Mohammad Hamed Mohammady
RCQI, Bratislava
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Thursday Oct 22, 2020 / 11:00-11:30 CEST
Conditional change in energy due to quantum measurements
We introduce a definition for conditional energy changes due to quantum measurements, as the change in the conditional energy evaluated before, and after, the measurement. By imposing minimal physical requirements on these conditional energies, we show that the most general expression for the conditional energy after the measurement is simply the expected value of the Hamiltonian given the post-measurement state. Conversely, the conditional energy before the measurement is shown to be given by the real component of the weak value of the Hamiltonian, post-selected by the measurement outcome.
Hi Philipp.
I am somewhat familiar with your Phys Rev E paper, but haven’t yet studied it in detail; I will do so soon!
I would say that the difference between the “naive” definition, and the one I discussed, rests on how we define the expected energy of a system “prior” to measurement; the naive definition takes this to be independent of the measurement outcome, whereas the definition I proposed takes this to be conditional on the measurement outcome – it is a conditional expectation value of energy. So which definition one chooses depends on what question is being asked.
As for the thermodynamic differences between the two definitions, this indeed needs to be looked at more closely. My main worry with the “naive” definition is its non-uniqueness for different preparation procedures for the same state rho – condition (ii) in my talk – and that in the “classical”, commutative limit, it will not give the energy change as zero – condition (iii). Of course, these are possibly independent of satisfying the first and second laws.
Hi Mohammad!
Nice talk and very nice idea! I was, however, wondering whether you are aware of my operational approach (see, e.g., my contributed talk yesterday or https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.022127 or https://quantum-journal.org/papers/q-2020-03-02-240/)?
I am indeed a proponent of what you called the “naive definition” (as you might have guessed from the question I asked after the talk). Personally, I cannot see any problems with the naive definition, I get a first and second law, I am consistent with previously known results, and I can use my framework to analyze a large class of quantum causal models.
Would be great to hear your opinion about it! 🙂