Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0604105

Estimating Information Gain in Measurements in Suboptimal Bases for Quantum State Tomography

Manas K. Patra

Published Apr 14, 2006• 0 citations
arXivHTMLPDF

Abstract

It is known that mutually unbiased bases, whenever they exist, are optimal in an information theoretic sense for the determination of unknown state of a quantum ensemble. These bases may not exist in most dimensions and some suboptimal choices have to be made. The present paper deals with estimates of the information loss in suboptimal choice of bases. The information is calculated directly in terms of transition probabilities. I give estimates for the information content of measurement in some approximate MUBs proposed recently.

DOI
10.48550/arxiv.quant-ph/0604105

Related papers

Quantum state determination: estimates for information gain and some exact calculations

Manas K. Patra

It is known that mutually unbiased bases (MUBs), whenever they exist, are optimal in an information theoretic sense for the determination of the unknown state of a quantum ensemble. Such bases may not exist for most dimensions. The present paper deals with information gain in some generalizations and approximations of MUBs. We give estimates of the information loss (relative to MUBs) in these suboptimal choice of bases. For some generalization of MUBs we give exact calculations for the information gain. It is calculated directly in terms of transition probabilities among the measurement bases. We also give the formal solutions for the problem of quantum state tomography in these casesSome of the results in this paper was reported in the proceedings of EQIS 2005. A large part of this work was done at CQCT, Macquarie University, Sydney..

Journal of Physics A Mathematical and Theoretical•Aug 14, 2007•6 citations

Measures to characterise Approximate Mutually Unbiased Bases

Ajeet Kumar, Uditanshu Sadual

Mutually Unbiased bases has various application in quantum information procession and coding theory. There can be maximum d + 1 MUBs in C^d and d/2 +1 MUBs in R^d. But , over R^d MUBs are known to be non existent when d is odd and for most of the other even d there are mostly 3 Real MUBs. In case of C^d the construction for complete set of MUBs are known for only Prime Power dimension. Thus in general large set of MUBs are not known, particularly for composite dimensions which are not of the form of prime powers. Because of this, there are many constructions of Approximate version of MUBs. In this paper we make an attempt to define certain measures to characterise the AMUBs. Our construction of measures derives its inspiration from the applications of MUBs, and based on them, we define certain quantifiable measures, which are can be computed and gives estimates of how close the Approximate MUBs are to the MUBs. We use geometric interpretation, projective design features of MUBs and applications like Optimal State determination and Entropic Uncertainty of MUBs. We show generic relationship between these measures and show that it can be evaluated for APMUBs without known the exact construction details, thereby showing that definition of APMUB is sufficient completely characterise it. We also evaluate these measure for an interesting class of AMUBs called Weak MUBs and certain AMUBs constructed using RBDs.

quant-pharXiv:2512.12828•Dec 16, 2025•0 citations

Optimal quantum tomography of permutationally invariant qubits

A. B. Klimov, Gunnar G. Bjork, Luis Lorenzo Sánchez-Soto

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, making some of the measurement bases superfluous. This is, for example, the case when multiqubit states belong to the permutationally invariant subspace. In this paper we derive the minimal sets of mutually unbiased bases needed to tomographically reconstruct such states.

arXiv:1301.2123•Physical Review A•Jan 10, 2013•25 citations

Experimental Quantum State Estimation in Mutually Unbiased Bases

Robert B. A. Adamson, Aephraim M. Steinberg

We present the first experiment in two-qubit quantum state tomography to take advantage of mutually unbiased bases. Measuring in these bases extracts the maximum information from a fixed number of copies of the state.

