Ordered Measurements of Permutationally-Symmetric Qubit Strings

Abstract

We show that any sequence of measurements on a permutationally-symmetric (pure or mixed) multi-qubit string leaves the unmeasured qubit substring also permutationally-symmetric. In addition, we show that the measurement probabilities for an arbitrary sequence of single-qubit measurements are independent of how many unmeasured qubits have been lost prior to the measurement. Our results are valuable for quantum information processing of indistinguishable particles by post-selection, e.g. in cases where the results of an experiment are discarded conditioned upon the occurrence of a given event such as particle loss. Furthermore, our results are important for the design of adaptive-measurement strategies, e.g. a series of measurements where for each measurement instance, the measurement basis is chosen depending on prior measurement results.

13 pages

References in corpus (17)

• Optimal Quantum Phase Estimation
• Quantum phase estimation with lossy interferometers
• Optimal states and almost optimal adaptive measurements for quantum interferometry
• Bell inequality, Bell states and maximally entangled states for n qubits
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• Machine Learning for Precise Quantum Measurement
• How to perform the most accurate possible phase measurements
• Classical and quantum communication without a shared reference frame
• Entanglement and permutational symmetry
• Quantum methods for clock synchronization: Beating the standard quantum limit without entanglement
• Loss-Induced Limits to Phase Measurement Precision with Maximally Entangled States
• Generation of Symmetric Dicke States of Remote Qubits with Linear Optics
• On the communication complexity of establishing a shared reference frame
• Lambda's, V's and optimal cloning with stimulated emission
• Robust strategies for lossy quantum interferometry
• Multi-pass classical vs. quantum strategies in lossy phase estimation
• Symmetric qubits from cavity states

Cited by in corpus (8)

• An Efficient Algorithm for Optimizing Adaptive Quantum Metrology Processes
• Permutation-invariant quantum codes
• Differential Evolution for Many-Particle Adaptive Quantum Metrology
• Robustness of Quantum-Enhanced Adaptive Phase Estimation
• Optimal quantum tomography of permutationally invariant qubits
• Feedback Ansatz for Adaptive-Feedback Quantum Metrology Training with Machine Learning
• Framework for Learning and Control in the Classical and Quantum Domains
• Practical implementation of mutually unbiased bases using quantum circuits