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Well, for the simple situations we’re talking about non-factorability is enough. There are a number of competing measures of the “degree of entanglement.” I don’t think there is a clearly acknowledged “winner” for more than two entangled systems. But this is a very interesting area of exploration. I’m definitely not up to speed on what’s current.…[Read more]

Just for the more immediate purposes of the talks I was thinking of (1). So when you are writing equations and diagrams on the board we know what you mean right then. I found Tai-Danae Bradley’s explanation of the degree of entanglement measured by the Schmidt rank of a state via SVD really helpful. But that’s just me.

Points 2 and 3 are very int…[Read more]

Just for the more immediate purposes of the talks I was thinking of (1). So when you are writing equations and diagrams on the board we know what you mean right then. I found Tai-Danae Bradley’s explanation of the degree of entanglement measured by the Schmidt rank of a state via SVD really helpful. But that’s just me.

Points 2 and 3 are very…[Read more]

Good question. Let me talk about it here briefly. (In my opinion) “what entanglement actually is” could potentially refer to three different things:

(1) What it is mathematically. Basically: If we have the state of (say) two systems, and if that state can’t be factored into two individual states, then those two systems are (mathematically)…[Read more]

Hi Mike,

Just going through your notes you discuss entanglement. Are you going to go over what entanglement actually is or is this something we need to understand well on our own before the talk?

Hmm … you shouldn’t have to actually restart the browser. There should be some way to refresh it (refresh, reload, or something like that — depending on which browser). On the version of Firefox I’m using, there’s an icon that looks like an arrow going in a circle. You can click on that to do a “partial” refresh and shift-click on it for a…[Read more]

Shutting down the browser updates it. I’ll follow your instructions to delete messages. Thank you.

Hmm … When I look at your account I see 19. It might be a matter of refreshing your browser? Not sure. Personally I think those notifications are kind of a pain. They never completely go away until you delete them. I generally go to the “notifications” tab on my profile every once in a while and select them all by clicking the checkbox at the…[Read more]

Those are GREAT answers, @Mike and @Wayne. I rarely understand something in higher mathematics that clearly.

I just posted Sunday’s video up at the top of this thread.

It’s basically a definition.

The vector space comes first and it has some set finite dimension. Say 3 dimensions like we are used to. Then every vector in that space is said to be three dimensional and can be represented by 3 numbers, its coordinates.

If you begin with a two dimensional space, like a white board or desk top, then all vectors in…[Read more]

Not exactly. There are an infinite number of possible vectors in a space. But all of them have the same dimension. Example: The space for a quantum bit is a complex, 2d space. That simply means that it contains vectors with two components — each of the two components is a complex number.

Hope that made sense.

It’s hard to know what’s going on there. I guess we forgot to start the video at the beginning. It’s possible that it’s just something I wrote simply to provide an example on the fly.
Remind me to start the video this Sunday!

I don’t see a problem on either sheet that the video seems to correspond to.

That aside, it’s nice to have these exercises as a way of gauging our abilities.

I’m not actually sure, but it looks like these were given out on the previous (June 7th) session (assuming I’m parsing things right.) Take a look at these two:

http://github.physicscafe.org/2020-QI-Series/Problems-Change-Basis.pdf

http://github.physicscafe.org/2020-QI-Series/Problems-Change-Basis-Complex.pdf

I’m looking at the video from June 14th. It starts with Mike in the middle of working a problem, but it doesn’t look like it corresponds to any of the 8 problems from the Notes pages 34-35 (Notes generated June 15 2020). Can anyone orient me as to what is being worked on?