Re: [FRIAM] Deriving quantum theory from information processing axioms
I just looked at *Theory of Nothing* on Amazonhttp://www.amazon.com/Theory-Nothing-Russell-Standish/dp/1921019638. Two very nice reviews. Amazon's Look Inside doesn't show much, but the book looks very much worth reading. The Introduction talks about Schrodinger's cat. It had never occurred to me that the cat *always *experiences a boring hour and then comes out alive--at least according to the Many Worlds View of QM. It's on my reading list. *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 * blog: *http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ *_* On Tue, Jul 26, 2011 at 3:13 PM, Grant Holland grant.holland...@gmail.comwrote: Exciting, Russ. I've downloaded your 2004 paperhttp://arxiv.org/pdf/physics/0001020v6, and will take a look. Thanks, Grant On 7/26/11 3:16 PM, Russell Standish wrote: Of course, I published a paper in 2004 (Why Occams Razor) doing essentially the same thing (I expanded on this somewhat in my 2006 book, Theory of Nothing). I would also say, that Lucien Hardy did something similar in 2001 (Quantum theory from five reasonable axioms). Also, there have been other works linking the uncertainty principle to the Cramer-Rao inequality from information theory. I expect this current paper (when I finally get around to read it), will be equivalent to what I've done. Ultimately, it may come down to history which method is preferred, or if some uber-clear version is presented (like Dirac did to Schroedinger and Heisenberg's theories). It would be all the more remarkable if this approach was fundamentally different. All I have to say now... On Tue, Jul 26, 2011 at 10:37:46AM -0700, Russ Abbott wrote: I expected this to have more of an impact than it seems to be having. What am I missing? *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 * blog: *http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ *_* On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott russ.abb...@gmail.com russ.abb...@gmail.com wrote: From APS Physics http://physics.aps.org/articles/v4/55 http://physics.aps.org/articles/v4/55. We know how to use the “rules” of quantum physics to build lasers, microchips, and nuclear power plants, but when students question the rules themselves, the best answer we can give is often, “The world just happens to be that way.” Yet why are individual outcomes in quantum measurements random? What is the origin of the Schrödinger equation? In a paper [1http://physics.aps.org/articles/v4/55#c1 http://physics.aps.org/articles/v4/55#c1] appearing in Physical Review A, Giulio Chiribella at the Perimeter Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo Perinotti at the University of Pavia, Italy, offer a framework in which to answer these penetrating questions. They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory. (Strictly speaking, their derivation only applies to systems that can be constructed from a finite number of quantum states, such as spin.) In this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s belief that one obtains “it from bit,” in other words, that our account of the universe is constructed from bits of information, and the rules on how that information can be obtained determine the “meaning” of what we call particles and fields. ... They assume five new elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—which define a broad class of theories of information processing. For example, the causality axiom—stating that one cannot signal from future measurements to past preparations—is so basic that it is usually assumed a priori. Both classical and quantum theory fulfil the five axioms. What is significant about Chiribella et al.’s work is that they show that a sixth axiom—the assumption that every state has what they call a “purification”—is what singles out quantum theory within the class. In fact, this last axiom is so important that they call it a postulate. The purification postulate can be defined formally (see below), but to understand its meaning in simple words, we can look to Schrödinger, who in describing entanglement gives the essence of the postulate: “Maximal knowledge of a total system does not necessarily include maximal knowledge of all its parts.” (Formally, the purification postulate states that every mixed state ρA of system A can always be seen as a state belonging to a part of a composite system AB that
Re: [FRIAM] Deriving quantum theory from information processing axioms
