# Re: Measuring a system in a superposition of states vs in a mixed state

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On Sunday, November 4, 2018 at 8:33:10 PM UTC, jessem wrote:
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>
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> On Wed, Oct 31, 2018 at 7:30 AM Bruno Marchal <mar...@ulb.ac.be
> <javascript:>> wrote:
>
>>
>> On 30 Oct 2018, at 14:21, agrays...@gmail.com <javascript:> wrote:
>>
>>
>>
>> On Tuesday, October 30, 2018 at 8:58:30 AM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 29 Oct 2018, at 13:55, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, October 29, 2018 at 10:22:02 AM UTC, Bruno Marchal wrote:
>>>>
>>>>
>>>> On 28 Oct 2018, at 13:21, agrays...@gmail.com wrote:
>>>>
>>>>
>>>>
>>>> On Sunday, October 28, 2018 at 9:27:56 AM UTC, Bruno Marchal wrote:
>>>>>
>>>>>
>>>>> On 25 Oct 2018, at 17:12, agrays...@gmail.com wrote:
>>>>>
>>>>>
>>>>>
>>>>> On Tuesday, October 23, 2018 at 10:39:11 PM UTC, agrays...@gmail.com
>>>>> wrote:
>>>>>>
>>>>>> If a system is in a superposition of states, whatever value measured,
>>>>>> will be repeated if the same system is repeatedly measured.  But what
>>>>>> happens if the system is in a mixed state? TIA, AG
>>>>>>
>>>>>
>>>>> If you think about it, whatever value you get on a single trial for a
>>>>> mixed state, repeated on the same system, will result in the same value
>>>>> measured repeatedly. If this is true, how does measurement distinguish
>>>>> superposition of states, with mixed states? AG
>>>>>
>>>>>
>>>>> That is not correct. You can distinguish a mixture of particles in the
>>>>> up or down states with a set of 1/sqrt(2)(up+down) by measuring them with
>>>>> the {1/sqrt(2)(up+down), 1/sqrt(2)(up-down}) discriminating apparatus.
>>>>> With
>>>>> the mixture, half the particles will be defected in one direction, with
>>>>> the
>>>>> pure state, they will all pass in the same direction. Superposition would
>>>>> not have been discovered if that was not the case.
>>>>>
>>>>
>>>>
>>>> *And someone will supply the apparatus measuring (up + down), and (up -
>>>> down)? No such apparatuses are possible since those states are inherently
>>>> contradictory. We can only measure up / down. AG*
>>>>
>>>>
>>>> You can do the experience by yourself using a simple crystal of calcium
>>>> (CaCO3, Island Spath), or with polarising glass. Or with Stern-Gerlach
>>>> devices and electron spin. Just rotating (90° or 180°) an app/down
>>>> apparatus, gives you an (up + down)/(up - down) apparatus.
>>>>
>>>
>>> *I don't understand. With SG one can change the up/down axis by
>>> rotation, but that doesn't result in an (up + down), or (up - down)
>>> measurement. If that were the case, what is the operator for which those
>>> states are eigenstates? Which book by Albert? AG *
>>>
>>>
>>> David Z Albert, Quantum Mechanics and Experience, Harvard University
>>> Press, 1992.
>>>
>>> https://www.amazon.com/Quantum-Mechanics-Experience-David-Albert/dp/0674741137
>>>
>>> Another very good books is
>>>
>>> D’Espagnat B. Conceptual foundations of Quantum mechanics,  I see there
>>> is a new edition here:
>>>
>>>
>>> It explains very well the difference between mixtures and pure states.
>>>
>>> Bruno
>>>
>>
>> *Thanks for the references. I think I have a reasonable decent
>> understanding of mixed states. Say a system is in a mixed state of phi1 and
>> phi2 with some probability for each. IIUC, a measurement will always result
>> in an eigenstate of either phi1 or phi2 (with relative probabilities
>> applying). *
>>
>>
>> If the measurement is done with a phi1/phi2 discriminating apparatus.
>> Keep in mind that any state can be seen as a superposition of other oblique
>> or orthogonal states.
>>
>
> I don't know if you're restricting the definition of phi1 and phi2 to some
> particular type of eigenstate or not, but in general aren't there pure
> states that are not eigenstates of any physically possible measurement
> apparatus, so there is no way to directly measure that a system is in such
> a state?
>```
```
*Yes, such states exist IIUC. That's why I don't understand Bruno's claim
that Up + Dn and Up - Dn can be measured with any apparatus, since they're
not eigenstates of the spin operator, or any operator. Do you understand
Bruno's argument in a previous post on this topic? AG *

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