeterministic manner. We are interested in joint ...
13
votes
1answer
315 views

How does one compute the state of a quantum system following imperfect measurement?

Suppose I have a quantum system $S$ ("system") with Hamiltonian $H_S$ and initial density matrix $\rho_S(0)$. I allow $S$ to interact with another system $P$ ("probe"), which has Hamiltonian $H_P$ and ...
9
votes
0answers
159 views

What are good books covering information theoretic approaches to theoretical physics?

I am about to finish my undergraduate studies and am very interested in going into the applications of information theory to either general relativity, or quantum mechanics. However I have been ...
9
votes
0answers
102 views

Does the trace distance specify a unique state

In quantum information, we frequently use the trace distance (see definition) to look at how similar two states are. If I had a known complete set of states $\{\rho_i\}$ and some unknown state $\...
9
votes
0answers
113 views

Topological quantum error correcting codes which are not CSS codes

The most promising-seeming quantum error correction codes for the medium-to-long term are the topological codes, of which the toric code (and variants such as planar surface codes) and colour codes ...
9
votes
0answers
195 views

A beautiful ion-trap proposal for Boson Sampling: what are its limitations?

A very beautiful recent paper, Scalable Implementation of Boson Sampling with Trapped Ions. C. Shen, Z. Zhang, and L.-M. Duan. Phys. Rev. Lett. 112 no. 5, 050504 (2014); arXiv:1310.4860 describes ...
8
votes
2answers
245 views

Homodyne detection as quantum measurement

How is homodyne detection a quantum measurement? In quantum mechanics, the way I'm used to think about obtaining the expectation value of an operator $A$ when the state is $| \psi \rangle $ is as ...
7
votes
0answers
277 views

Understanding the Renormalization Group for Entanglement Entropy

I'm trying to understand the renormalization group (RG), and in particular, how it is used to study entanglement entropy (EE) and c-theorems in quantum field theory (QFT). But I'm having trouble with ...
7
votes
0answers
61 views

Structure theorems of Bravyi-Vyalyi and zero conditional mutual information

A fundamental result in quantum information is that of Bravyi and Vyalyi (Lemma 8, https://arxiv.org/abs/quant-ph/0308021). Result 1: It states that for commuting hermitian operators $H_{ab}\otimes ...
7
votes
0answers
161 views

A 'distance' measure that involves 3 quantum states

The following question was asked by my friend Elie Wolfe. Given two quantum (or even classical) states $\rho, \sigma$, there are various measures that say how 'far' these two quantum states are, such ...
7
votes
0answers
139 views

Completely positive maps and symmetric states

Let $\mathcal{N}$ be a completetely positive trace preserving map (aka a quantum channel) acting on a finite dimensional system $\mathrm{A}$, and let $\pi$ denote the maximally mixed state on $\mathrm{...
7
votes
1answer
475 views

Using open system dynamics to define a quantum state

Background The density matrix of a closed quantum system with Hilbert space $\mathscr H$ evolves according to the von Neumann equation \begin{align*} i\hbar\dot\rho=[H,\rho]. \end{align*} Given a ...
7
votes
0answers
208 views

Is there a way to obtain an RG flow equation for Quantum spin systems using MERA

We restrict ourselves to ground states of translationally invariant 1d quantum systems. I understand that there is the scale invariant MERA(multiscale entanglement renormalization ansatz) which ...
6
votes
0answers
193 views

Kraus operators for two interacting harmonic oscillators: Problem with the calculation (Ex. 8.21 of Nielsen-Chuang)

I'm working with Exercise 8.21 of the Nielsen-Chuang book on quantum information. It illustrates the amplitude-damping quantum channel by the interaction between two harmonic oscillators (the first ...
6
votes
0answers
123 views

The physical picture of uncle Hamiltonian?

Uncle Hamiltonian was built to show the complex relationship between MPS (Matrix Product State) states and Hamiltonians, which claims that for a block injective MPS state, we can build a local ...
6
votes
0answers
75 views

The number of mutually-unbiased bases in dimension $d$

This recent answer points to the concept of a mutually-unbiased pair of bases, which are orthonormal bases $\{e_1,\ldots, e_d\}$ and $\{f_1,\ldots, f_d\}$ of a $d$-dimensional Hilbert space $\mathcal ...
6
votes
0answers
130 views

Hayden and Preskill's paper “Black holes as mirrors” - Classical model of black hole

If someone's read the "black holes as mirrors" paper by Hayden and Preskill which can be found here , Can you please explain to me how the probability of failure in the classical model of the black ...
6
votes
0answers
121 views

What quantum measurement formalism is easiest to implement physically?

