Timeline for $n$ qubit vs. a $d=2^n$ qudit states and measurements
Current License: CC BY-SA 4.0
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| Dec 30, 2022 at 7:37 | comment | added | glS♦ | @MarkS a harmonic oscillator is an infinite-dimensional system so that somewhat complicates things, though the same principle will apply. But I mean the classical analogy is superposition : entanglement = single probability distribution : correlations between outcomes. Of course in the quantum case the correlations are at the "deeper" level of amplitudes, but the principle that you can in principle arbitrarily partition the outcomes into different parties is identical. You can discuss nonlocality and LHV for these things but w/o an actual notion of locality it's probably not very useful | |
| Dec 30, 2022 at 2:22 | comment | added | Mark Spinelli | Well, a superposition of a single qudit can be isomorphic to an entanglement of smaller subsystems. In that sense, there’s no classical counterpart. A harmonic oscillator with four modes on a single particle can be in a superposition and be isomorphic to a Bell pair - but there’s no spatial locality to confuse things with a four mode qudit in superposition. Could we play the CHSH game with such a qudit? Does that even make sense? | |
| Dec 30, 2022 at 0:32 | comment | added | glS♦ | yes, I'd say so. I'm not sure how "profound" this actually is though. I think of it as the quantum counterpart of the fact that for any (classical) probability vector over $pq$ outcomes, we can talk about "correlations between two outcomes" (making a choice on how to assign the $pq$ outcomes to the two parties), one with $p$ and the other with $q$ outcomes. | |
| Dec 29, 2022 at 19:33 | comment | added | Mark Spinelli | I find the sentence "On the other hand, if you reinterpret the states as those of a number of qubits, then you can meaningfully talk of entanglement between the different modes" to be quite profound. If $n$ is a power of two can we think of an $n$-mode qudit as a tensor-product of $\log_2 n$ "virtual" qubits? As long as $n$ is composite I guess, we can always factor $n$ to its constituent qudits. Then, a superposition of modes of the $n$-mode qudit would correspond to entanglement among the virtual qubits. | |
| Jun 19, 2019 at 21:35 | history | edited | glS♦ | CC BY-SA 4.0 |
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| Jun 19, 2019 at 12:05 | vote | accept | mavzolej | ||
| Jun 18, 2019 at 13:38 | history | answered | glS♦ | CC BY-SA 4.0 |