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

Single qubit estimation from repeated unsharp measurements

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

When estimating an unknown single pure qubit state, the optimum fidelity is 2/3. As it is well known, the value 2/3 can be achieved in one step, by a single ideal measurement of the polarization along a random direction. I analyze the opposite strategy which is the long sequence of unsharp polarization measurements. The evolution of the qubit under the influence of repeated measurements is quite complicated in the general case. Fortunately, in a certain limit of very unsharp measurements the qubit will obey simple stochastic evolution equations known for long under the name of time-continuous measurement theory. I discuss how the outcomes of the very unsharp measurements will asymptotically contribute to our knowledge of the original qubit. It is reassuring that the fidelity will achieve the optimum 2/3 for long enough sequences of the unsharp measurements. 1

Related papers

Single qubit estimation from repeated unsharp measurements

Lajos Diósi

Abstract When estimating an unknown single pure qubit state, the optimum fidelity is 2/3. As it is well known, the value 2/3 can be achieved in one step, by a single ideal measurement of the polarization along a random direction. I analyze the opposite strategy which is the long sequence of unsharp polarization measurements. The evolution of the qubit under the influence of repeated measurements is quite complicated in the general case. Fortunately, in a certain limit of very unsharp measurements the qubit will obey simple stochastic evolution equations known for long under the name of time‐continuous measurement theory. I discuss how the outcomes of the very unsharp measurements will asymptotically contribute to our knowledge of the original qubit. It is reassuring that the fidelity will achieve the optimum 2/3 for long enough sequences of the unsharp measurements.

arXiv:quant-ph/0205150•Fortschritte der Physik•Feb 26, 2003•6 citations

Advancement of estimation fidelity in continuous quantum measurement

Lajos Diósi

We estimate an unknown qubit from the long sequence of n random polarization measurements of precision Δ. Using the standard Ito stochastic equations of the a posteriori state in the continuous measurement limit, we calculate the advancement of fidelity. We show that the standard optimum value 2/3 is achieved asymptotically for n ≫ Δ 2 /96 ≫ 1. We append a brief derivation of novel Ito equations for the estimate state.

arXiv:quant-ph/0202052•Journal of Physics A Mathematical and General•Mar 15, 2002•5 citations

Fidelity-optimized quantum state estimation

Amir Kalev, Itay Hen

We describe an optimized, self-correcting procedure for the Bayesian inference of pure quantum states. By analyzing the history of measurement outcomes at each step, the procedure returns the most likely pure state, as well as the optimal basis for the measurement that is to follow. The latter is chosen to maximize, on average, the fidelity of the most likely state after the measurement. We also consider a practical variant of this protocol, where the available measurement bases are restricted to certain limited sets of bases. We demonstrate the success of our method by considering in detail the single-qubit and two-qubit cases, and comparing the performance of our method against other existing methods.

arXiv:1409.1952•New Journal of Physics•Sep 10, 2015•15 citations

Qubit State Monitoring by Measurement of Three Complementary Observables

Rusko Ruskov, Alexander N. Korotkov, Klaus Mølmer

We consider the evolution of a qubit (spin $1/2$) under the simultaneous continuous measurement of three noncommuting qubit operators ${\stackrel{^}{\ensuremath{\sigma}}}_{x}$, ${\stackrel{^}{\ensuremath{\sigma}}}_{y}$, and ${\stackrel{^}{\ensuremath{\sigma}}}_{z}$. For identical ideal detectors, the qubit state evolves by approaching a pure state with a random direction in the Bloch vector space and by undergoing locally isotropic diffusion in the perpendicular directions. The quantum state conditioned on the complete detector record is used to assess the fidelity of classically inspired estimates based on running time averages and discrete time bin detector outputs.