And speaking of multiverses, this was just published on the Scientific American websitehttp://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universe . *In the August issue of*Scientific American,* cosmologist George Ellis describes why he's skeptical about the concept of parallel universes. Here, multiverse proponents Alexander Vilenkinhttp://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universeWT.mc_id=SA_WR_20110727# and http://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universeWT.mc_id=SA_WR_20110727# **Max Tegmarkhttp://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universeWT.mc_id=SA_WR_20110727# offer counterpoints, explaining why the multiverse would account for so many features of our universe—and how it might be tested.* *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 * blog: *http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ *_* On Wed, Jul 27, 2011 at 12:54 PM, Russ Abbott russ.abb...@gmail.com wrote: I just looked at *Theory of Nothing* on Amazonhttp://www.amazon.com/Theory-Nothing-Russell-Standish/dp/1921019638. Two very nice reviews. Amazon's Look Inside doesn't show much, but the book looks very much worth reading. The Introduction talks about Schrodinger's cat. It had never occurred to me that the cat *always *experiences a boring hour and then comes out alive--at least according to the Many Worlds View of QM. It's on my reading list. *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 * blog: *http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ *_* On Tue, Jul 26, 2011 at 3:13 PM, Grant Holland grant.holland...@gmail.com wrote: Exciting, Russ. I've downloaded your 2004 paperhttp://arxiv.org/pdf/physics/0001020v6, and will take a look. Thanks, Grant On 7/26/11 3:16 PM, Russell Standish wrote: Of course, I published a paper in 2004 (Why Occams Razor) doing essentially the same thing (I expanded on this somewhat in my 2006 book, Theory of Nothing). I would also say, that Lucien Hardy did something similar in 2001 (Quantum theory from five reasonable axioms). Also, there have been other works linking the uncertainty principle to the Cramer-Rao inequality from information theory. I expect this current paper (when I finally get around to read it), will be equivalent to what I've done. Ultimately, it may come down to history which method is preferred, or if some uber-clear version is presented (like Dirac did to Schroedinger and Heisenberg's theories). It would be all the more remarkable if this approach was fundamentally different. All I have to say now... On Tue, Jul 26, 2011 at 10:37:46AM -0700, Russ Abbott wrote: I expected this to have more of an impact than it seems to be having. What am I missing? *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 * blog: *http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ *_* On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott russ.abb...@gmail.com russ.abb...@gmail.com wrote: From APS Physics http://physics.aps.org/articles/v4/55 http://physics.aps.org/articles/v4/55. We know how to use the “rules” of quantum physics to build lasers, microchips, and nuclear power plants, but when students question the rules themselves, the best answer we can give is often, “The world just happens to be that way.” Yet why are individual outcomes in quantum measurements random? What is the origin of the Schrödinger equation? In a paper [1http://physics.aps.org/articles/v4/55#c1 http://physics.aps.org/articles/v4/55#c1] appearing in Physical Review A, Giulio Chiribella at the Perimeter Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo Perinotti at the University of Pavia, Italy, offer a framework in which to answer these penetrating questions. They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory. (Strictly speaking, their derivation only applies to systems that can be constructed from a finite number of quantum states, such as spin.) In this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s belief that one obtains “it from bit,” in other words, that our account of the universe is constructed from bits of information, and the rules on how that information can
Re: [FRIAM] Deriving quantum theory from information processing axioms
Russ,
That was actually a very good article! I remain amongst those skeptical that
one can really test the theory, but it is nice to see the theory explained such
a straightforward way, and to know there are people making solid attempts to
test it.
One major cop-out / overtly-overstated-claim though is Vilenkin's speculation
that:
This picture of the universe...
explains the long-standing mystery of why the constants of nature appear
to be fine-tuned for the emergence of life. The reason is that intelligent
observers exist only in those rare
bubbles in which, by pure chance, the constants happen to be just right
for life to evolve.
That, at least in my mind, sidesteps the question, as it can be reduced to:
The reason nature appears to be fine-tuned for the emergence of
life is because it is.
Another way to phrase this is that if we are going to be happy (as scientists)
with the answer that things are the way they are due to pure chance, we
didn't need multiverse theory to be happy.
Also, my favorite bit is in Tegmark's article. He states:
Remember: Parallel universes are not a theory—they are
predictions of certain theories.
Speaking with most of my sociology-of-science knowledge revolving around the
field of psychology, the ability to maintain that distinction is admirable,
incredibly valuable to the progress of a field, and I wish more people could do
it.
Eric
On Wed, Jul 27, 2011 04:28 PM, Russ Abbott russ.abb...@gmail.com wrote:
And speaking of multiverses, this was just published on the
http://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universe.
