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I recently started reading "Quantum Mechanics" by Leonard Susskind, and need some clarification reg. an experiment that was described in the first chapter.

I'm not really sure if this is a thought exercise, or an actual experiment. I think the book is trying to present/impress on the reader that quantum states are different from classical mechanics states, and that the act of measuring also invariably modifies the thing you are trying to measure.

The goal of the experiment is to determine the state (spin) of a qubit. We have an apparatus A (which has a "this side up" notation - let's call it TSU) that can detect the state of the qubit. If the apparatus reads +1, it means that the qubit spin is aligned with the "this side up" of the apparatus, and a -1 indicates that the qubit spin is 180° away from (the opposite of) "this side up". The apparatus can only detect +1 or -1 or be blank (during a reset).

The book then goes on to describe that the first reading from the apparatus is a "preparation", and the next reading is a "confirmation". When the qubit spin is +1 and apparatus TSU is aligned with the qubit spin, the appartus reads +1 repeatably. If the qubit spin is +1, and the appartus TSU is 180° away from the spin, the apparatus first "prepares" a -1, and then repeatably reads a -1.

Question:
What is the "true" state of the qubit spin? Did it change to -1 (destroyed/reset by the apparatus) or does it remain +1 and our apparatus is telling us -1 (apparatus has a memory)? Or are we saying the apparatus tells us it's -1, but we don't know the actual "true" state (cannot know current state without setting it)?

Explanation 1 - Apparatus destroys the state:
What is the qualitative difference between the prepare and confirm phases of the experiment? It almost sounds like the apparatus does a setAndGet() operation on the qubit (set the value to the current orientation of the apparatus "this side up", and return an existing value that is force type-casted to either +1 and -1 -> and hence the random readings if the value is not actually aligned). This means that the apparatus is destroying the state of the qubit on every reading.

Explanation 2 - Apparatus has a memory:
If the apparatus is not destroying the state, then the other possibility might be that the apparatus has some kind of "memory". An analogy would be perhaps that the apparatus behaves like a setIfNotPresent() kind of operation while it's (the apparatus) orientation ("this side up") is not changed? This means that we are currently incapable of building a better apparatus, and maybe we should focus on that instead?

Explanation 3 - We can never measure the current state of a quantum system (a logical extension to Explanation 1):
Just because the apparatus reads a +1 or -1, there is no indication of what the actual state of the qubit was. We essentially destroyed the state by the act of measurement. Does this mean that we cannot know the "existing" state of a qubit with certainty? We can only ever set it's value, and repeatably confirm the value, but we cannot find the current state of the system?

Explanation 4:
Maybe my entire thought process is wrong in that I'm trying to I'm trying to draw deterministic analogies to probabilistic experiments/outcomes. If this is true, any pointers reg. how I should be thinking/analyzing this experiment and it's results?

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Before interacting with the apparatus, the state of the qubit is specified by the probability that we will measure +1 versus -1. After the qubit is measured, textbook quantum mechanics tells us that the state of the qubit has "collapsed." Whatever state we measure, the qubit will stay in that state, and our apparatus will continue to measure the same spin (unless and until the qubit interacts with some other system in a way that changes the qubit state).

Since the initial state of the qubit is given by the probabilities for the apparatus to measure either +1 or -1, we cannot determine what the state of the qubit was initially from a single measurement. Even repeated measurements of the same qubit won't help us, because after the first measurement the state has "collapsed" to one in which we measure either +1 or -1 with probability 1. To know the initial state the qubit was in, we would have to prepare many qubits in an identical state and then make many measurements, recording the probability with which we see +1 versus -1.

It seems like your Explanation 3 corresponds most closely to this.

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  • $\begingroup$ Why does the act of measurement align the qubit spin along the apparatus? Is it something that will be uncovered as I progress further into the world of quantum mechanics? Or is it just an observation that was made by multiple scientists after a LOT of experiments? $\endgroup$ – skittish Oct 13 at 21:58
  • $\begingroup$ That is something of an open question, and it is one of the more mysterious aspects of quantum mechanics. In textbook quantum mechanics, it is just taken as an assumption of the theory because it gives the right experimental predictions. Today, I think most physicists who care to think about the issue would say it has to do with something called "decoherence" (en.wikipedia.org/wiki/Quantum_decoherence). However, I don't think there is a completely understood theory of quantum mechanics that doesn't take wavefunction collpase as a given. $\endgroup$ – d_b Oct 13 at 23:55

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