Iterative maximum-likelihood reconstruction in quantum homodyne tomography

By Alexander I. Lvovsky. 2003

302 citations recorded by the source corpus.

I propose an iterative expectation maximization algorithm for reconstructing the density matrix of an optical ensemble from a set of balanced homodyne measurements. The algorithm applies directly to the acquired data, bypassing the intermediate step of calculating marginal distributions. The advantages of the new method are made manifest by comparing it with the traditional inverse Radon transformation technique.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/32fcaa7f4f32ab5cf69905d276541f63050956ec

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

A high-fidelity noiseless amplifier for quantum light states (2010, methodology): “About 1 × 10 5 quadrature measurements distributed in 11 values of the LO phase in the [0, π] interval are then acquired to perform a quantum tomographic reconstruction of the states based on an iterative maximum-likelihood algorith”
Confined quantum Zeno dynamics of a watched atomic arrow (2014, methodology): “MaxLike analysis We reconstruct the complete atomic density operator ρt in the basis of the |ne, k〉 and |ng, k〉 states for all k values using the MaxLike algorithm [26].”
Continuous-variable optical quantum-state tomography (2009, methodology): “Another source of error in OHT MaxLik estimation can be the incomplete character of the homodyne mea- surements: the sum of the projection operators Ĝ = î Qi , i is not an identity operator even in the truncated Fock space .”
Preparation of non-local superpositions of quasi-classical light states (2009, methodology): “From these distributions, using a numerical maximal likelihood (MaxLike) algorith”
Midcircuit Operations Using the omg Architecture in Neutral Atom Arrays (2023, methodology): “We use an iterative maximum likelihood estimation algorithm to reconstruct the (lossless) MCM process, constraining the process to be completely positive and trace preserving [76,106,107].”
Entanglement distillation from Gaussian input states (2010, methodology): “After calculating the corresponding values of x̂±, we reconstruct the density matrices for the “+” and “−” modes by the conventional maximum likelihood estimation [24] without any correction of detection losses.”
Enlargement of optical Schrödinger's cat states (2016, methodology): “The reconstruction of both the initial and amplified SC states is performed using the iterative maximumlikelihood algorithm [28, 29].”
Quantum-optical state engineering up to the two-photon level (2009, methodology): “The phase-quadrature pairs from the acquisition were then fed to a maximum-likelihood reconstruction algorith”