Deutsch and Hayden on locality

[martinbn]

I couldn't find out if the following article had been discussed (it is probably well known), but there were many threads on locality/non-locality, so it might be of interest. On first reading I like it quite a lot, made some things clearer for me, but it will need some thinking and probably a second reading. Curious to see what people here think of it.

http://xxx.lanl.gov/abs/quant-ph/9906007

Abstract:All information in quantum systems is, notwithstanding Bell's theorem, localised. Measuring or otherwise interacting with a quantum system S has no effect on distant systems from which S is dynamically isolated, even if they are entangled with S. Using the Heisenberg picture to analyse quantum information processing makes this locality explicit, and reveals that under some circumstances (in particular, in Einstein-Podolski-Rosen experiments and in quantum teleportation) quantum information is transmitted through 'classical' (i.e. decoherent) information channels.

 

[Demystifier]

There are several different DEFINITIONS of locality used by physicists. According to some definitions entanglement is local, according to other definitions entanglement is nonlocal. Needless to say, definitions by themselves are neither right nor wrong, but for various reasons different physicists prefer different definitions.

 

[martinbn]

There are several different DEFINITIONS of locality used by physicists. According to some definitions entanglement is local, according to other definitions entanglement is nonlocal. Needless to say, definitions by themselves are neither right nor wrong, but for various reasons different physicists prefer different definitions.

Of course, everyone knows this. What about the paper?

 

[Jano L.]

martinbn,

I have a hard time understanding the premises. Let's begin with the first sentence.

It is widely believed (see e.g. Bennett and Shor (1998)) that in general a complete
description of a composite quantum system is not deducible from complete
descriptions of its subsystems unless the 'description' of each subsystem S depends
on what is going on in other subsystems from which S is dynamically isolated.

Let's consider the case of two distant non-interacting systems that interacted in the past.

What is meant by "complete description of a composite quantum system"?

Is it density matrix R of the whole system and two reduced density matrices r1, r2 of subsystems? If so, then the validity of the statement attributed to Bennet and Shor is trivial, since the density matrix R cannot be reconstructed from the reduced matrices r1, r2 alone.

Or is it Einstein's complete description?

Or is it something different?


But let's try to continue.

If this were so, then in quantum systems information would be a nonlocal quantity -
that is to say, the information in a composite system would not be deducible from
the information located in all its subsystems

Here the authors reveal their belief that information is a physical quantity that can be located in physical objects and their parts. Translated ad absurdum, this leads to an idea of information density in all points of the space in such a way that its integral over some region would give the information contained in this region.

Such a view is incompatible with the ordinary notion of information. When I see a woman on a street and find her attractive, I have acquired information about her, but this was not stored bit by bit in her body parts. It was not stored anywhere - it was created in my mind due to physical interaction.

Information is not potato mash. It is the knowledge man has about the world.

The authors choose to operate with concepts like localized information or information flow which they do not define. They say they do not need the definition of information, but then the claims about the "flow of information" do not have make any sense to me. In the two requirements they give at page 3 they misinterpret information for physical quantity. They are even contradictory.

Since there is no accepted definition of information located in space, and they do not give one, the subsequent reading is very unattractive. One cannot be sure what they are talking about.

Perhaps you know more of this - what do you think is the information flow they are talking about?

...quantum physics is entirely consistent with Einstein's criterion.

In my opinion here the authors replace quantum physics by their pet formal theory of qubits and also Einstein's criterion for their understanding of it. They do not discuss the EPR paper from 1935, much less they show error in the the reasoning there. Einstein and coauthors clearly showed that QT does not fulfill their own criterion of a complete theory.

 

[Demystifier]

Of course, everyone knows this. What about the paper?

I have not studied the paper in detail, but after a superficial reading it is my impression that authors use such a definition of locality that allows them to show that QM is local.

 

[martinbn]

Jano L., I am not sure I understand your comments. They do not believe that information is a physical quantity, they use the term as understood in information theory. They do say what they mean by 'information flow' and so on!

 

[Jano L.]

The problem is, I do not believe that information resides in physical objects. Information is the state of man's mind. Their paper is based on assumption that information is stored in physical objects (qubits) and flows from one to another.

But they say they do not need to define what it is.

Although we shall express our results in terms of the location and flow of information, we
shall not require a quantitative definition of information.

Then it is hard to understand what they mean by the above expressions. Perhaps there is a quantitative definition of localized information elsewhere - can you post a link?

They give two rules of deciding whether the object contains information or not. I have thought about them a bit, but find it strange that they depend on Einstein's completeness criterion and the notion of probability. My understanding of information does not require any of them. Can you give some simple explicit example of parameter q and situation where these two postulates imply that the object contains information about q?

 

[yoda jedi]

martinbn,

I have a hard time understanding the premises. Let's begin with the first sentence.



Let's consider the case of two distant non-interacting systems that interacted in the past.

What is meant by "complete description of a composite quantum system"?

Is it density matrix R of the whole system and two reduced density matrices r1, r2 of subsystems? If so, then the validity of the statement attributed to Bennet and Shor is trivial, since the density matrix R cannot be reconstructed from the reduced matrices r1, r2 alone.

Or is it Einstein's complete description?

Or is it something different?


But let's try to continue.



Here the authors reveal their belief that information is a physical quantity that can be located in physical objects and their parts. Translated ad absurdum, this leads to an idea of information density in all points of the space in such a way that its integral over some region would give the information contained in this region.

Such a view is incompatible with the ordinary notion of information. When I see a woman on a street and find her attractive, I have acquired information about her, but this was not stored bit by bit in her body parts. It was not stored anywhere - it was created in my mind due to physical interaction.

Information is not potato mash. It is the knowledge man has about the world.

The authors choose to operate with concepts like localized information or information flow which they do not define. They say they do not need the definition of information, but then the claims about the "flow of information" do not have make any sense to me. In the two requirements they give at page 3 they misinterpret information for physical quantity. They are even contradictory.

Since there is no accepted definition of information located in space, and they do not give one, the subsequent reading is very unattractive. One cannot be sure what they are talking about.

Perhaps you know more of this - what do you think is the information flow they are talking about?



In my opinion here the authors replace quantum physics by their pet formal theory of qubits and also Einstein's criterion for their understanding of it. They do not discuss the EPR paper from 1935, much less they show error in the the reasoning there. Einstein and coauthors clearly showed that QT does not fulfill their own criterion of a complete theory.

and the previous position of einstein:

...The argument Einstein gave at the 1927 Solvay conference requires only a single measurement to be performed, whereas from 1935 onwards he adopted an argument requiring a measurement to be chosen from two possibilities. Why did Einstein complicate the argument in this way? Indeed, as has been noted by many authors, this complication was actually detrimental to the effectiveness of the argument, given that most of the criticisms directed against the two-measurement form of the argument (Bohr’s included) focus upon his use of counterfactual reasoning, an avenue that is not available in the 1927 version...

...

...“For reasons of language this [paper*] was written by Podolsky after many discussions.
But still it has not come out as well as I really wanted; on the contrary, the main point was,
so to speak, buried by the erudition.”...
einstein


1935 paper*