Impressionistic searches for the Golden Fleece of entanglement signaling (without the classical signal key) both within and beyond orthodox quantum theory. Stapp accepts Daryl Bem's "feeling the future" data as indicating the latter - we all agree about that. I still don't want to leave any stone unturned on the former, though I am fighting a rear guard action in that case.

The mainstream papers assume no entanglement signaling and deduce the bounds on the fidelity of imperfect copying from that. This may be dangerous circular logic.

Of course no one doubts that only mutually orthogonal states can be perfectly cloned with linear unitary operators.

Also when they use non-unitary operators in open quantum computers they want to use error-correction codes to restore the original bit pattern rather than trying to use the non-unitarity as a value added to get entanglement signaling.

Dan Greenberger wrote that Schrodinger Tigers allow superluminal entanglement signals.

D. Greenberger, “If one could build a macroscopical Schrodinger cat state, one could communicate superluminally”, PhysicaScripta,T76,

57-60 (1998).

http://www.ornl.gov/~webworks/cpr/pres/107480_.pdf

"A deep-rooted concept in quantum theory is the linear

superposition principle which follows from the linearity

of the equations of motion [1]. Linear superposition

of states is the key feature which elevates

a two-state system into a qubit. The possibility of

exploiting greater information processing ability using

qubits is now being investigated in the emerging

field of quantum computation and information technology

[2]. Further, linear evolution makes certain

operations impossible on arbitrary superpositions of

quantum states. For example, one of the simplest, yet

most profound, principles of quantum theory is that

we cannot clone an unknown quantum state exactly

[3,4]. Indeed, stronger statements may be made with

stronger assumptions: unitarity of quantum evolution

requires that even a specific pair of non-orthogonal

states cannot be perfectly copied [5]. If we give up

the requirement of perfect copies then it is possible to

copy an unknown state approximately by deterministic

cloning machines [6–11]. Recent work shows that

non-orthogonal states from a linearly independent set

can be probabilistically copied exactly [12,13] and can

evolve into a superposition of differing numbers of

copy states [14].

Notwithstanding the above, we might ask: what

could go wrong if one were to clone an arbitrary state?

In 1982 Herbert argued that the copying of half of an

entangled state, such as by a laser amplifier, would

allow one to send signals faster than light [15]. That

same year the no-cloning theorem demonstrated the

flaw in this proposed violation of causality [3,4]. Thus,

the linear evolution of even non-relativistic quantum

theory and special relativity were not in contradiction.

In fact, one can go a step further and ask if the

no-signalling condition (the impossibility of instantaneous

communication) lies behind some of the basic

axiomatic structure of quantum mechanics [16].

It turns out that the achievable fidelity of imperfect

cloning follows from this no-signalling condition [17,

18]. Further, it can be shown that even probabilistic exact

cloning cannot violate the no-signaling condition

[19]."

Physics Letters A 315 (2003) 208–212

www.elsevier.com/locate/pla

Quantum deleting and signalling

Arun K. Pati a,b,∗, Samuel L. Braunstein b

a Institute of Physics, Bhubaneswar-751005, Orissa, India

b Informatics, Bangor University, Bangor, LL57 1UT, UK

Received 26 May 2003; received in revised form 30 June 2003; accepted 1 July 2003

Abstract

"It is known that if one could clone an arbitrary quantum state then one could send signals faster than the speed of light.

Here, we show that deletion of an unknown quantum state for which two copies are available would also lead to superluminal signalling. However, the (Landauer) erasure of an unknown quantum state does not allow faster-than-light communication."

So far, so good, for Stapp's theorem (based only on linear unitarity and the Born rule) that orthodox quantum theory does not permit pure entanglement signals without a classical signal key to unlock the nonlocally encoded message. The classical key restores luminal (or subluminal signaling). However,

"We conclude with a remark that classical information

is physical but has no permanence. By contrast,

quantum information is physical and has permanence

(in view of the recent stronger no-cloning and nodeleting

theorems in quantum information [26]). Here,

permanence refers to the fact that to ‘duplicate’ quantum

information the copy must have already existed

somewhere in the universe and to ‘eliminate’ it, it must

be moved to somewhere else in the universe where it

will still exist. It would be interesting to see if the violation

of this permanence property of quantum information

can itself lead to superluminal signalling.

That it should be true is seen here partly (since deleting

implies signalling). It remains to be seen whether

negating the stronger no-cloning theorem leads to signalling."

Quantum Copying: Beyond the No-Cloning Theorem

Vladimir Buzek, Mark Hillery

(Submitted on 20 Jul 1996)

We analyze to what extent it is possible to copy arbitrary states of a two-level quantum system. We show that there exists a "universal quantum copying machine", which approximately copies quantum mechanical states in such a way that the quality of its output does not depend on the input. We also examine a machine which combines a unitary transformation with a selective measurement to produce good copies of states in a neighborhood of a particular state. We discuss the problem of measurement of the output states.

The Wootters-Zurek no-cloning theorem forbids the copying of an arbitrary quantum state. If one does not demand that the copy be perfect, however, possibilities emerge. We have examined a number of these. A quan-tum copying machine closely related to the one used by Wootters and Zurek in the proof of their no-cloning theorem copies some states perfectly and others poorly. That is, the quality of its output depends on the input. A second type of machine, which we called a universal quantum copying machine, has the property that the quality of its output is independent of its input. Finally, we examined a machine which combines a unitary transformation and a selective measurement to produce good copies of states in the neighborhood of a particular state.

A problem with all of these machines is that the copy and original which appear at the output are entangled. This means that a measurement of one affects the other. We found, however, that a nonselective measurement of the one of the output modes will provide information about the input state and not disturb the reduced density matrix of the other mode. Therefore, the output of these xerox machines is useful.

