Is it possible to distinguish between pure and mixed states?

Click For Summary
SUMMARY

This discussion centers on the distinction between pure and mixed quantum states, particularly in the context of ensembles of particles with measured spins. It is established that while pure states can be identified by their ability to yield consistent measurement results along a specific axis, mixed states do not exhibit this property. The conversation references John Baez's insights on the transformation of pure states into mixed states, emphasizing that a pure state contains more information than a mixed state, which is represented by a density matrix. The implications for black holes and the information paradox are also explored, concluding that without a theory of quantum gravity, definitive answers remain elusive.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly pure and mixed states.
  • Familiarity with density matrices and wavefunctions.
  • Knowledge of quantum measurement and spin properties.
  • Basic concepts of black hole thermodynamics and information theory.
NEXT STEPS
  • Study the differences between pure states and mixed states in quantum mechanics.
  • Learn about the density matrix formalism and its applications in quantum systems.
  • Research the implications of quantum measurement on state determination.
  • Explore the black hole information paradox and current theories in quantum gravity.
USEFUL FOR

Quantum physicists, students of quantum mechanics, researchers exploring quantum information theory, and anyone interested in the foundational aspects of quantum states and their implications in black hole physics.

  • #31
Larry Pendarvis said:
Is it possible to prepare an ensemble of particles that are in some kind of Indeterminate spin state?

Others have given various ways of doing this; but none of these will give you what you said you wanted in Ensemble B, namely a "mixed" state. A mixed state is something different from what you are calling an "indeterminate" state. And the original quote you gave regarding the black hole information paradox was talking about mixed states (vs. pure states), not about indeterminate states (as opposed to determinate states).

If you still haven't picked up on my advice to consult a textbook and learn the technical meanings of all these terms you are using, do so. Once you have done so, please start a new thread if you still have questions about pure vs. mixed states. This thread is closed.
 
  • Like
Likes   Reactions: vanhees71 and bhobba

Similar threads

Undergrad Entanglement, Mixed or Pure State?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Mixed states from entangled state
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Mixed states vs pure states - physical POV
  • · Replies 65 ·
3
Replies
65
Views
9K
Undergrad Difference between superposition and mixed state
  • · Replies 15 ·
Replies
15
Views
4K
Graduate Pure, proper mixed, and improper mixed states in laymen's terms
  • · Replies 12 ·
Replies
12
Views
4K
Graduate Quick question on ensembles of pure states
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Entangled system pure state or not?
  • · Replies 80 ·
3
Replies
80
Views
7K
Undergrad Entanglement may reveal more about black holes? ...Even micro ones!
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Do black holes destroy quantum states?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Difference between Quantum Superposition and Mixed States
  • · Replies 1 ·
Replies
1
Views
2K