In the August issue ofScientific American, cosmologist George Ellis describes
why he's skeptical about the concept of parallel universes. Here, multiverse
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Re: [FRIAM] Deriving quantum theory from information processing axioms
I expected this to have more of an impact than it seems to be having. What am I missing? *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 * blog: *http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ *_* On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott russ.abb...@gmail.com wrote: From APS Physics http://physics.aps.org/articles/v4/55. We know how to use the “rules” of quantum physics to build lasers, microchips, and nuclear power plants, but when students question the rules themselves, the best answer we can give is often, “The world just happens to be that way.” Yet why are individual outcomes in quantum measurements random? What is the origin of the Schrödinger equation? In a paper [1http://physics.aps.org/articles/v4/55#c1] appearing in Physical Review A, Giulio Chiribella at the Perimeter Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo Perinotti at the University of Pavia, Italy, offer a framework in which to answer these penetrating questions. They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory. (Strictly speaking, their derivation only applies to systems that can be constructed from a finite number of quantum states, such as spin.) In this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s belief that one obtains “it from bit,” in other words, that our account of the universe is constructed from bits of information, and the rules on how that information can be obtained determine the “meaning” of what we call particles and fields. ... They assume five new elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—which define a broad class of theories of information processing. For example, the causality axiom—stating that one cannot signal from future measurements to past preparations—is so basic that it is usually assumed a priori. Both classical and quantum theory fulfil the five axioms. What is significant about Chiribella et al.’s work is that they show that a sixth axiom—the assumption that every state has what they call a “purification”—is what singles out quantum theory within the class. In fact, this last axiom is so important that they call it a postulate. The purification postulate can be defined formally (see below), but to understand its meaning in simple words, we can look to Schrödinger, who in describing entanglement gives the essence of the postulate: “Maximal knowledge of a total system does not necessarily include maximal knowledge of all its parts.” (Formally, the purification postulate states that every mixed state ρA of system A can always be seen as a state belonging to a part of a composite system AB that itself is in a pure state ΨAB. This pure state is called “purification” and is assumed to be unique up to a reversible transformation on B). Chiribella et al. conclude there is only one way in which a theory can satisfy the purification postulate: it must contain entangled states. (The other option, that the theory must not contain mixed states, that is, that the probabilities of outcomes in any measurement are either 0 or 1 like in classical deterministic theory, cannot hold, as one can always prepare mixed states by mixing deterministic ones.) The purification postulate alone allows some of the key features of quantum information processing to be derived, such as the no-cloning theorem or teleportation [7http://physics.aps.org/articles/v4/55#c7]. By combining this postulate with the other five axioms, Chiribella et al. were able to derive the entire mathematical formalism behind quantum theory. *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 * blog: *http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ *_* FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
Re: [FRIAM] Deriving quantum theory from information processing axioms
Russ, I had the same feeling about my recent missive - entitled Uncertainty vs Information - redux and resolution - in which I too make various claims about information theory. I believe I had only one response - from Eric. I expected more, maybe from Owen and Frank and yourself. The APS Physics review you attached discussed an Italian paper from the U of Pavia. About that paper the review says They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory. Understandably, such a view is likely to be sacrosanct among many. I must confess however that I have considerable sympathy with it. In my recent posting on /Uncertainty and Information/, I cited the Oxford Info Theorist Vlatko Vedral. In his book _Decoding Reality: The Universe as Quantum Information_, he states: This book will state that information (and not matter or energy or love) is the building block on which everything is constructed. Information is far more fundamental than matter or energy because it can be successfully applied to both macroscopic interactions, such as economic and social phenomena, and, as I will argue, information can also be used to explain the origin and behavior of microscopic interactions such as energy and matter. Evidently, there is a body of information theorist out there who are making a play for the proposition that Information Theory is more fundamental than physics. Of course, my recent posting argues that uncertainty is more foundational then information (even though, according to Shannon, entropy measures them both). This is because, as argued by Khinchin, information derives from uncertainty through realization. Maybe together we can get a thread started about the primacy of physics, information or uncertainty - or maybe something else? Oh, yeah, there is already one going about the primacy of physics vs philosophy. Maybe we can add information and uncertainty to the mix! On 7/26/11 11:37 AM, Russ Abbott wrote: I expected this to have more of an impact than it seems to be having. What am I missing? /-- Russ Abbott/ /_/ / Professor, Computer Science/ / California State University, Los Angeles/ / Google voice: 747-/999-5105 / blog: /http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ /_/ On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott russ.abb...