Pure vs. mixed quantum states

📚 Probability arises in quantum mechanics every time we perform a measurement. However, probability also features more generally in science to describe systems for which we only have partial information. In this video, we consider what happens when we have a system for which we only have partial information, but this system is a quantum system. In these cases, we need to consider both types of probability, and to do so we use pure states and mixed states.

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Director and writer: BM
Producer and designer: MC

[physicsphilosophy]

Came here after the recommendation by #Parth G

Good Explanation
Loved it👌👌👌🙏♥️

[slgnssp]

Something that changed the way I looked at superposition was noting the fact that a superposition is as much a characteristic of the state as of the basis (and/or observable) - you can have a superposition in a given basis but not in another, for the same state: the state "itself" just kind of /is/.

[snjy]

00:02 Comparing pure and mixed quantum states
01:40 Quantum measurements lead to state collapses and probabilities of eigenvalues.
03:22 Quantum states can be represented as statistical mixtures of states
05:06 Quantum mechanics and classical mechanics give the same measurement results.
06:40 Measurement of pure vs. mixed quantum states
08:29 Superposition states require interference term for accurate predictions.
10:13 Quantum systems have pure and mixed states.
11:47 Mixed quantum states contain partial information and use probabilities to describe the system.

[PTGaonkar]

Oh my god parth g suggested this and this is amazing 🤩

[guoxinxin]

This is the best quantum mechanics! Thanks! I love them!

[bobdorsett]

Nice explanation! Density operator for mixed states coming soon, I hope?

[gnrwashere]

Thanks for this awesome video, the best explanation that i could possibly get, thank you so much!!!!

[shubhamvernekar]

Found this video very useful, These are the type of videos that will help me get through my masters. Thank you!!

[aalonsobizzi]

Great explanation - way better than a textbook!

[youngphilosophy]

I think it’s easier to define a pure state and a mixed state in the following way. A pure state is just a state where we can define a fixed phase between the states. For example, in the superposition pure state there is interference term that carries a phase for both u1 and u2. The same can’t be said about mixed states. The mixed state doesn’t have a fixed phase. Mixed states are just classical statistical ensembles. I hope this helps someone. 😊

[davidwright]

I'm guessing this is really important in dealing with error correction in quantum computation? Because it looks like the error correction for some 'computational target', itself needs error correction - iterate until you're as sure of the computational outcome, as you need? Please indicate if I'm talking sense - or not!

[jj]

I am so glad that I found your channel. Nice video and extremely useful content :DDD

[shiprasaha]

Thanku for the clear and crisp explanation.. looking for more of this ;)

[claudiozambrella]

Best explaination ever! I finally understand this topic 😍

[vasjaforutube]

Thank you for this video, your explanation is very clear.

[paulbk]

Thank you so very much for such lucid explanation.

[jesmaljalal]

Good one! Can you do a video about bell states and entanglement?

[anoopkumarpandey]

At 12:13, you say that for mixed states, we don't know the actual state but rather a mixture of states with respective probabilities. My question is how do we get this probability distribution? There are infinite states. When we don't know about the system, how can we tell that it may exist in |psi_1> to |psi_n> with some associated probabilities?

[williamberquist]

At 7:40 you have the prefactor of 2Re. You say that the sum of a number plus its complex conjugate results in twice its real part. This makes sense to me. Does this mean that we only take the real number part of the term inside the brackets { ... }, and this is signified by the Re prefactor?

Why is the complex conjugate * symbol removed from the c_1 and <v_m|u_1> terms, but not the c_2 and <v_m|u_2> term? Will that symbol be removed once we apply the Re prefactor, and the * is left for clarity in the proof?

Or am I missing something about this?

[aminamouhamed]

Very helpful, thaank you! Could you please give me an example of the Stern-Gerlach experiment to get an intuition? When do we have a mixed state and when do we have a pure state? What is the difference between state selection and preparation?