Consequences when a measurement is destroyed?

[Buzz Bloom]

TL;DR Summary

I recall reading somewhere (I cannot remember where) that there are situations in which the consequences of a measurement change if the result of the measurement is destroyed.

I would much appreciate it if someone can help me find a source discussing this topic. I tried a search on the Internet with several alternative ways to express the question, but nothing worked.

I have in mind a particular example, but I do not know if it is applicable to this question as a demonstration of a change.

Two particles are created with entangled spin. Each particle has a detector to measure it's spin. There is an angle between the orientations of the two detectors. The fraction of experiments in which the two detectors assign the same spin value to the two particles depends on this angle. What happens if two detectors are at different distances from the creation of the particle pair, and the closer detector destroys its measurement a very short time after the measurement was made if the value is "up"?

 

[Morbert]

A measurement generates an irreversible record, even if that record is inaccessible to humans. A detector would not be able to destroy the record of its measurement. At best it could render it unreadable by humans.

 

[Nugatory]

What happens if two detectors are at different distances from the creation of the particle pair, and the closer detector destroys its measurement a very short time after the measurement was made if the value is "up"?

Once something thermodynamically irreversible (in this case, the "earlier" detection at the closer detector) it has happened. The statistics at the other detector are the same whether the result of the measurement is preserved or not.

This is just another manifestation of decoherence turning a quantum superposition into a classical statistical state; if you choose to use a collapse interpretation to describe this situation you will say that the "earlier" detection collapsed the wave function, but we don't know which way.

Also note the scare-quotes around the word "earlier" above. If the two measurements events are space-like separated, then which one happened first is frame dependent. That should be a very strong hint that no amount of manipulation of the output of one detector can affect the other.

 

[Jarek 31]

Summary:: I recall reading somewhere (I cannot remember where) that there are situations in which the consequences of a measurement change if the result of the measurement is destroyed.

Do you mean delayed choice quantum eraser? https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser
Walborn's is even nicer: rotating polarizer in one arm, you change between classical and quantum double slits statistics on the second: https://web.archive.org/web/20150516123842/http:/grad.physics.sunysb.edu:80/~amarch/

Gathered some more such experiments: https://www.dropbox.com/s/0zl18yttgnpc52w/causality.pdf

 

[Nugatory]

Do you mean delayed choice quantum eraser?

No, the thought experiment in this thread is Bohm’s version of the original EPR argument, using as non-commuting observables spin on different axes instead of position and momentum as in the original.

 

[Jarek 31]

Measuring entangled photons in different axes is the base of quantum cryptography protocols like BB84.
Destroying information through measurement is nicely seen e.g. in sequential Stern-Gerlach: https://en.wikipedia.org/wiki/Stern–Gerlach_experiment#Sequential_experiments

 

[Buzz Bloom]

Thank you all for your responses.

 

[Morbert]

Do you mean delayed choice quantum eraser? https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser

A quick note on the DCQE: If we understand a measurement to be a correlation between a quantum property of the measured system and a classical property of the apparatus, the ambiguity in the DCQE experiment goes away.

A traditional presentation of DCQE might describe detectors $D_1$ and $D_2$ as erasing a previous "which-slit" measurement. But with the above understanding of a measurement, a which-slit measurement only occurs if detectors $D_3$ or $D_4$ are activated. Before this time, no irreversible record exists, and so no measurement has occurred. If a measurement has not occurred, how can it be destroyed by $D_1$ or $D_2$?

Maybe a better name would be DCQM or "delayed choice quantum measurement".

 

[vanhees71]

Take the DCQE as described in

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, PRA 65 033818 (2002)

There you have a once and for all fixed measurement protocol, i.e., a data set about the entire ensemble of registered entangled photon pairs. Of course, this data set doesn't change anymore as it should be for a well built experiment.

You "erase" the which-way information by choosing certain subensembles of the photons, which is possible due to the information stored in the measurement protocol, and for that subensembles you get two-slit interference fringes though there are no interference fringes for the total ensemble.

This delayed choice of which ensemble you use is possible due to the preparation of the photon pairs and polarization-entangled pairs via parametric downconversion. Of course this does not imply that you somehow have retrocausal actions into the past or other esoterical ideas sometimes envoked to sell bad popular-science books on QT.

 

[Jarek 31]

Morbert, in this (Kim et al.) version we indeed have no control if the which-path information will be erased, as it is randomly decided by choosing one of 4 detectors.

But this weakness is overcame in later Walborn's version I have mentioned ( https://journals.aps.org/pra/abstract/10.1103/PhysRevA.65.033818 ), where we directly decide if which-path information should be erased.
Specifically, this information is encoded in polarization of a photon there - this way can be erased or not depending on rotation of polarizer on the way.

Shor's algorithm can be seen as DCQE on steroids: we split calculations into two branches, enter input in one branch, read its output in second branch.
Even more, it also needs auxiliary qubits - which naively could be discarded after all, but measuring them would cripple calculation - Peter Shor writes we need to "uncompute" them before discarding: https://physics.stackexchange.com/q...final-collapse-of-the-auxiliary-qubits-crippl

 

[Morbert]

Morbert, in this (Kim et al.) version we indeed have no control if the which-path information will be erased, as it is randomly decided by choosing one of 4 detectors.

But this weakness is overcame in later Walborn's version I have mentioned ( https://journals.aps.org/pra/abstract/10.1103/PhysRevA.65.033818 ), where we directly decide if which-path information should be erased.
Specifically, this information is encoded in polarization of a photon there - this way can be erased or not depending on rotation of polarizer on the way.

This is probably an answer more suited to the interpretations forum but:

If a measurment is the production of an classical record correlated with a measured quantum property, then the measurements in the above experiment occur when $D_s$ and $D_p$ produce classical records, as opposed to when the photons are entangled with a secondary beam. Under this understanding, no which-path measurement is erased.

The paper is perfectly correct. I just think the language can be ambiguous.

 

[Morbert]

Measuring entangled photons in different axes is the base of quantum cryptography protocols like BB84.
Destroying information through measurement is nicely seen e.g. in sequential Stern-Gerlach: https://en.wikipedia.org/wiki/Stern–Gerlach_experiment#Sequential_experiments

P.S. I was thinking about this example.

Consider an experiment consisting of a particle $s$ and 3 SG devices with filters, arranged to sequentially measure spins $z,x,z$ etc, and the environment $\epsilon$. The Hilbert space for this setup looks like $$\mathcal{H} = \mathcal{H}_s\otimes\mathcal{H}_{SG_1}\otimes\mathcal{H}_{SG_2}\otimes\mathcal{H}_{SG_3}\otimes\mathcal{H}_\epsilon$$. If the experiment concludes and the particle makes it through all the devices, the particle will be in the state $|z^+\rangle_s$ but the information about past measurements would still be recorded. There will be a projector $R$ onto a subspace of $\mathcal{H}$ $$R = \Pi_{s}^{z^+}\Pi_{SG_1}^{z^+}\Pi_{SG_2}^{x^+}\Pi_{SG_3}^{z^+}\Pi_{\epsilon}^{z^+,x^+,z^+}$$ which corresponds to a classical record of all three measurements. Even as the particle moves on to the next SG device, the previous measurement is recorded by properties of the previous SG device and the environment.