Pure VS Mixed States | Quantum Information

In this video, we will talk about the difference between pure and mixed states in quantum mechanics. In short, a pure state can be written in terms of a ket state, whereas a mixed state cannot.

Contents:
00:00 Pure States
01:52 Mixed States / Ensembles
02:52 Distinguish them

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[pearbq]

This video feels like the physics equivalent of the channel "The bright side of Mathematics", just straight to the point, concise and very very good

[BorisNVM]

This calms down a lot of doubts. I LOVE U

[shubhamvernekar]

Very well explained, I was having trouble understanding these two terms. Thank You!!

[NikolajKuntner]

Nice quick summary. I suppose you could also make one about entanglement and possibly contrast it to pure/mixed, since I think this is often mixed up. No pun intended.
I'm not sure if the prompt for "don't call this 50%-50%" is all that helpful, even if <0| paired with the state A|1> might not be zero for generic A. Your two states |0> and |1> are orthonormal after all. It will be half-chance when trying to measure your example two-level state in either of those two basis states that span your space. Speaking mathematically, I mean the case where your measurement A is the projection onto either, A = P_{|0>} = |0><0| respectively A = P_{|1>}.
And I feel reserving the 50% language for the mixed case gives standard statistical probability theory precedence over QM, which potentially is the fundamental physical framework. But okay, it's just nomenclature I suppose.

[dbd]

an important remind， in the mixed state density, it is the outer product, not the X or multiplied symbol.

[tawe]

3:30 that's interesting... I thought that points on the surface of Bloch sphere were enough to describe any 1 qubit quantum state, could you please give some example of such state?
(edit) nvm... I see it doesn't work... so how we can visualise such state?
btw this and next weekend I have workshops on quantum programming, so view from diffrent side might really help to understand the topic :) thanks for uploading

[louisbsr]

Sorry, in the beginning of the video around 0:27, is the definition correct for mixed state? What I understand is that mixed density matrices is an ensemble of pure state (which is generally a linear combination of basis states). But what you defined the mixed states is an ensemble of basis states, is that general enough? Thanks!

[maximerousseau]

Nice short and concies video!
I am currently doing my last year work on quantum cryptography, it is a good reminder!

Do you think you could do a simmilar video which explain with some example the difference between projective mesurment and POVM ?
The difference between those is still blury in my mind ahah.

[sayanjitb]

dear sir, when we talk about the superposition of electron states and we loosely say electrons can exist in any one of the states until it is being observed. Observation causes the state to collapse. So, in this scenario do we talk about a mixed state or a pure state? TIA

[wowshamanful]

Hi,
For the statistical ensemble, could you elaborate on the impossibility to write the system as | Ψ > ?
Many thanks for the video,

[annguyendang]

Dear Sir, pure state is used for a single quantum system and mixed state is used for an ensemble of the single quantum system?

[AnshulSharma]

At 1:51, if the basis vector are orthonormal, then why can't one say there is a 50-50% in measurements?

[wawan_ikhwan]

So, what is the different between pure state and mixed state?

[lavaeimeraua]

Hey,
first of all thanks for the video. It was very helpful!
I have a question regarding the the probabilities you mentioned in the case of the pure state. You said, that the ket state does not really describe a quantum system with 50% being measured as |1> and 50% being measured as |0>. However, every other source I found sais indeed that the probabilities are 50% for both and they do not mention the interference. E.g. Wikipedia or the Qiskit Textbook