# Least-bias state estimation with incomplete unbiased measurements

@article{ehek2015LeastbiasSE, title={Least-bias state estimation with incomplete unbiased measurements}, author={Jaroslav Řeh{\'a}{\vc}ek and Zdeněk Hradil and Yong Siah Teo and Luis L. S{\'a}nchez-Soto and Hui Khoon Ng and Jing Hao Chai and B. G. Englert}, journal={Physical Review A}, year={2015}, volume={92}, pages={052303} }

Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing unbiasedness on the probabilities for the unmeasured bases does not generally yield the estimator with the largest von Neumann entropy, a popular figure of merit in this context. Furthermore, this imposition typically leads to mock density matrices that are not even… Expand

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#### References

SHOWING 1-10 OF 69 REFERENCES

Quantum state tomography: Mean squared error matters, bias does not

- Physics, Mathematics
- 2014

Because of the constraint that the estimators be bona fide physical states, any quantum state tomography scheme - including the widely used maximum likelihood estimation - yields estimators that may… Expand

Quantum-state reconstruction by maximizing likelihood and entropy.

- Mathematics, Medicine
- Physical review letters
- 2011

A reconstruction scheme is derived where both the likelihood and the von Neumann entropy functionals are maximized in order to systematically select the most-likely estimator with the largest entropy, that is, the least-bias estimator, consistent with a given set of measurement data. Expand

Optimal, reliable estimation of quantum states

- Physics
- 2010

Accurately inferring the state of a quantum device from the results of measurements is a crucial task in building quantum information processing hardware. The predominant state estimation procedure,… Expand

Verification of state and entanglement with incomplete tomography

- Physics, Computer Science
- 2012

This work proposes an estimation scheme, catered to measurement data of this kind, to search for the exact maximum-likelihood-maximum-entropy estimator using semidefinite programming and a standard multi-dimensional function optimization routine. Expand

Optimal state-determination by mutually unbiased measurements

- Physics
- 1989

For quantum systems having a finite number N of orthogonal states, we investigate a particular relation among different measurements, called “mutual unbiasedness,” which we show plays a special role… Expand

Constructing Mutually Unbiased Bases in Dimension Six

- Physics
- 2009

The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist… Expand

Quantum state tomography with incomplete data: Maximum entropy and variational quantum tomography

- Physics
- 2013

Whenever we do not have an informationally complete set of measurements, the estimate of a quantum state can not be uniquely determined. In this case, among the density matrices compatible with the… Expand

Numerical evidence for the maximum number of mutually unbiased bases in dimension six

- Physics
- 2007

Abstract The question of determining the maximal number of mutually unbiased bases in dimension six has received much attention since their introduction to quantum information theory, but a… Expand

Optimal quantum tomography of permutationally invariant qubits

- Physics
- 2013

Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exists,… Expand

Hedged maximum likelihood quantum state estimation.

- Mathematics, Physics
- Physical review letters
- 2010

This Letter proposes and analyzes a new method for quantum state estimation, called hedged maximum likelihood (HMLE), a straightforward modification of maximum likelihood estimation (MLE), which can be used as a plug-in replacement for MLE. Expand