DOCSLIB.ORG

Quantum Theory Needs No 'Interpretation'

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Theory Needs No 'Interpretation' O PINION Quantum Theory Needs No ‘Interpretation’ Christopher A. Fuchs and Asher Peres ecently there has been a spate of of our experimental activity, then we carry an umbrella. Probability theory Rarticles, reviews, and letters in must be prepared for that, too. is simply the quantitative formulation PHYSICS TODAY promoting various The thread common to all the non- of how to make rational decisions in “interpretations” of quantum theory standard “interpretations” is the the face of uncertainty. (see March 1998, page 42; April 1998, desire to create a new theory with fea- We do not deny the possible exis- page 38; February 1999, page 11; July tures that correspond to some reality tence of an objective reality independ- 1999, page 51; and August 1999, page independent of our potential experi- ent of what observers perceive. In par- 26). Their running theme is that from ments. But, trying to fulfill a classical ticular, there is an “effective” reality the time of quantum theory’s emer- worldview by encumbering quantum in the limiting case of macroscopic gence until the discovery of a particu- mechanics with hidden variables, phenomena like detector clicks or lar interpretation, the theory was in a multiple worlds, consistency rules, or planetary motion: Any observer who crisis because its foundations were spontaneous collapse, without any happens to be present would acknowl- unsatisfactory or even inconsistent. improvement in its predictive power, edge the objective occurrence of these We are seriously concerned that the only gives the illusion of a better events. However, such a macroscopic airing of these opinions may lead understanding. Contrary to those description ignores most degrees of some readers to a distorted view of desires, quantum theory does not freedom of the system and is neces- the validity of standard quantum describe physical reality. What it does sarily incomplete. Can there also be a mechanics. If quantum theory had is provide an algorithm for computing “microscopic reality” where every been in a crisis, experimenters would probabilities for the macroscopic detail is completely described? No have informed us long ago! events (“detector clicks”) that are the description of that kind can be given Our purpose here is to explain the consequences of our experimental by quantum theory, nor by any other internal consistency of an “interpre- interventions. This strict definition of reasonable theory. John Bell formally tation without interpretation” for the scope of quantum theory is the only showed3 that any objective theory giv- quantum mechanics. Nothing more is interpretation ever needed, whether ing experimental predictions identical needed for using the theory and by experimenters or theorists. to those of quantum theory would nec- understanding its nature. To begin, Quantum probabilities, like all essarily be nonlocal. It would eventu- let us examine the role of experiment probabilities, are computed by using ally have to encompass everything in in science. An experiment is an active any available information. This can the universe, including ourselves, and intervention into the course of include, but is not limited to informa- lead to bizarre self-referential logical Nature: We set up this or that exper- tion about a system’s preparation. paradoxes. The latter are not in the iment to see how Nature reacts. We The mathematical instrument for realm of physics; experimental physi- have learned something new when we turning the information into statisti- cists never need bother with them. can distill from the accumulated data cal predictions is the probability rule We have experimental evidence a compact description of all that was postulated by Max Born.1 The conclu- that quantum theory is successful in seen and an indication of which fur- siveness of Born’s rule is known today the range from 10–10 to 1015 atomic ther experiments will corroborate to follow from a theorem due to radii; we have no evidence that it is that description. This is what science Andrew Gleason.2 It is enough to universally valid. Yet, it is legitimate is about. If, from such a description, assume that yes–no tests on a physical to attempt to extrapolate the theory we can further distill a model of a free- system are represented by projection beyond its present range, for instance, standing “reality” independent of our operators P, and that probabilities are when we probe particle interactions interventions, then so much the bet- additive over orthogonal projectors. at superhigh energies, or in astro- ter. Classical physics is the ultimate Then there exists a density matrix r physical systems, including the entire example of such a model. However, describing the system such that the universe. Indeed, a common question there is no logical necessity for a real- probability of a “yes” answer is tr(rP). is whether the universe has a wave- istic worldview to always be obtain- The compendium of probabilities rep- function. There are two ways to able. If the world is such that we can resented by the “quantum state” r cap- understand this. If this “wavefunction never identify a reality independent tures everything that can meaningful- of the universe” has to give a complete ly be said about a physical system. description of everything, including CHRIS FUCHS , previously the Lee DuBridge Here, it is essential to understand ourselves, we again get the same Prize Postdoctoral Fellow at Caltech, is now a Director-Funded Fellow at Los Alamos that the validity of the statistical meaningless paradoxes. On the other National Laboratory. His daytime research nature of quantum theory is not hand, if we consider just a few collec- focuses on quantum information theory and restricted to situations where there tive degrees of freedom, such as the quantum computation. ASHER PERES is the are a large number of similar systems. radius of the universe, its mean den- Gerard Swope Distinguished Professor of Statistical predictions do apply to sin- sity, total baryon number, and so on, Physics at Technion—Israel Institute of Tech- gle events. When we are told that the we can apply quantum theory only to nology, in Haifa, Israel. He is the author of probability of precipitation tomorrow these degrees of freedom, which do not Quantum Theory: Concepts and Methods is 35%, there is only one tomorrow. include ourselves and other insignifi- (Kluwer, Dordrecht, 1995). This tells us that it is advisable to cant details. This is not essentially 70 MARCH 2000 PHYSICS TODAY © 2000 American Institute of Physics, S-0031-9228-0003-230-0 Downloaded 25 Sep 2012 to 162.105.13.196. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms different from quantizing the mag- teleportation process.4 In order to spond to quantum states. This analo- netic flux and the electric current in a teleport a quantum state from one gy is misleading: Attributing reality SQUID while ignoring the atomic photon to another, the sender (Alice) to quantum states leads to a host of details. For sure, we can manipulate and the receiver (Bob) need to divide “quantum paradoxes.” These are due a SQUID more easily than we can between them a pair of photons in a solely to an incorrect interpretation of manipulate the radius of the uni- standard entangled state. The exper- quantum theory. When correctly used, verse, but there is no difference in iment begins when Alice receives quantum theory never yields two con- principle. another photon whose polarization tradictory answers to a well-posed Does quantum mechanics apply to state is unknown to her but known to question. In particular, no wavefunc- the observer? Why would it not? To be a third-party preparer. She performs tion exists either before or after we quantum mechanical is simply to be a measurement on her two photons— conduct an experiment. Just as clas- amenable to a quantum description. one from the original, entangled pair sical cosmologists got used to the idea Nothing in principle prevents us from and the other in a state unknown to that there is no “time” before the big quantizing a colleague, say. Let us her—and then sends Bob a classical bang or after the big crunch, so too examine a concrete example: must we be careful about using The observer is Cathy (an “before” and “after” in the quan- experimental physicist) who tum context. enters her laboratory and sends Quantum theory has been a photon through a beam split- accused of incompleteness ter. If one of her detectors is because it cannot answer some activated, it opens a box con- questions that appear reason- taining a piece of cake; the able from the classical point of other detector opens a box with view. For example, there is no a piece of fruit. Cathy’s friend way to ascertain whether a sin- Erwin (a theorist) stays outside gle system is in a pure state or is the laboratory and computes part of an entangled composite Cathy’s wavefunction. Accord- system. Furthermore, there is no ing to him, she is in a 50/50 dynamical description for the superposition of states with “collapse” of the wavefunction. some cake or some fruit in her In both cases the theory gives no stomach. There is nothing answer because the wavefunc- wrong with that; this only rep- tion is not an objective entity. resents his knowledge of Cathy. Collapse is something that hap- She knows better. As soon as pens in our description of the one detector was activated, her system, not to the system itself. wavefunction collapsed. Of “What do you mean, ‘a quantum fluctuation?’ Likewise, the time dependence course, nothing dramatic hap- Didn’t we discuss cause and effect?” of the wavefunction does not pened to her. She just acquired represent the evolution of a the knowledge of the kind of food she message of only two bits, instructing physical system.
Load more