arXiv:1006.2013•Physical Review Letters•Sep 2, 2010•42 citations

Optimal reconstruction of a pure qubit state with local measurements

E. Bagán, M. Baig, Alex Monràs +1 more

We analyse the reconstruction of an unknown pure qubit state. We derive the optimal guess that can be inferred from any set of measurements on N identical copies of the system with the fidelity as a figure of merit. We study in detail the estimation process with individual von Neumann measurements and demonstrate that they are very competitive as compared to (complicated) collective measurements. We compute the expressions of the fidelity for large $N$ and show that individual measurement schemes can perform optimally in the asymptotic regime.

arXiv:quant-ph/0312167•Dec 19, 2003•0 citations

Optimal estimation of two-qubit pure-state entanglement

Antonio Acín, R. Tarrach, Guifré Vidal

We present optimal measuring strategies for an estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general measuring strategies are considered in both situations, to conclude in the first case that a local, although collective, measurement suffices to estimate entanglement, a nonlocal property, optimally.

arXiv:quant-ph/9911008•Physical Review A•May 16, 2000•32 citations
When estimating an unknown single pure qubit state, the optimum fidelity is 2/3. As it is well known, the value 2/3 can be achieved in one step, by a single ideal measurement of the polarization along a random direction. I analyze the opposite strategy which is the long sequence of unsharp polarization measurements. The evolution of the qubit under the influence of repeated measurements is quite complicated in the general case. Fortunately, in a certain limit of very unsharp measurements the qubit will obey simple stochastic evolution equations known for long under the name of time-continuous measurement theory. I discuss how the outcomes of the very unsharp measurements will asymptotically contribute to our knowledge of the original qubit. It is reassuring that the fidelity will achieve the optimum 2/3 for long enough sequences of the unsharp measurements. 1
Abstract When estimating an unknown single pure qubit state, the optimum fidelity is 2/3. As it is well known, the value 2/3 can be achieved in one step, by a single ideal measurement of the polarization along a random direction. I analyze the opposite strategy which is the long sequence of unsharp polarization measurements. The evolution of the qubit under the influence of repeated measurements is quite complicated in the general case. Fortunately, in a certain limit of very unsharp measurements the qubit will obey simple stochastic evolution equations known for long under the name of time‐continuous measurement theory. I discuss how the outcomes of the very unsharp measurements will asymptotically contribute to our knowledge of the original qubit. It is reassuring that the fidelity will achieve the optimum 2/3 for long enough sequences of the unsharp measurements.
We describe an optimized, self-correcting procedure for the Bayesian inference of pure quantum states. By analyzing the history of measurement outcomes at each step, the procedure returns the most likely pure state, as well as the optimal basis for the measurement that is to follow. The latter is chosen to maximize, on average, the fidelity of the most likely state after the measurement. We also consider a practical variant of this protocol, where the available measurement bases are restricted to certain limited sets of bases. We demonstrate the success of our method by considering in detail the single-qubit and two-qubit cases, and comparing the performance of our method against other existing methods.
We consider the evolution of a qubit (spin 1/21/21/2) under the simultaneous continuous measurement of three noncommuting qubit operators ${\stackrel{^}{\ensuremath{\sigma}}}_{x}$, ${\stackrel{^}{\ensuremath{\sigma}}}_{y}$, and ${\stackrel{^}{\ensuremath{\sigma}}}_{z}$. For identical ideal detectors, the qubit state evolves by approaching a pure state with a random direction in the Bloch vector space and by undergoing locally isotropic diffusion in the perpendicular directions. The quantum state conditioned on the complete detector record is used to assess the fidelity of classically inspired estimates based on running time averages and discrete time bin detector outputs.
We analyse the reconstruction of an unknown pure qubit state. We derive the optimal guess that can be inferred from any set of measurements on N identical copies of the system with the fidelity as a figure of merit. We study in detail the estimation process with individual von Neumann measurements and demonstrate that they are very competitive as compared to (complicated) collective measurements. We compute the expressions of the fidelity for large NNN and show that individual measurement schemes can perform optimally in the asymptotic regime.