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Purity estimation with separable measurements.

E Bagan1, M A Ballester, R Muñoz-Tapia

  • 1Grup de Física Teòrica and IFAE, Facultat de Ciències, Edifici Cn, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain.

Physical Review Letters
|October 4, 2005
PubMed
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Separable measurements are as efficient as joint measurements for estimating qubit state purity when classical communication is used. This finding indicates quantum memories offer no advantage for entanglement estimation in this scenario.

Area of Science:

  • Quantum Information Science
  • Quantum Measurement Theory
  • Entanglement Characterization

Background:

  • Estimating the purity of quantum states is crucial for quantum information processing.
  • Joint quantum measurements are theoretically optimal for characterizing quantum states.
  • The role of quantum memories in state estimation protocols requires clarification.

Purpose of the Study:

  • To investigate the efficiency of separable measurement protocols for estimating qubit state purity.
  • To compare the performance of separable measurements with optimal joint measurements.
  • To determine if quantum memories offer an advantage in entanglement estimation.

Main Methods:

  • Utilizing a large number N of qubit state copies.
  • Employing separable-measurement protocols with classical communication.

Related Experiment Videos

  • Analyzing the asymptotic efficiency of these protocols.
  • Discussing the connection to global Bayesian inference and the quantum Cramér-Rao bound.

    • Main Results:

    • Separable-measurement protocols achieve the same efficiency as optimal joint-measurement protocols when classical communication is available.
    • Asymptotic optimal estimation of two-qubit state entanglement is possible with fully separable measurements.
    • Quantum memories do not provide an advantage for this specific state estimation task.

    Conclusions:

    • Classical communication enables separable measurements to match the efficiency of joint measurements for purity estimation.
    • Entanglement estimation can be achieved efficiently without relying on quantum memories.
    • The study highlights the power of separable measurements in specific quantum information tasks.