In practice how do we prepare a desired quantum state?

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Discussion Overview

The discussion revolves around the practical methods for preparing a desired quantum state, specifically focusing on creating superposition states with specified wavefunctions. Participants explore the challenges and methodologies involved in achieving this in a laboratory setting.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about how to prepare a superposition state with a specified wavefunction, expressing difficulty in finding relevant information.
  • Another participant suggests that the preparation of a state can be done using the specified wavefunction and mentions that the nature of superposition is not inherently defined by the wavefunction but rather by the analysis approach taken.
  • A follow-up question seeks clarification on how to associate electrons with a given wavefunction, indicating confusion about the practical implementation.
  • A participant responds that the feasibility of preparing states can vary, comparing the task to placing a stone at a distant location, and emphasizes the need for clever laboratory procedures and Hamiltonians to approximate the desired wavefunction.
  • The same participant notes that while some methods may be straightforward (like in a double slit experiment), others may be impossible due to physical limitations, and draws a parallel to the challenges of preparing specific gravitational fields.

Areas of Agreement / Disagreement

Participants express differing views on the practicality and feasibility of preparing quantum states, with some suggesting that certain methods are straightforward while others highlight significant challenges. The discussion remains unresolved regarding the specific techniques that can be reliably employed.

Contextual Notes

Participants acknowledge the variability in difficulty associated with different tasks and the limitations imposed by the physical universe, but do not provide specific mathematical frameworks or definitions that could clarify the discussion further.

kof9595995
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Let say we want to prepare a particular superposition state with a specified wavefunction, how can we accomplish that? I tried google but nothing useful showed up. Thanks.
 
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You just prepare your state with the specified wave function. You can then, if you want to, decompose it in thousands of ways as or complicated superpositions. The fact that it is a superposition is not coded in the wave function itself. It is coded in the way you want to analyze what happens.
 
arkajad said:
You just prepare your state with the specified wave function. You can then, if you want to, decompose it in thousands of ways as or complicated superpositions. The fact that it is a superposition is not coded in the wave function itself. It is coded in the way you want to analyze what happens.

Sorry I'm lost, can you elaborate more? For example I give you a lot of electrons and write you down a wavefunction, how do you make the electrons associated to the wavefunction I wrote you?
 
kof9595995 said:
... how do you make the electrons associated to the wavefunction I wrote you?

Well, some tasks will be easy, some difficult, some impossible. It is like with stones. I give you a stone and ask you to put it at the position of Alpha Centauri. Normally, you see what is available in your lab and try to invent a laboratory procedure that will approximately realize your wave wave function, for instance by inventing a clever Hamiltonian.

But probably you wanted to formulate your question in a different way, something like that:

"Suppose I have two laboratory procedures that prepare my electrons in pure states |a> and |b> respectively. Can I use them in a clever way to prepare my electrons in |a>+|b>?"

Sometimes the answer will be easy (like in a double slit experiment), sometimes it will be impossible due to our limitations of manipulating the universe in which we live. We learn by examples. The same with gravitational fields. In general we can't prepare a gravitational field that corresponds to a given solution of Einstein field equations!
 

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