Measurement of a Hydrogen qubit?

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Discussion Overview

The discussion revolves around the measurement of a hydrogen atom conceptualized as a qubit, particularly in a superimposed state involving its ground and first excited states. Participants explore the implications of quantum mechanics on measurement and the nature of observables in this context.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions how to measure a hydrogen atom in a superimposed state to determine its two possible states.
  • Another participant argues that the original question is poorly posed, emphasizing that the state of a system is not an observable, and that observables are represented by hermitian operators.
  • A third participant points out that the energy eigenfunctions of a hydrogen atom are infinite, suggesting that it is not accurately described as a two-state system.
  • A later reply clarifies that the ground and first excited states of a hydrogen atom can be considered as a qubit in quantum computing, and discusses the measurement of probabilities for these states after alteration by a quantum algorithm.
  • This participant notes the necessity of repeated measurements to estimate the probabilities of the qubit being in either state.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the hydrogen atom as a two-state system and the formulation of the measurement question. There is no consensus on the best approach to measuring the superimposed state or the characterization of the system.

Contextual Notes

Participants highlight limitations in the original question's formulation and the complexity of defining observables in quantum mechanics, as well as the implications of infinite energy eigenfunctions in the context of measurement.

Julian Blair
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Given a 2 state hydrogen atom in a superimposed state, how does one measure it for either of its two states?
 
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I don't think your question is well posed. In quantum mechanics the state of a system is not an "observable". The observables (the quantities that you measure in experiments) are represented by hermitian operators that act on the states of the system.
 
The energy eigenfunctions of a hydrogen atom are infinite - its not a two state system.

Thanks
Bill
 
OK, let me explain a bit better. The ground and 1st excited states of an Hydrogen atom are often given as an example of a qubit for use in quantum computing. The energies of these states are definitely eigenstates of the Hamiltonian. My question has to do with an Hydrogen qubit in a superimposed state comprising both the ground and 1st excited state. If this qubit has been altered via a quantum algorithm, then one would like to measure the probabilities that it is in state |0> or state |1>. How could this be done?
Of course this measurement would have to be re-done multiple times to arrive at an estimation of the probabilities.
 

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