In this paper, we derive analytic expressions for the starting (initial) values of the parameters of the T-matrix that is frequently employed in the construction of a theoretical density matrix in a Maximum Likelihood Estimate (MLE) procedure; this optimization procedure is used to fit the experimental data pertaining to single qubit state tomography. Appropriate starting values are critical in achieving a global minimum in the fitting process. We also indicate an analytic way of making the experimentally determined density matrix physical without resorting to the MLE process, if optimality in quantum state tomography can be disregarded, since the ultimate goal is optimality in quantum process tomography.In this paper, we derive analytic expressions for the starting (initial) values of the parameters of the T-matrix that is frequently employed in the construction of a theoretical density matrix in a Maximum Likelihood Estimate (MLE) procedure; this optimization procedure is used to fit the experimental data pertaining to single qubit state tomography. Appropriate starting values are critical in achieving a global minimum in the fitting process. We also indicate an analytic way of making the experimentally determined density matrix physical without resorting to the MLE process, if optimality in quantum state tomography can be disregarded, since the ultimate goal is optimality in quantum process tomography.

arXiv:1407.6668Jul 24, 20143 citations

Realizing the Optimal Tomography through a Sequence of Collective Weak Measurements

Ezad Shojaee, Christopher S. Jackson, Carlos A. Riofrío +2 more

Bulletin of the American Physical SocietyMar 7, 20180 citations

On spurious fixed points in iterative maximum likelihood reconstruction for quantum tomography

Florian Oberender

Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density matrix in practice. Contradicting these practical observations, we will show that convergence to a true solution is not guaranteed in general by constructing examples for spurious fixed points. To deal with this newly found problem, we then provide a criterion based on first order optimality conditions to check if the result of the algorithm is indeed the desired solution. Furthermore, we generalize the algorithm and show that it is equivalent to factorized gradient descent.Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density matrix in practice. Contradicting these practical observations, we will show that convergence to a true solution is not guaranteed in general by constructing examples for spurious fixed points. To deal with this newly found problem, we then provide a criterion based on first order optimality conditions to check if the result of the algorithm is indeed the desired solution. Furthermore, we generalize the algorithm and show that it is equivalent to factorized gradient descent.

arXiv:2508.14549Aug 20, 20250 citations

Quantum tomography of $H \to ZZ, WW$ beyond leading orderQuantum tomography of $H \to ZZ, WW$ beyond leading order

J. A. Aguilar-Saavedra, Pier Paolo Giardino

We revisit quantum tomography of $H \to ZZ$ and $H \to WW$ in the presence of higher-order corrections. We verify that neither the use of an effective spin analysing power (only for $ZZ$ ) or a photon veto are sufficient to render the naively-constructed spin density operators physical. A subtraction of higher-order corrections is thus necessary to perform consistent quantum tomography. Such corrections are small when compared to expected experimental uncertainties with current data. As a by-product, we point out the striking possibility to observe parity-violating effects in $H \to WW$ .We revisit quantum tomography of $H \to ZZ$ and $H \to WW$ in the presence of higher-order corrections. We verify that neither the use of an effective spin analysing power (only for $ZZ$) or a photon veto are sufficient to render the naively-constructed spin density operators physical. A subtraction of higher-order corrections is thus necessary to perform consistent quantum tomography. Such corrections are small when compared to expected experimental uncertainties with current data. As a by-product, we point out the striking possibility to observe parity-violating effects in $H \to WW$.

hep-phCross-listedarXiv:2603.11288Mar 13, 2026

On density matrix reconstruction from measured distributions

Matteo G. A. Paris

Optics CommunicationsMar 1, 199615 citations

Quantum tomography of

H \to ZZ, WW

beyond leading order

We revisit quantum tomography of

H \to ZZ

and

H \to WW

in the presence of higher-order corrections. We verify that neither the use of an effective spin analysing power (only for

ZZ

) or a photon veto are sufficient to render the naively-constructed spin density operators physical. A subtraction of higher-order corrections is thus necessary to perform consistent quantum tomography. Such corrections are small when compared to expected experimental uncertainties with current data. As a by-product, we point out the striking possibility to observe parity-violating effects in

H \to WW