International Conference on Quantum Information•Jan 1, 2008•2 citations

Improving Quantum State Estimation with Mutually Unbiased Bases

Robert B. A. Adamson, Aephraim M. Steinberg

When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state tomography of two-qubit polarization states to take advantage of mutually unbiased bases. We demonstrate improved state estimation as compared to standard measurement strategies and discuss how this can be understood from the structure of the measurements we use. We experimentally compared our method to the standard state estimation method for three different states and observe that the infidelity was up to 1.84 ± 0.06 times lower by using our technique than it was by using standard state estimation methods.

arXiv:0808.0944•Physical Review Letters•Jul 16, 2010•186 citations

Choice of mutually unbiased bases and outcome labeling affecting measurement outcome secrecy

Mirdit Doda, Matej Pivoluska, Martin Plesch

Mutually unbiased bases (MUBs) are a crucial ingredient for many protocols in quantum information processing. Measurements performed in these bases are unbiased to the maximally possible extent, which is used to prove the randomness or secrecy of measurement results. In this work we show that certain properties of sets of MUBs crucially depend on their specific choice, including, somewhat surprisingly, measurement outcome labeling. If measurements are chosen in a coherent way, the secrecy of the result can be completely lost for specific sets of MUB measurements but partially retained for others. This could potentially impact a broad spectrum of applications where MUBs are utilized.

arXiv:2006.08226•Physical Review A•Mar 4, 2021•1 citation
It is known that mutually unbiased bases, whenever they exist, are optimal in an information theoretic sense for the determination of unknown state of a quantum ensemble. These bases may not exist in most dimensions and some suboptimal choices have to be made. The present paper deals with estimates of the information loss in suboptimal choice of bases. The information is calculated directly in terms of transition probabilities. I give estimates for the information content of measurement in some approximate MUBs proposed recently.
It is known that mutually unbiased bases (MUBs), whenever they exist, are optimal in an information theoretic sense for the determination of the unknown state of a quantum ensemble. Such bases may not exist for most dimensions. The present paper deals with information gain in some generalizations and approximations of MUBs. We give estimates of the information loss (relative to MUBs) in these suboptimal choice of bases. For some generalization of MUBs we give exact calculations for the information gain. It is calculated directly in terms of transition probabilities among the measurement bases. We also give the formal solutions for the problem of quantum state tomography in these casesSome of the results in this paper was reported in the proceedings of EQIS 2005. A large part of this work was done at CQCT, Macquarie University, Sydney..
Mutually Unbiased bases has various application in quantum information procession and coding theory. There can be maximum d + 1 MUBs in C^d and d/2 +1 MUBs in R^d. But , over R^d MUBs are known to be non existent when d is odd and for most of the other even d there are mostly 3 Real MUBs. In case of C^d the construction for complete set of MUBs are known for only Prime Power dimension. Thus in general large set of MUBs are not known, particularly for composite dimensions which are not of the form of prime powers. Because of this, there are many constructions of Approximate version of MUBs. In this paper we make an attempt to define certain measures to characterise the AMUBs. Our construction of measures derives its inspiration from the applications of MUBs, and based on them, we define certain quantifiable measures, which are can be computed and gives estimates of how close the Approximate MUBs are to the MUBs. We use geometric interpretation, projective design features of MUBs and applications like Optimal State determination and Entropic Uncertainty of MUBs. We show generic relationship between these measures and show that it can be evaluated for APMUBs without known the exact construction details, thereby showing that definition of APMUB is sufficient completely characterise it. We also evaluate these measure for an interesting class of AMUBs called Weak MUBs and certain AMUBs constructed using RBDs.
When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state tomography of two-qubit polarization states to take advantage of mutually unbiased bases. We demonstrate improved state estimation as compared to standard measurement strategies and discuss how this can be understood from the structure of the measurements we use. We experimentally compared our method to the standard state estimation method for three different states and observe that the infidelity was up to 1.84 ± 0.06 times lower by using our technique than it was by using standard state estimation methods.
Mutually unbiased bases (MUBs) are a crucial ingredient for many protocols in quantum information processing. Measurements performed in these bases are unbiased to the maximally possible extent, which is used to prove the randomness or secrecy of measurement results. In this work we show that certain properties of sets of MUBs crucially depend on their specific choice, including, somewhat surprisingly, measurement outcome labeling. If measurements are chosen in a coherent way, the secrecy of the result can be completely lost for specific sets of MUB measurements but partially retained for others. This could potentially impact a broad spectrum of applications where MUBs are utilized.