@gmail.com mailto:russ.abb...@gmail.com wrote: From APS Physics http://physics.aps.org/articles/v4/55. We know how to use the rules of quantum physics to build lasers, microchips, and nuclear power plants, but when students question the rules themselves, the best answer we can give is often, The world just happens to be that way. Yet why are individual outcomes in quantum measurements random? What is the origin of the Schrödinger equation? In a paper [1 http://physics.aps.org/articles/v4/55#c1] appearing in Physical Review A, Giulio Chiribella at the Perimeter Institute inWaterloo, Canada, and Giacomo Mauro D'Ariano and Paolo Perinotti at the University of Pavia, Italy, offer a framework in which to answer these penetrating questions. They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory. (Strictly speaking, their derivation only applies to systems that can be constructed from a finite number of quantum states, such as spin.) In this sense, Chiribella et al.'s work is in the spirit of John Wheeler's belief that one obtains it from bit, in other words, that our account of the universe is constructed from bits of information, and the rules on how that information can be obtained determine the meaning of what we call particles and fields. ... They assume five new elementary axioms---causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning---which define a broad class of theories of information processing. For example, the causality axiom---stating that one cannot signal from future measurements to past preparations---is so basic that it is usually assumed a priori. Both classical and quantum theory fulfil the five axioms. What is significant about Chiribella et al.'s work is that they show that a sixth axiom---the assumption that every state has what they call a purification---is what singles out quantum theory within the class. In fact, this last axiom is so important that they call it a postulate. The purification postulate can be defined formally (see below), but to understand its meaning in simple words, we can look to Schrödinger, who
Re: [FRIAM] Deriving quantum theory from information processing axioms
As a universal layman, with a BS in physics and history from MIT in 1964, I have always been keenly interested as to the actual deep meaning of quantum theory. Can someone give a simple dynamic geometrical model which can embody these axioms, fleshing out their abstract meanings in a simple way, somewhat accessible to common sense? A video game or YouTube video? Thanks, Rich Murray rmfor...@gmail.com 505-819-7388 FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
Re: [FRIAM] Deriving quantum theory from information processing axioms
Of course, I published a paper in 2004 (Why Occams Razor) doing essentially the same thing (I expanded on this somewhat in my 2006 book, Theory of Nothing). I would also say, that Lucien Hardy did something similar in 2001 (Quantum theory from five reasonable axioms). Also, there have been other works linking the uncertainty principle to the Cramer-Rao inequality from information theory. I expect this current paper (when I finally get around to read it), will be equivalent to what I've done. Ultimately, it may come down to history which method is preferred, or if some uber-clear version is presented (like Dirac did to Schroedinger and Heisenberg's theories). It would be all the more remarkable if this approach was fundamentally different. All I have to say now... On Tue, Jul 26, 2011 at 10:37:46AM -0700, Russ Abbott wrote: I expected this to have more of an impact than it seems to be having. What am I missing? *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 * blog: *http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ *_* On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott russ.abb...@gmail.com wrote: From APS Physics http://physics.aps.org/articles/v4/55. We know how to use the “rules” of quantum physics to build lasers, microchips, and nuclear power plants, but when students question the rules themselves, the best answer we can give is often, “The world just happens to be that way.” Yet why are individual outcomes in quantum measurements random? What is the origin of the Schrödinger equation? In a paper [1http://physics.aps.org/articles/v4/55#c1] appearing in Physical Review A, Giulio Chiribella at the Perimeter Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo Perinotti at the University of Pavia, Italy, offer a framework in which to answer these penetrating questions. They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory. (Strictly speaking, their derivation only applies to systems that can be constructed from a finite number of quantum states, such as spin.) In this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s belief that one obtains “it from bit,” in other words, that our account of the universe is constructed from bits of information, and the rules on how that information can be obtained determine the “meaning” of what we call particles and fields. ... They assume five new elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—which define a broad class of theories of information processing. For example, the causality axiom—stating that