There is further work to be done; we have only explored some of the possibilities. It would be interesting to know, for example, what the best input-state independent quantum copying machine is. One can also consider machines which make multiple copies. Does the quality of the copies decrease as their number increases? These questions remain for the future.

http://arxiv.org/pdf/quant-ph/9607018v1

they do not mention entanglement signaling in the above paper

Quantum copying: A network

V. Buzek, S.L. Braunstein, M. Hillery, D. Bruss

(Submitted on 24 Mar 1997)

We present a network consisting of quantum gates which produces two imperfect copies of an arbitrary qubit. The quality of the copies does not depend on the input qubit. We also show that for a restricted class of inputs it is possible to use a very similar network to produce three copies instead of two. For qubits in this class, the copy quality is again independent of the input and is the same as the quality of the copies produced by the two-copy network

It is possible to construct devices which copy the information in a quantum state as long as one does not demand perfect copies. One can build either a duplicator, which produces two copies, or a triplicator, which produces three. Both of these devices can be realized by simple networks of quantum gates, which should make it possible to construct them in the laboratory.

There are a number of unanswered questions about quantum copiers. Perhaps the most obvious is which quantum copier is the best. Recently it has been shown [5] that the UQCM described in this paper is the best quantum copier able to produce two copies of the original qubit. It is not known, however, how to construct the best quantum triplicator (or, in general, a device which will produce multiple copies, the so-called multiplicator). There exist bounds on how well one can do, which follow from unitarity, but they are not realized by existing copiers [8]. This is at least partially the fault of the bounds which are probably lower than they have to be.

A quantum copier takes quantum information in one system and spreads it among several. It would be nice to be able to see how this happens qualitatively, but, at the moment, it is not clear how to do this. The problem is that we are interested in how only a part of the information flows through the machine. It is only the information in the input state, and not that in the two input qubits, which enter the machine in standard states, the so-called “blank pieces of paper”, which matters, but it seems to be difficult to separate the effect of the two in the action of the machine.

This issue is connected to another, which is how to best use the copies to gain information about the input state. In a previous paper we showed how nonselective measurements of a single quantity on one of the copies can be used to gain information about the original and leave the one-particle reduced density matrix of the other copy unchanged. An interesting extension of this would be to ask, for a given number of copies, how much information we can gain about the original state by performing different kinds of measurements on the copies.

It is clear that quantum copying still presents both theoretical and experimental challenges. We hope to be able to address some of issues raised by the questions in the preceding paragraphs in future publications.

http://arxiv.org/pdf/quant-ph/9703046v1

Quantum communication can send both classical and quantum information. By use of this way, we can implement pure quantum communication in directly sending classical information, Ekert’s quantum cryptography[9] and the quantum teleportation[10-13] without the help of classical communications channel.

Bell’s inequality[19] continues to be examined[20]. If Bell’s inequality can be proved and we can get long time EPR pairs against decoherence in future, pure quantum communication implies that sending information can be faster than light! We believe that this will excite much studies on many relative issues.

In summary, I design a simple way of distinguishing non-orthogonal quantum states with perfect reliability using only quantum CNOT gates in the condition. We emphasize that the key of distinguishing the two set states is the difference of discrete and two convergent values of the statistical distribution. We expect that the conditional quantum distinguishability will be proved in experiments and those pure quantum communications can be implemented."

He talks of perfect reliability and he is probably wrong. However, e.g.

http://www.physics.utoronto.ca/~aephraim/2206/2206-09-lect18.pdf

http://arxiv.org/pdf/quant-ph/0509093

he's not the only one - growing group of physicists using imperfect measurements to distinguish non-orthogonal quantum states.

"The security of quantum cryptography relies on the fact that we cannot distinguish, with certainty, several quantum nonorthogonal states ( with 100% efficiency ). That is, if we can distinguish the several quantum nonorthogonal states used as the information carriers in quantum cryptography, then we can successfully eavesdrop it. However, there is one exception in the indistinguishability: in the case of two nonorthogonal states, we can distinguish between them

with certainty, albeit with an efficiency η < 1 [7]-[9] ... Thus the one at site 2 can distinguish the two mixtures and can implement the superluminal communication. It follows that the unambiguous measurement is not possible in this case from the impossibility of the superluminal communication."

However, if we have ambiguous discrimination of non-orthogonal states we may have albeit uncertain superluminal communication?"

Phys. Rev. A 64, 022311 (2001) [10 pages]

Optimum unambiguous discrimination between linearly independent nonorthogonal quantum states and its optical realization

Abstract

Yuqing Sun1, Mark Hillery1, and János A. Bergou1,2

1Department of Physics, Hunter College, City University of New York, 695 Park Avenue, New York, New York 10021

2Institute of Physics, Janus Pannonius University, H-7624 Pécs, Ifjúság útja 6, Hungary

Received 24 October 2001; published 13 July 2001

Unambiguously distinguishing between nonorthogonal but linearly independent quantum states is a challenging problem in quantum information processing. In principle, the problem can be solved by mapping the set of nonorthogonal quantum states onto a set of orthogonal ones, which then can be distinguished without error. Such nonunitary transformations can be performed conditionally on quantum systems; a unitary transformation is carried out on a larger system of which the system of interest is a subsytem, a measurement is performed, and if the proper result is obtained the desired nonunitary transformation has been performed on the subsystem. We show how to construct generalized interferometers (multiports), which when combined with measurements on some of the output ports, implement nonunitary transformations of this type. The input states are single-photon states in which the photon is divided among several modes. A number of explicit examples of distinguishing among three nonorthogonal states are discussed, and the networks that optimally distinguish among these states are presented.

© 2001 The American Physical Society

to be continued