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Can you give a more technical description of "each photon carries one bit?" I don't doubt it, but it seems like a remarkable result! The number of photons is i

Can you give a more technical description of "each photon carries one bit?" I don't doubt it, but it seems like a remarkable result! The number of photons is itself a quantum observable (number operator) which is non-commuting with other observables. Does "each photon carries one bit" mean that if there are known N photons (eigenstate of number operator) there are N bits? Or is it saying something about distributions?

pdonis 6y ago
> Can you give a more technical description of "each photon carries one bit?" The strictly technically correct version applies (as I've said in response to others) to polarization in a setting like quantum information or quantum computing experiments, where the polarization is controlled in various ways, and where measuring the polarization of a single photon at the end of the experiment corresponds to "reading out" one bit of the result. For cases like the radio telescope observations of light from the black hole in the article this discussion was originally about, the "one bit" more or less corresponds to a "pixel" of the image that gets constructed from the data collected by multiple telescopes and combined by computers. > The number of photons is itself a quantum observable (number operator) which is non-commuting with other observables. There isn't a single "number operator" for photons. There is a number operator for each "mode" (or Fock state in more technical language), which means for each possible combination (k, u) of momentum k and polarization u. Eigenstates of the number operator for each mode are also eigenstates of the Hamiltonian and the polarization operator, so it is not true that the number operators do not commute with any other observables. Actual states in laboratory experiments are not always Fock states, but AFAIK they are close to it in quantum information and quantum computing experiments. However, the states being detected by the radio telescopes are not Fock states or anything close to it; they are coherent states, which are basically classical EM field states and are not eigenstates of the number operator, or indeed of any observable.

pdonis 6y ago

> Can you give a more technical description of "each photon carries one bit?" The strictly technically correct version applies (as I've said in response to others) to polarization in a setting like quantum information or quantum computing experiments, where the polarization is controlled in various ways, and where measuring the polarization of a single photon at the end of the experiment corresponds to "reading out" one bit of the result. For cases like the radio telescope observations of light from the black hole in the article this discussion was originally about, the "one bit" more or less corresponds to a "pixel" of the image that gets constructed from the data collected by multiple telescopes and combined by computers. > The number of photons is itself a quantum observable (number operator) which is non-commuting with other observables. There isn't a single "number operator" for photons. There is a number operator for each "mode" (or Fock state in more technical language), which means for each possible combination (k, u) of momentum k and polarization u. Eigenstates of the number operator for each mode are also eigenstates of the Hamiltonian and the polarization operator, so it is not true that the number operators do not commute with any other observables. Actual states in laboratory experiments are not always Fock states, but AFAIK they are close to it in quantum information and quantum computing experiments. However, the states being detected by the radio telescopes are not Fock states or anything close to it; they are coherent states, which are basically classical EM field states and are not eigenstates of the number operator, or indeed of any observable.