one cannot signal from future measurements to past preparations—is so basic that it is usually assumed a priori. Both classical and quantum theory fulfil the five axioms. What is significant about Chiribella et al.’s work is that they show that a sixth axiom—the assumption that every state has what they call a “purification”—is what singles out quantum theory within the class. In fact, this last axiom is so important that they call it a postulate. The purification postulate can be defined formally (see below), but to understand its meaning in simple words, we can look to Schrödinger, who in describing entanglement gives the essence of the postulate: “Maximal knowledge of a total system does not necessarily include maximal knowledge of all its parts.” (Formally, the purification postulate states that every mixed state ρA of system A can always be seen as a state belonging to a part of a composite system AB that itself is in a pure state ΨAB. This pure state is called “purification” and is assumed to be unique up to a reversible transformation on B). Chiribella et al. conclude there is only one way in which a theory can satisfy the purification postulate: it must contain entangled states. (The other option, that the theory must not contain mixed states, that is, that the probabilities of outcomes in any measurement are either 0 or 1 like in classical deterministic theory, cannot hold, as one can always prepare mixed states by mixing deterministic ones.) The purification postulate alone allows some of the key features of quantum information processing to be derived, such as the no-cloning theorem or teleportation [7http://physics.aps.org/articles/v4/55#c7]. By combining this postulate with the other five axioms, Chiribella et al. were able to derive the entire mathematical formalism behind quantum theory. *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* *
Re: [FRIAM] Deriving quantum theory from information processing axioms
Exciting, Russ. I've downloaded your 2004 paper http://arxiv.org/pdf/physics/0001020v6, and will take a look. Thanks, Grant On 7/26/11 3:16 PM, Russell Standish wrote: Of course, I published a paper in 2004 (Why Occams Razor) doing essentially the same thing (I expanded on this somewhat in my 2006 book, Theory of Nothing). I would also say, that Lucien Hardy did something similar in 2001 (Quantum theory from five reasonable axioms). Also, there have been other works linking the uncertainty principle to the Cramer-Rao inequality from information theory. I expect this current paper (when I finally get around to read it), will be equivalent to what I've done. Ultimately, it may come down to history which method is preferred, or if some uber-clear version is presented (like Dirac did to Schroedinger and Heisenberg's theories). It would be all the more remarkable if this approach was fundamentally different. All I have to say now... On Tue, Jul 26, 2011 at 10:37:46AM -0700, Russ Abbott wrote: I expected this to have more of an impact than it seems to be having. What am I missing? *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 * blog: *http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ *_* On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbottruss.abb...@gmail.com wrote: From APS Physicshttp://physics.aps.org/articles/v4/55. We know how to use the “rules” of quantum physics to build lasers, microchips, and nuclear power plants, but when students question the rules themselves, the best answer we can give is often, “The world just happens to be that way.” Yet why are individual outcomes in quantum measurements random? What is the origin of the Schrödinger equation? In a paper [1http://physics.aps.org/articles/v4/55#c1] appearing in Physical Review A, Giulio Chiribella at the Perimeter Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo Perinotti at the University of Pavia, Italy, offer a framework in which to answer these penetrating questions. They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory. (Strictly speaking, their derivation only applies to systems that can be constructed from a finite number of quantum states, such as spin.) In this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s belief that one obtains “it from bit,” in other words, that our account of the universe is constructed from bits of information, and the rules on how that information can be obtained determine the “meaning” of what we call particles and fields. ... They assume five new elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—which define a broad class of theories of information processing. For example, the causality axiom—stating that one cannot signal from future measurements to past preparations—is so basic that it is usually assumed a priori. Both classical and quantum theory fulfil the five axioms. What is significant about Chiribella et al.’s work is that they show that a sixth axiom—the assumption that every state has what they call a “purification”—is what singles out quantum theory within the class. In fact, this last axiom is so important that they call it a postulate. The purification postulate can be defined formally (see below), but to understand its meaning in simple words, we can look to Schrödinger, who in describing entanglement gives the essence of the postulate: “Maximal knowledge of a total system does not necessarily include maximal knowledge of all its parts.” (Formally, the purification postulate states that every mixed state ρA of system A can always be seen as a state belonging to a part of a composite system AB that itself is in a pure state ΨAB. This pure state is called “purification” and is assumed to be unique up to a reversible transformation on B). Chiribella et al. conclude there is only one way in which a theory can satisfy the purification postulate: it must contain entangled states. (The other option, that the theory must not contain mixed states, that is, that the probabilities of outcomes in any measurement are either 0 or 1 like in classical deterministic theory, cannot hold, as one can always prepare mixed states by mixing deterministic ones.) The purification postulate alone allows some of the key features of quantum information processing to be derived, such as the no-cloning theorem or teleportation [7http://physics.aps.org/articles/v4/55#c7]. By combining this postulate with the other five axioms, Chiribella et al. were able to derive the entire mathematical formalism behind quantum theory. *-- Russ Abbott* *_* *** Professor, Computer Science* *
