3 ms·

> In other words, we can always ask, what if we don't know which quantum state we have? For example, what if we have a 1/2 probability of state1 and a 1/2 proba

• Attrecomet 4y ago
  Yes, that's how you get things like entanglement and interference of states.
  • qbit42 4y ago
    Can you explain? That's not how I interpret either. Every quantum state can be realized as a classical mixture of pure quantum states (i.e. as a density matrix).
    • tgflynn 4y ago
      No, the fact that what you said is not true is basically the core concept of quantum mechanics. EDIT: As another comment pointed out I was wrong about this, please ignore.
      • kgwgk 4y ago
        In what sense is that not true? It seems true at least if we accept that a pure state is a mixture of itself with nothing else. Any quantum state CAN be represented by a density matrix. That's what density matrices are for. That quantum state may be pure or may be a mixture. (A mixture density matrix could also be a partial trace representing a subsystem of a larger system instead of a true mixture of pure states.)
        • tgflynn 4y ago
          Yes, I you're right. I misinterpreted "pure quantum states" as "basis states" (I'm not much in the habit of thinking about QM these days). I believe the "(i.e. as a density matrix)", which makes my mistake more obvious, was added after I commented.
• ivansavz 4y ago
  Superpositions and probabilistic mixtures are two different ways to combine |0> and |1>. The superposition a|0> + b|1> describes a linear combination of the two solutions |0> and |1> to some differential equation, but there is no notion of "mixture". A good analogy to understand superpositions is the solutions to simple harmonic motion (like mass attached to a spring). If you start the system from stretched state and zero velocity, it will oscillate like cos(ωt). If instead you give it a "kick" at zero displacement, it will oscillate like sin(ωt). Since any other combination is possible (e.g. kick while stretching), the most general solution to the equation of motion of the mass spring system is acos(ωt) + bsin(ωt), where a and b are the amplitudes. In practice we usually write acos(ωt) + bsin(ωt), so there is nothing "fancy" going on for superpositions: they are just linear combinations of the possible states. (You don't hear anyone talking about a mass-spring system oscillating like cos and like sin at the same time, do you?) Off topic note for completeness: in physics class we rewrite acos(ωt) + bsin(ωt) as A*cos(ωt-φ), but it's the so you don't see the cos and sin separately, but they are there. As for "mixtures" those represent our state of knowledge, or rather ignorance. The mixture of 50% |0> and 50% |1> is represented as a density matrix, which has the same "statistics" under measurement. It's hard to do matrices in plain text so I'll cut if off here... but you can look it up.
  • kgwgk 4y ago
    An even simpler analogy: The difference between a mixture and a superposition is the difference between going either in the North direction or in the West direction with 50/50 probability and going in the Northwest direction.