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Can anyone with a background in quantum information theory tell me how QI models the distinction between a quantum system being measured or unitarily evolved? N

Can anyone with a background in quantum information theory tell me how QI models the distinction between a quantum system being measured or unitarily evolved? Nicole Yunger Halpern talks about these things as if the measurement process were a well-defined thing happening at a specific instant in time. How and what do quantum information theorists think about the measurement problem these days? On another note, having read John Preskill's article (https://quantumfrontiers.com/2015/11/06/wouldnt-you-like-to-know-whats-going-on-in-my-mind/ https://quantumfrontiers.com/2015/11/06/wouldnt-you-like-to-...) on the whole topic, including his reference to the zebrafish (https://www.nature.com/news/flashing-fish-brains-filmed-in-action-1.12621 https://www.nature.com/news/flashing-fish-brains-filmed-in-a...): Assuming that quantum mechanics does influence cognition as proposed by Matthew Fisher, wouldn't mapping the (zebrafish's) brain then influence how it works?

krastanov 7y ago
Most QI professionals do not worry about the philosophical "measurement problem", because it does not matter in their daily work (the math just works). However, it is certainly interesting and it might end up being important for the foundations of quantum mechanics. By the way, here is something you might want to look up: in the context of Lindbladian (non-unitary) evolution or in the context of weak quantum measurements, the measurement problem is not particularly obvious or disturbing. At the end it is still there, but these toolkits give you a way to reinterpret it as an uninteresting detail of the theory, not as a horrible stain.
mathgenius 7y ago
> the distinction between a quantum system being measured or unitarily evolved When you try to describe a part of an entangled quantum system, independently of the whole, you will be forced to use probabilities in your description. This is quantum measurement.
- codethief 7y ago
  I don't think I would call this a "measurement". A measurement, in the Copenhagen interpretation, is a fundamentally non-unitary process. What you're describing is simply tracing out the environment, so that we end up with a mixed state. The complete density matrix, however, is still being governed by the Von-Neumann equation and therefore evolving unitarily. So I assume what you're saying is that we don't need to model measurements separately since their results would be described by statistical ensembles and, at the level of a subsystem, you can't really tell the difference between a genuinely entangled state and a statistical ensemble, anyway?
gaze 7y ago
You treat them as separate things. Kinda. You have the measurement mechanism and you have the unitary evolution mechanism. There are varying degrees of sophistication for modeling the measurement mechanism, and there's ways to have unitary evolution with simultaneous measurement, as well as weak measurement, and there's systems where you can probe the dynamics of a measurement. For instance, you can "watch" a quantum jump or even stop and reverse it (Z. K. Minev et. al. 2018). Generally these things are all modeled using the Stochastic Master Equation. In the end though, the SME is just unitary evolution of a small system coupled to a large markovian bath, with a Bayesian update added. In other words, one could derive the SME by taking an infinitesimal evolution of the unitary system (coupled to the bath) followed by an infinitesimal bayesian update, followed by unitary, followed by Bayesian update, etc. These things are all well covered by Gardiner Zoller 97, and Dan Steck's quantum optics notes, available at http://atomoptics-nas.uoregon.edu/~dsteck/teaching/quantum-optics/quantum-optics-notes.pdf http://atomoptics-nas.uoregon.edu/~dsteck/teaching/quantum-o... . Some would say that the SME is the fundamental thing, the Maxwell's equations of quantum information with measurement, and that the instantaneous measurement you may be familiar with is just a limit of the SME's evolution. Some might also say that the SME is a thing you derive from weakly coupling a stream qubits to a system and then performing hard, instantaneous measurement on those qubits. The math makes no distinction.
- codethief 7y ago
  Thanks a lot for the reference, I will have a look!

krastanov 7y ago

Most QI professionals do not worry about the philosophical "measurement problem", because it does not matter in their daily work (the math just works). However, it is certainly interesting and it might end up being important for the foundations of quantum mechanics. By the way, here is something you might want to look up: in the context of Lindbladian (non-unitary) evolution or in the context of weak quantum measurements, the measurement problem is not particularly obvious or disturbing. At the end it is still there, but these toolkits give you a way to reinterpret it as an uninteresting detail of the theory, not as a horrible stain.

mathgenius 7y ago

> the distinction between a quantum system being measured or unitarily evolved When you try to describe a part of an entangled quantum system, independently of the whole, you will be forced to use probabilities in your description. This is quantum measurement.

codethief 7y ago
I don't think I would call this a "measurement". A measurement, in the Copenhagen interpretation, is a fundamentally non-unitary process. What you're describing is simply tracing out the environment, so that we end up with a mixed state. The complete density matrix, however, is still being governed by the Von-Neumann equation and therefore evolving unitarily. So I assume what you're saying is that we don't need to model measurements separately since their results would be described by statistical ensembles and, at the level of a subsystem, you can't really tell the difference between a genuinely entangled state and a statistical ensemble, anyway?

gaze 7y ago

You treat them as separate things. Kinda. You have the measurement mechanism and you have the unitary evolution mechanism. There are varying degrees of sophistication for modeling the measurement mechanism, and there's ways to have unitary evolution with simultaneous measurement, as well as weak measurement, and there's systems where you can probe the dynamics of a measurement. For instance, you can "watch" a quantum jump or even stop and reverse it (Z. K. Minev et. al. 2018). Generally these things are all modeled using the Stochastic Master Equation. In the end though, the SME is just unitary evolution of a small system coupled to a large markovian bath, with a Bayesian update added. In other words, one could derive the SME by taking an infinitesimal evolution of the unitary system (coupled to the bath) followed by an infinitesimal bayesian update, followed by unitary, followed by Bayesian update, etc. These things are all well covered by Gardiner Zoller 97, and Dan Steck's quantum optics notes, available at http://atomoptics-nas.uoregon.edu/~dsteck/teaching/quantum-optics/quantum-optics-notes.pdf http://atomoptics-nas.uoregon.edu/~dsteck/teaching/quantum-o... . Some would say that the SME is the fundamental thing, the Maxwell's equations of quantum information with measurement, and that the instantaneous measurement you may be familiar with is just a limit of the SME's evolution. Some might also say that the SME is a thing you derive from weakly coupling a stream qubits to a system and then performing hard, instantaneous measurement on those qubits. The math makes no distinction.

codethief 7y ago
Thanks a lot for the reference, I will have a look!