As part of my studies and research, I have learned to work with three different measurement formalism which I define to avoid any ambiguity with the nomenclature: General measurements, which are ...
6
votes
0answers
119 views

Known properties of a specific class of quantum states

Recently, I have been studying a quantum protocol for the "Hidden Matching" problem that makes use of states that can be expressed as $$|\psi\rangle=\frac{1}{\sqrt{n}}\sum_{i=1}^n (-1)^{x_i}|i\rangle$$...
6
votes
1answer
139 views

What is the difference between the three types of bosonic reservoirs : sub-ohmic, ohmic and super-ohmic?

I want to ask what is the difference between the three types of bosonic reservoirs that we use in the theory of quantum decoherence: sub-ohmic, ohmic and super-ohmic. I know that there is a parameter "...
6
votes
1answer
347 views

Trying to understand mixed states

I took a basic quantum chemistry course (McQuarrie's "Quantum Chemistry"), but it never dealt with mixed states -- only pure states (or if it did, we never got to it in class). So I'm trying to ...
5
votes
0answers
81 views

Isn't the Church-Turing-Deutsche (CTD) Principle an empirical question?

The Church-Turing-Deutsche (CTD) Principle is the idea that all physical processes are computable by a quantum computer (i.e. quantum Turing machine). Before I knew this idea had a name, I always ...
5
votes
0answers
93 views

Kochen-Specker property in infinite dimensional systems

Motivation Entanglement and entanglement measures are traditionally defined in finite dimensional systems. Nowadays there are very well-known definitions of entanglement measures in quantum field ...
5
votes
0answers
958 views

Relation between Kraus operators and the Choi matrix

Let $\Phi$ be a CPTP map on density operators for a fixed $n-$dimensional state space and fix a basis $\{ | j\rangle \}$. I'm trying to understand the relationship between the Choi matrix $$M_\Phi:= \...
5
votes
0answers
146 views

What's the physical meaning of the eigenvalues of the spin-flipped density matrix?

In the computation of the entanglement of formation(EoF) of a 2 qubits mixed state, $\rho$, according to Wooters, we need to compute the concurrence of the state by computing the eigen values $\{\...
5
votes
0answers
115 views

Is Quantum Correlation A Correlation in Statistics?

One can read in Wikipedia that quantum correlations are the expectation value of the product of the outcomes on the two sides which indicates that $QC(a,b)=\langle( \vec\sigma \cdot \vec a)^{(1)}(\...
5
votes
0answers
119 views

Entanglement inequality (Gaussian vs. non-Gaussian states)

I'm considering a quantum system with $N$ bosonic degrees of freedom labelled by pairs $(x^i,p^i)$, such that the Hilbert space is $\mathcal{H}=L^2(\mathbb{R}^N)$. Given an arbitrary quantum state $|\...
5
votes
1answer
460 views

How to understand Bloch sphere representation?

I'm really new to quantum computation. Now, I'm going through a tutorial article Quantum Computation: a Tutorial (NB: PDF). I was confused by certain points over there. So, on page 5, when the ...
5
votes
0answers
166 views

How can information ever get lost at the event horizon of a black hole?

In the drawing, A and B are two entangled particles in Kruskal coordinates, A is falling into the black hole, B is remaining outside. The lines going through the center are the time coordinates of ...
5
votes
0answers
252 views

About the relation between entropy and Fisher information matrix

It's well known that the Fisher information metric can be given by $$g_{i,j}=-E\left[\frac{\partial \ln(p(x,\theta))}{\partial \theta_{i}}\frac{\partial \ln(p(x,\theta))}{\partial \theta_{j}}\right],$$...
5
votes
0answers
126 views

Distinguishing orthonormal states and measurement operators

In Nielsen and Chuang's text, p.86, they discuss distinguishing states: Suppose states $|\psi_i \rangle$ are orthonormal. Define measurement operators $M_i = |\psi_i \rangle \langle \psi_i|$ for ...
5
votes
0answers
184 views

Reference request: QFT and AdS/CFT for information theorists

There is a lot of buzz recently about connections between quantum information theory and quantum field theory/string theory. I would like to understand in particular how quantum information methods ...
5
votes
0answers
175 views

Geometric measure of entanglement for fermions or bosons?

For a system consisting of multiple components, say, a spin chain consisting of $N\geq 3 $ spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner ...
5
votes
0answers
141 views

Local unitary transformation that maximizes overlap

Could anyone point me in the right direction (reference to papers would suffice) regarding the following: Given two quantum states $|\psi\rangle ,|\phi\rangle \in (\mathbb{C}^d)^{\otimes n}$, where ...
5
votes
0answers
231 views

What is meant by “quantum steering”?