Re: [FRIAM] Deriving quantum theory from information processing axioms
http://www.sciencenews.org/view/generic/id/332557/title/Quantum_theory_gets_physical Quantum theory gets physical New work finds physical basis for quantum mechanics By Devin Powell Web edition : Tuesday, July 19th, 2011 Physicists in Canada and Italy have derived quantum mechanics from physical principles related to the storage, manipulation and retrieval of information. The new work is a step in a long, ongoing effort to find fundamental physical motivation for the math of quantum physics, which describes processes in the atomic and subatomic realms with unerring accuracy but defies commonsense understanding. “We’d like to have a set of axioms that give us a little better physical understanding of quantum mechanics,” says Michael Westmoreland, a mathematician at Denison University in Granville, Ohio. Quantum theory’s foundations currently rest on abstract mathematical formulations known as Hilbert spaces and C* algebras. These abstractions work well for calculating the probability of a particular outcome in an experiment. But they lack the intuitive physical meaning that physicists crave -- the elegance of Einstein’s theory of special relativity, for instance, which says that the speed of light is constant and that laws of physics don’t change from one reference frame to the next. Giulio Chiribella, a theoretical physicist at the Perimeter Institute for Theoretical Physics in Ontario, Canada, and colleagues based their approach on a postulate called “purification.” A system with uncertain properties (a “mixed state”) is always part of a larger “pure state” that can, in principle, be completely known, the team proposes in the July Physical Review A. Consider the pion. This particle, which has a spin of zero, can decay into two spinning photons. Each single photon is in a mixed state – it has an equal chance of spinning up or down. The pair of photons together, though, comprise a pure state in which they must always spin in opposite directions. “We can be ignorant of the part, but we can have maximal knowledge of the whole,” says Chiribella. This purification principle requires the quantum phenomenon known as entanglement, which connects the parts to the whole. It also explains why quantum information can’t be copied without destroying it but can be “teleported” -- replicated at a distant location after being destroyed at its point of origin. Building on this principle, Chiribella and colleagues reproduced the mathematical structure of quantum mechanics with the aid of five additional axioms related to information processing. Their axioms include causality, the idea that a measurement now can’t be influenced by future measurements, and “ideal compression,” meaning that information can be encoded in a physical system and then decoded without error. Other axioms involve the ability to distinguish states from each other and the ability of measurements to create pure states. “They nail it,” says Christopher Fuchs, a theoretical physicist at the Perimeter Institute. “This now approaches something that I think is along the lines of trying to find a crisp physical principle.” Whether this new derivation of quantum theory will prove to the simplest and most physically meaningful remains to be seen. “What is simple or physically plausible is a matter of taste,” says Časlav Brukner, a physicist at the University of Vienna in Austria who has developed an alternative set of axioms. Some speculate that recasting quantum theory in terms of information could help to solve outstanding problems in physics, such as how to unify quantum mechanics and gravity. “If you have lots of formulations of the same theory, you’re more likely to have one that leads to whatever the next physics is,” says Ben Schumacher, a theoretical physicist at Kenyon College in Gambier, Ohio. SUGGESTED READING : L. Hardy. Quantum theory from five reasonable axioms. arXiv:quant-ph/0101012v4 Posted Sep. 25, 2001. [Go to] B. Dakić and C. Brukner. Quantum theory and beyond: Is entanglement special? arXiv:0911.0695v1 Posted Nov. 3, 2009. [Go to] C. Brukner. Questioning the rules of the game. Physics. Published online July 11, 2011. doi:10.1103/Physics.4.55. [Go to] CITATIONS REFERENCES : G. Chiribella, G.M. D’Ariano and P. Perinotti. Informational derivation of quantum theory. Physical Review A. Vol. 84, July 2011, p. 012311-1. doi:10.1103/PhysrevA.84.012311. [Go to] http://arxiv.org/abs/1011.6451 http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.6451v3.pdf 47 pages Informational derivation of Quantum Theory Giulio Chiribella ∗ Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Ontario, Canada N2L 2Y5. † Giacomo Mauro D’Ariano ‡ and Paolo Perinotti § QUIT Group, Dipartimento di Fisica “A. Volta” and INFN Sezione di Pavia, via Bassi 6, 27100 Pavia, Italy ¶ (Dated: July 18, 2011) We derive Quantum Theory from purely informational principles. Five elementary axioms -- causality, perfect distinguishability, ideal
