Does the Zeno effect freeze all the commuting observables?

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Hi Pfs
Take a two level system up-down in its up level, There are other observables that commute
with that. is it true that applying the Zeno's effect by fast repeated measure of that
observable will also freeze the system on up?
thanks.
 
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Heidi said:
Hi Pfs
Take a two level system up-down in its up level, There are other observables that commute
with that. is it true that applying the Zeno's effect by fast repeated measure of that
observable will also freeze the system on up?
thanks.
It depends on the state of the system. If the state can be separated into a product state of each observable, then measuring one observable will not affect the other. However, of the state cannot be separated like that, then measuring one is equivalent to measuring the other, and the Zeno effect can freeze the other observable.
 
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FAQ: Does the Zeno effect freeze all the commuting observables?

What is the Zeno effect in quantum mechanics?

The Zeno effect, also known as the Quantum Zeno Effect, is a phenomenon in quantum mechanics where the frequent observation of a quantum system can inhibit its evolution. Essentially, if a system is measured repeatedly at very short intervals, it can be "frozen" in its initial state due to the collapse of the wave function upon each measurement.

Does the Zeno effect apply to all types of measurements?

No, the Zeno effect specifically applies to projective measurements, which are idealized, instantaneous measurements that collapse the wave function. It does not necessarily apply to weak measurements or continuous monitoring, where the system is not fully collapsed but rather gently perturbed.

Can the Zeno effect freeze all commuting observables simultaneously?

In theory, the Zeno effect can freeze all commuting observables simultaneously because commuting observables share a common set of eigenstates. When a system is frequently measured in relation to one observable, it collapses into an eigenstate that is also an eigenstate of the other commuting observables, thus effectively freezing all of them.

What is the role of non-commuting observables in the Zeno effect?

Non-commuting observables do not share a common set of eigenstates, so frequent measurements of one observable will not necessarily freeze the state in terms of the other. The Zeno effect is less straightforward in such cases because the measurement of one observable can disturb the eigenstates of the other, preventing simultaneous freezing.

Are there practical applications of the Zeno effect?

Yes, the Zeno effect has practical applications in quantum computing and quantum control. It can be used to protect quantum states from decoherence by frequently measuring them, thus maintaining their coherence over longer periods. This is particularly useful in quantum error correction and the stabilization of quantum bits (qubits).

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