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Title: Quantum state estimation when qubits are lost: a no-data-left-behind approach

Abstract

We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we report the first closed-form Bayesian mean and maximum likelihood estimates for the ideal single qubit. Due to computational constraints, we utilize numerical sampling to determine the Bayesian mean estimate for a photonic two-qubit experiment in which our novel analysis reduces burdens associated with experimental asymmetries and inefficiencies. This method can be applied to quantum states of any dimension and experimental complexity.

Authors:
ORCiD logo [1];  [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Quantum Information Science Group
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1349952
Alternate Identifier(s):
OSTI ID: 1352764
Grant/Contract Number:
AC05-00OR22725; Contract No. DE-AC05-00OR22725
Resource Type:
Journal Article: Published Article
Journal Name:
New Journal of Physics
Additional Journal Information:
Journal Volume: 19; Journal Issue: 4; Journal ID: ISSN 1367-2630
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; quantum state estimation; Bayesian; qubit; inference; slice sampling; Monte Carlo

Citation Formats

Williams, Brian P., and Lougovski, Pavel. Quantum state estimation when qubits are lost: a no-data-left-behind approach. United States: N. p., 2017. Web. doi:10.1088/1367-2630/aa65de.
Williams, Brian P., & Lougovski, Pavel. Quantum state estimation when qubits are lost: a no-data-left-behind approach. United States. doi:10.1088/1367-2630/aa65de.
Williams, Brian P., and Lougovski, Pavel. Thu . "Quantum state estimation when qubits are lost: a no-data-left-behind approach". United States. doi:10.1088/1367-2630/aa65de.
@article{osti_1349952,
title = {Quantum state estimation when qubits are lost: a no-data-left-behind approach},
author = {Williams, Brian P. and Lougovski, Pavel},
abstractNote = {We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we report the first closed-form Bayesian mean and maximum likelihood estimates for the ideal single qubit. Due to computational constraints, we utilize numerical sampling to determine the Bayesian mean estimate for a photonic two-qubit experiment in which our novel analysis reduces burdens associated with experimental asymmetries and inefficiencies. This method can be applied to quantum states of any dimension and experimental complexity.},
doi = {10.1088/1367-2630/aa65de},
journal = {New Journal of Physics},
number = 4,
volume = 19,
place = {United States},
year = {Thu Apr 06 00:00:00 EDT 2017},
month = {Thu Apr 06 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1088/1367-2630/aa65de

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  • We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we report the first closed-form Bayesian mean and maximum likelihood estimates for the ideal single qubit. Due to computational constraints, we utilize numerical sampling to determine the Bayesian mean estimate for a photonic two-qubit experiment in which our novel analysis reduces burdens associated with experimental asymmetries and inefficiencies. This method can be applied to quantum states of any dimension and experimental complexity.
  • Non-Markovian dynamics is studied for two interacting qubits strongly coupled to a dissipative bosonic environment. We derive a non-Markovian quantum-state-diffusion (QSD) equation for the coupled two-qubit system without any approximations, and in particular, without the Markov approximation. As an application and illustration of our derived time-local QSD equation, we investigate the temporal behavior of quantum coherence dynamics. In particular, we find a strongly non-Markovian regime where entanglement generation is significantly modulated by the environmental memory. Additionally, we study residual entanglement in the steady state by analyzing the steady-state solution of the QSD equation. Finally, we discuss an approximate QSD equation.
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