Integral Identities





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The GHZ experiment cartoon

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I'm still a bit obsessed with the GHZ experiment.  This is the one where you prepare a GHZ state $\lvert 000 \rangle + \lvert 111 \rangle$ and send one qubit to each of 3 protagonists: Alice, Bob, and Charlie.  (I will be ignoring shared normalizer constants throughout this post, as I find they don't add anything to the understanding.) If you do the maths it turns out that when all three choose to measure in the $\lvert + \rangle$, $\lvert - \rangle$ basis (shorthand for $\lvert 0 \rangle + \lvert 1\rangle$ and $\lvert 0 \rangle - \lvert 1\rangle$) then they are guarranteed to get a parity zero result.  On the other hand if only one measures in this basis and the other two measure in the $\lvert +i\rangle$, $\lvert -i\rangle$ basis (shorthand for $\lvert 0 \rangle + i\lvert 1\rangle$ and $\lvert 0 \rangle - i\lvert 1\rangle$) they are guarranteed to get a parity one result.  As I showed in an earlier post this appears to be incompatible with the outcomes being prede...
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Is "scale insensitivity" destroying climate activism?

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Here's an image you're probably familiar with: it's the BBC News website banner.  The space between "InDepth" and "UK" is reserved for quick links to the most important issues of the day, and right now it reads "Israel-Gaza war | War in Ukraine | Climate".  It's fair to assume that the highest priority issues are closer to the left, based on how frequently these issues end up in the headline article. So, I wondered, how has the priority - according to the BBC - of the biggest issues changed over time?  I decided to sample the website using the wayback machine , once per year from September 2020 to September 2025, and here's the result:   Over these 6 years the BBC News banner has had between 1 and 4 quick links.  And it seems to be a consistent feature that whenever a new story comes along that threatens fewer lives, it takes a higher priority position in the banner.  "Climate" didn't turn up until 2022, and when it did it...
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FSM library

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I did a little embedded project recently.  Years ago I bought a binary coded decimal clock which no longer works, and I thought I could replace it with one I built myself.  (In reality this was simply an excuse to play with programming a Raspberry Pi Pico.) Broken BCD clock (left) and home grown replacement (right).  The LEDs are in 6 columns and represent time in hh:mm:ss format, with each decimal digit represented in binary. During the project I realised I needed to create a little Finite State Machine to enable setting of the time using the bootsel button.  So I searched around on the internet and found tens of different libraries, but each with its own drawbacks. Some required a wizard executable to auto-generate code which you then edit, which has the drawback that if you change the input to the wizard you then need to manually merge new auto-generated code with your changes.  Other libraries, had this strange thing where each state had its own "enter" and...
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