Bell's theorem in the presence of classical communication
I explain what kinds of correlation or even direct classical communication between detectors invalidate Bell's theorem, and what kinds do not.
quant-ph↗
arXiv subjects
N. David Mermin
Publications and source records attributed to N. David Mermin.
From Cbits to Qbits: Teaching computer scientists quantum mechanics
A strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory. Although the article as a whole addresses teachers of physics, well versed in quantum mechanics, the central pedagogical development is addressed directly to computer scientists and mathematicians, with only occasional asides to their teacher. Physicists uninterested in quantum pedagogy may be amused (or irritated) by some of the views of standard quantum mechanics that arise naturally from this unorthodox perspective.
quant-ph↗
Shedding (red and green) light on "time related hidden parameters"
I explain in elementary terms why the critique of Hess and Philipp in Section 3.2 of quant-ph/0103028 fails to invalidate the nontechnical version of Bell's theorem I gave twenty years ago, involving two detectors with 3-pole switches and red and green lights.
quant-ph↗
Deconstructing Dense Coding
The remarkable transmission of two bits of information via a single qubit entangled with another at the destination, is presented as an expansion of the unremarkable classical circuit that transmits the bits with two direct qubit-qubit couplings between source and destination
quant-ph↗
From Classical State-Swapping to Quantum Teleportation
The quantum teleportation protocol is extracted directly out of a standard classical circuit that exchanges the states of two qubits using only controlled-NOT gates. This construction of teleportation from a classically transparent circuit generalizes straightforwardly to d-state systems.
quant-ph↗
How much state assignments can differ
We derive necessary and sufficient conditions for a group of density matrices to characterize what different people may know about one and the same physical system.
quant-ph↗
Whose Knowledge?
Sir Rudolph Peierls, in a reply to John Bell's last critique of the state of our understanding of quantum mechanics, maintained that it is easy to give an acceptable account of the physical significance of the quantum theory. The key is to recognize that all the density matrix characterizing a physical system ever represents is knowledge about that system. In answer to Bell's implicit rejoinder "Whose knowledge?" Peierls offered two simple consistency conditions that must be satisfied by density matrices that convey the knowledge different people might have about one and the same physical system: their density matrices must commute and must have a non-zero product. I describe a simple counterexample to his first condition, but show that his second condition, which holds trivially if the first does, continues to be valid in its absence. It is an open question whether any other conditions must be imposed.
quant-ph↗
Notes on a Paulian Idea: Foundational, Historical, Anecdotal and Forward-Looking Thoughts on the Quantum
This document is the first installment of three in the Cerro Grande Fire Series. It is a collection of letters written to various colleagues, most of whom regularly circuit this archive, including Howard Barnum, Paul Benioff, Charles Bennett, Herbert Bernstein, Doug Bilodeau, Gilles Brassard, Jeffrey Bub, Carlton Caves, Gregory Comer, Robert Griffiths, Adrian Kent, Rolf Landauer, Hideo Mabuchi, David Mermin, David Meyer, Michael Nielsen, Asher Peres, John Preskill, Mary Beth Ruskai, Ruediger Schack, Abner Shimony, William Wootters, Anton Zeilinger, and many others. The singular thread sewing all the letters together is the quantum. Some of the pieces are my best efforts to date to give substance to an evanescent thought I see rising from the field of quantum information---I call it the Paulian idea. To the extent I have communicated its misty shadow to my correspondents and seen a twinkle of enthusiasm, it seemed worthwhile to expand the jury on this anniversary occasion.
quant-ph↗
A Kochen-Specker Theorem for Imprecisely Specified Measurement
A recent claim that finite precision in the design of real experiments ``nullifies'' the impact of the Kochen-Specker theorem, is shown to be unsupportable, because of the continuity of probabilities of measurement outcomes under slight changes in the experimental configuration.
quant-ph↗
What is quantum mechanics trying to tell us?
I explore whether it is possible to make sense of the quantum mechanical description of physical reality by taking the proper subject of physics to be correlation and only correlation, and by separating the problem of understanding the nature of quantum mechanics from the hard problem of understanding the nature of objective probability in individual systems, and the even harder problem of understanding the nature of conscious awareness. The resulting perspective on quantum mechanics is supported by some elementary but insufficiently emphasized theorems. Whether or not it is adequate as a new Weltanschauung, this point of view toward quantum mechanics provides a different perspective from which to teach the subject or explain its peculiar character to people in other fields.
quant-ph↗
What Do These Correlations Know About Reality? Nonlocality and the Absurd
In honor of Daniel Greenberger's 65th birthday I record for posterity two superb examples of his wit, offer a proof of an important theorem on quantum correlations that even those of us over 60 can understand, and suggest, by trying to make it look silly, that invoking ``quantum nonlocality'' as an explanation for such correlations may be too cheap a way out of the dilemma they pose.
quant-ph↗
Nonlocality and Bohr's reply to EPR
Henry Stapp's commentary (quant-ph/9711060) does not capture the point I was trying to make in my essay (quant-ph/9711052) on how a subtle flaw in his ``proof of quantum nonlocality'' clearly illustrates a central issue in Bohr's reply to EPR. I therefore wish to emphasize what I do and do not say in that essay and even, with some trepidation, what Bohr did and did not say in his reply to EPR.
quant-ph↗
Nonlocal character of quantum theory?
In a recent article under the above title (but without the question mark) Henry Stapp presented arguments which lead him to conclude that under suitable conditions ``the truth of a statement that refers only to phenomena confined to an earlier time'' must ``depend on which measurement an experimenter freely chooses to perform at a later time.'' I point out that the reasoning leading to this conclusion relies on an essential ambiguity regarding the meaning of the expression ``statement that refers only to phenomena confined to an earlier time'' when such a statement contains counterfactual conditionals. As a result the argumentation does not justify the conclusion that there can be frames of reference in which future choices can affect present facts. But it does provide an instructive and interestingly different opportunity to illustrate a central point of Bohr's reply to Einstein, Podolsky, and Rosen.
quant-ph↗
The Ithaca Interpretation of Quantum Mechanics
I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and I discuss two simple theorems. One, as far as I know, is new; the other was only noted a few years ago. Both have important implications for such a sensible interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)
quant-ph↗
Crystallography Without Periodicity
Text of a talk given at the International Colloquium on Group Theoretic Methods in Physics, Salamanca, July, 1992. Another futile attempt to persuade the world that space groups can be fun.
cond-mat↗
Copernican Crystallography
Redundancies are pointed out in the widely used extension of the crystallographic concept of Bravais class to quasiperiodic materials. Such pitfalls can be avoided by abandoning the obsolete paradigm that bases ordinary crystallography on microscopic periodicity. The broadening of crystallography to include quasiperiodic materials is accomplished by defining the point group in terms of indistinguishable (as opposed to identical) densities.
hep-th↗