Hi all,

Just back from dinner, sorry to be joining so late.

Since you’ve been discussing the two different implementations of a PM (adiabatic and Zeno), here’s a question for Shan. Do you think a Zeno-type PM is equally indicative of the reality of the wave function as an adiabatic PM? If yes, why? If not, what do you see as the…[Read more]

OK, Matt. Have a good night! Best, Shan

Matt #1048:

I think there is an essential difference between we know nothing about the measured system and we know something about it.

If we know nothing about the measured system, then we cannot surely measure the wave function of a single system, and we cannot distinguish nonorthogonal states either, while if we know something about it, we may…[Read more]

I’m also done for today, but I’ll keep on eye on this tomorrow in case there are further thoughts.

Thanks to everyone for the stimulating responses that I think will, in the true spirit of a workshop, lead to improvements in the paper whenever it finally appears!

Matt

Hi Max,

why not say something about Matt’s ideas. Please join in! We may extend our discussions if you have time.

Shan

Thanks Matt, and everybody else for some interesting ideas. My bedtime has arrived. Bob Griffiths

Hi Bob,

Thanks for your further comments! I fully agree with you. Yes, what PMs measures are just the density and flux density. The wave function is then constructed from these. My conclusion from PMs is that the wave function describes a property of a single quantum system. But which property it describes is a further problem. I have even…[Read more]

Shan #1046,

The claims you refer to apply only when one considers the totality of Bob and Charlie’s actions as a measurement procedure on the system from Alice. (Imagine putting Bob and Charlie in a huge black box, that has an input for the quantum system and a classical output of Bob’s estimate of the state.)

Since an arbitrarily sequence of…[Read more]

Bob #1045,

You might be interested to know that your example is pretty much exactly what protective measurement amounts to when carried out within the Bartlett, Rudolph, Spekkens model.

Yours,
Matt

Hi Matt,

Relative to #1041, I now think there are no essential difference, and yours may be regarded as an interesting extension of the original Zeno PM.

My another point is that even if your alternative protocol does not establish the reality of the wave-function, this does not necessarily imply that the original PM cannot do that.

Moreover,…[Read more]

Dear Shan,

I am a bit bothered by your idea that measuring the wave function
piece by piece is evidence that it is “real”. Imagine a classical
particle whizzing around in some sort of confining potential, moving
so fast that it looks like a cloud. You send slow projectiles through
the cloud and get is density at different points. But you are…[Read more]

Shan #1042,

We should be able to reach agreement at least on this narrow point: Thinking of the protection-by-measurement (aka Zeno) scheme, does the protection amount to repeated applications of the channel given by eq. (1) in my notes?

(How this compares to the protection in the Hamiltonian-based scheme is probably a question for another day.…[Read more]

Hi Matt, this answer is relative to #1034. I will respond your reply #1041 later.

Hi Matt (P),

Thanks for your kind reply!

My point is still that the resources provided by your protecting channel is not exactly those provide by a PM. An adiabatic PM can provide more resources (when the protection based on energy conservation is ensured, e.g. when a
lower bound of the energy gaps to other levels is known beforehand). These…[Read more]

Thinking on the spot now, is there actually any difference between a small time-slice of a von-Neumann type strong measurement and a weak measurement? Weak measurements are normally obtained by reducing the interaction strength, but wouldn’t interacting for a shorter time amount to exactly the same thing?

If there is no difference, then my…[Read more]

Hi Matt (L),

Relative to #1033, I think it is an interesting idea, which has not been discussed in the literature. That will require to transform the time parameter in the adiabatic scheme into the frequency parameter in the Zeno scheme.

Shan

I think this may also answer Bob’s comments. Thanks Bob!

Hi Matt,

Thank you very much for your clarification!

I think the measurement in Matt’s notes is not exactly the Zeno-type PM either. There is at least one difference as far as I can see. In the Zeno version, there are indeed frequent projective measurements to protect the measured state. But the measurement of the studied observable is usually a…[Read more]

Dear Matt,
This may be a bit off the subject, but you said you were asking for
comments. I haven’t had time to work through the toy model in your
section 4, which you say is based on work by Spekkens and
collaborators, including Bartlett, Rudolph, and Spekkens,
“Reconstruction of Gaussian quantum mechanics from Liouville mechanics
with an…[Read more]

Hi Shan,

Having returned to one of the original papers, I can see that you’re right that my “recap” of protective measurement does not quite agree with the original scheme, in which the “protecting” measurements are done during Bob’s measurement rather than only between them. Perhaps I heard about this scheme elsewhere and somehow I confused it…[Read more]