# Accurate quantum state estimation via "Keeping the experimentalist honest"

@article{BlumeKohout2006AccurateQS, title={Accurate quantum state estimation via "Keeping the experimentalist honest"}, author={Robin Blume-Kohout and Patrick M. Hayden}, journal={arXiv: Quantum Physics}, year={2006} }

In this article, we derive a unique procedure for quantum state estimation from a simple, self-evident principle: an experimentalist's estimate of the quantum state generated by an apparatus should be constrained by honesty. A skeptical observer should subject the estimate to a test that guarantees that a self-interested experimentalist will report the true state as accurately as possible. We also find a non-asymptotic, operational interpretation of the quantum relative entropy function.

## 21 Citations

Near-optimal quantum tomography: estimators and bounds

- Mathematics, Computer Science
- 2015

Borders on the average fidelity achievable by any quantum state estimator are given, and it is shown that the Bayesian mean estimator is ideal in the sense of performing close to the bound without requiring optimization.

Numerical Estimation Schemes for Quantum Tomography

- Physics
- 2013

This is a PhD dissertation on the latest numerical quantum estimation schemes as of 2012, submitted to the National University of Singapore. The main content of the thesis focuses on accessing…

Statistical Methods for Quantum State Tomography

- Mathematics
- 2013

In quantum state tomography we want to be able to construct an estimate ρ̂ after performing repeated measurements on some unknown ρ. The most widely used method right now to contruct ρ̂ is maximum…

Maximum likelihood quantum state tomography is inadmissible

- Mathematics
- 2018

Maximum likelihood estimation (MLE) is the most common approach to quantum state tomography. In this letter, we investigate whether it is also optimal in any sense. We show that MLE is an…

Choice of measurement sets in qubit tomography

- Mathematics
- 2008

Optimal generalized measurements for state estimation are well understood. However, practical quantum state tomography is typically performed using a fixed set of projective measurements, and the…

A gambling interpretation of some quantum information-theoretic quantities

- EconomicsArXiv
- 2013

It is shown that the difference in their doubling rates is the quantum discord and a quantum extension of Kelly's gambling setup in the classical case gives a doubling rate that is upper bounded by the Holevo information.

Characterization, Verification and Control for Large Quantum Systems

- Computer Science
- 2015

A novel genetic algorithm for quantum control design, MOQCA, is introduced that utilizes quantum coprocessors to design robust control sequences, and extensions to existing OCT algorithms that allow for including models of classical electronics as well as quantum dynamics, enabling higher-fidelity control to be designed for cutting-edge experimental devices.

Quantum Cross Entropy and Maximum Likelihood Principle

- Computer Science, PhysicsArXiv
- 2021

This work defines its quantum generalization, the quantum cross entropy, and investigates its relations with the quantum fidelity and the maximum likelihood principle.

Tomography for quantum diagnostics

- Physics
- 2008

The quantification of relevant statistical errors is an indispensable but often neglected part of any tomographic scheme used for quantum diagnostic purposes. We introduce a novel resolution measure,…

Experiments on Multiphoton Entanglement

- Physics
- 2007

Entanglement lies at the heart of quantum mechanics and challenged the intuition of physicists ever since it was discovered. At the same time, it is a powerful tool that serves as a key resource for…

## References

SHOWING 1-10 OF 28 REFERENCES

Quantum-state estimation

- Mathematics
- 1997

An algorithm for quantum-state estimation based on the maximum-likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be…

The Likelihood Principle: A Review

- Generalizations, and Statistical Implications (with discussion)., IMS Lecture Notes-Monograph Series
- 1988

"J."

- PhilosophyThe New Yale Book of Quotations
- 2021

however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)…

Annals of Physics 207

- 140
- 1991

Journal of Chemical Physics 121

- 6117
- 2004

Phys

- Rev. Lett 94, 070402
- 2005