Open main menu
Home
Random
Log in
Settings
About Quantum Protocol Zoo
Disclaimers
Quantum Protocol Zoo
Search
Editing
Compressed Sensing Tomography
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
==Notation== * <math>n</math>: number of qubits in the system * <math>d</math>: Dimension of the Hilbert space. <math>d = 2^n</math> * <math>\mathcal{P}</math>: Set of all <math>d^2</math> Pauli operators. * <math>P</math>: Pauli operator in <math>\mathcal{P}</math>. <math>P = \sigma_1 \otimes ... \otimes \sigma_n</math> * <math>\sigma_i</math>: This belongs to the set of Pauli matrices <math>\{I, \sigma^x, \sigma^y, \sigma^z\}</math> * <math>m</math>: Selected number of Pauli operators. <math>m = O((rd) log d)</math> * <math>\rho</math>: unknown quantum state * <math>t</math>: total number of copies of <math>\rho</math>. <math>t = O((\frac{rd}{\epsilon})^2 log d)</math>, <math>r</math> is the unknown rank and <math>\epsilon</math> is the accuracy in the trace distance * <math>\mathcal{A}</math>: Sampling operator which is a linear map defined for all <math>i \in [m]</math>. Normalisation is chosen because <math>\mathbb{E}\mathcal{A}^*\mathcal{A} = I</math> * <math>\mathbb{E}</math>: expectation value of a random variable * <math>z</math>: statistical noise due to the finite number of samples, or even due to an adversary * <math>y</math>: Vector to describe the measurement procedure * <math>X</math>: Matrix that fits data <math>y</math> * <math>\rho_{DS}</math>: Estimate for the matrix using matrix Dantzig selector * <math>\lambda</math>: Parameter for trace minimisation which is set according to the noise in the data * <math>\rho_{Lasso}</math>: Estimate for the matrix using matrix Lasso * <math>\mu</math>: regularization parameter which is set according to the noise level * <math>C_0, C_1, C^{'}_0, C^{'}_1</math>: fixed absolute constants * <math>\rho_c</math>: For any quantum state <math>\rho</math>, we write <math>\rho = \rho_c + \rho_r</math> where <math>\rho_r</math> is the best rank-r approximation to <math>\rho</math> and <math>\rho_c</math> is the residual part.
Summary:
Please note that all contributions to Quantum Protocol Zoo may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see
Quantum Protocol Zoo:Copyrights
for details).
Do not submit copyrighted work without permission!
To protect the wiki against automated edit spam, we kindly ask you to solve the following CAPTCHA:
Cancel
Editing help
(opens in new window)