I have become interested in quantum steering after listening a talk and tried to read more about it. I think I am more confused now. My understanding is as follows: Sharing a (entangled) state, Bob ...
5
votes
0answers
175 views

Can a quantum state with infinite variance of photon number be found in nature or artificially created?

Suppose we have a quantum state $\rho$ and let's denote the photon number operator $\hat{n}=\hat{a}^\dagger\hat{a}$ where $\hat{a}$ is the annihilation operator. Let mean photon number $\bar{n}=\...
5
votes
0answers
1k views

projective measurement & POVM

Let us consider the following completely positive map $\mathcal{B}(\mathbb{C}^n)\ni\rho\mapsto L\rho L^\dagger$, where $L\in\mathcal{B}(\mathbb{C}^n)$ is any arbitrary operator (and can have rank $>...
5
votes
1answer
214 views

Tracing out an observable vs integrating over unitaries

Let $O$ be an observable on a Hilbert space $\mathcal{H}$, and let $B$ be a subset of the spins composing $\mathcal{H}$, and let $\bar{B}$ be its complement. Now define $$\displaystyle O_B = \frac{1}{...
4
votes
0answers
54 views

Why can time-translation invariant quantum operations never increase coherence between energy eigenspaces?

Set $\hbar =1$. Let $U(t) = e^{-itH}$ be evolution under a Hamiltonian $H$ (for convenience let's assume $H$ is not degenerate). A time-translation invariant quantum operation $\mathcal{E}$ is one ...
4
votes
0answers
72 views

How can blackholes be fast information scramblers?

I noticed that there was already a post discussing the fast scrambling property of black holes. But it seems no satisfactory answer was given. As mentioned by L. Susskind et. al, the fast scrambling ...
4
votes
0answers
137 views

Von Neumann entropy in the algebraic approach

In the algebraic approach to QM a quantum system has associated to it one $\ast$ algebra $\mathfrak{A}$ generated by its observables. A state is a positive, normalized linear functional $\omega : \...
4
votes
0answers
112 views

Black holes in AdS/CFT

In Swingle's work Entanglement Renormalization and Holography, he mentioned that a black hole in AdS bulk corresponds to a finite temperature boundary state. With the MERA picture of the entanglement ...
4
votes
0answers
143 views

equivalence between grassmann fermion states and $SO(2N,\mathbb{R})$ fermion coherent states

I am importing this question from https://www.physicsoverflow.org/39342/equivalence-between-grassmann-fermion-mathbb-fermion-coherent Cahill and Glauber in the paper 'Density operators for Fermions' ...
4
votes
0answers
68 views

Bounds on the effect of strong coupling

I am interested in bounding the effects of system-environment interaction. Suppose I have an initial state $\rho \in \mathcal{H}_S \otimes \mathcal{H}_E$ where the system and environment might be ...
4
votes
1answer
291 views

Master Equation under a classical fluctuating noise

I have a system as a qubit with Hamiltonian $H_S = \frac{\Delta}{2}\sigma_z$ The interaction Hamiltonian is $H_I = \frac{V(t)}{2}\sigma_z$ where $V(t)$ is a stochastic fluctuating variable. One can ...
4
votes
0answers
96 views

How long does it take to a local perturbation to propagate along a quantum system?

Imagine to have a one-dimensional system in its ground state, and to apply a local perturbation at one edge of the system. How does the system evolve after being perturbed? More specifically, how ...
4
votes
0answers
193 views

Situation after Saini & Stojkovic's paper on unitarity in gravitational collapse and non-formation of black holes?

In their paper, Anshul Saini and Dejan Stojkovic [1] claimed that by calculations it is possible to demonstrate that in a gravitational collapse of a disk, an event horizon is never made for a far ...
4
votes
0answers
58 views

SU(3) interferometry with qutrits

It is well known that a two-mode interferometer can be described in terms of $SU(2)$ group Smerzi. I wonder if something symilar exists for three mode interferometer and qutrit states ? Not only ...
4
votes
0answers
853 views

Quantum vs classical degrees of freedom

It is sometimes stated that any classical underpinnings (rightly non-local) of a general quantum system are unrealistic or unphysical because these require exponentially more information to store what ...
4
votes
0answers
229 views

Eigenvalue of the adiabatic Hamiltonian of Farhi's three qubit 2-SAT problem

I was trying to reproduce example 3.3 of Quantum Computation by Adiabatic Evolution by Edward Farhi et. al. This is an adiabatic algorithm to solve an instance of three qubits 2-SAT problem. I think ...