Recommended publications
  • Quantum Theory Needs No 'Interpretation'
    Quantum Theory Needs No ‘Interpretation’ But ‘Theoretical Formal-Conceptual Unity’ (Or: Escaping Adán Cabello’s “Map of Madness” With the Help of David Deutsch’s Explanations) Christian de Ronde∗ Philosophy Institute Dr. A. Korn, Buenos Aires University - CONICET Engineering Institute - National University Arturo Jauretche, Argentina Federal University of Santa Catarina, Brazil. Center Leo Apostel fot Interdisciplinary Studies, Brussels Free University, Belgium Abstract In the year 2000, in a paper titled Quantum Theory Needs No ‘Interpretation’, Chris Fuchs and Asher Peres presented a series of instrumentalist arguments against the role played by ‘interpretations’ in QM. Since then —quite regardless of the publication of this paper— the number of interpretations has experienced a continuous growth constituting what Adán Cabello has characterized as a “map of madness”. In this work, we discuss the reasons behind this dangerous fragmentation in understanding and provide new arguments against the need of interpretations in QM which —opposite to those of Fuchs and Peres— are derived from a representational realist understanding of theories —grounded in the writings of Einstein, Heisenberg and Pauli. Furthermore, we will argue that there are reasons to believe that the creation of ‘interpretations’ for the theory of quanta has functioned as a trap designed by anti-realists in order to imprison realists in a labyrinth with no exit. Taking as a standpoint the critical analysis by David Deutsch to the anti-realist understanding of physics, we attempt to address the references and roles played by ‘theory’ and ‘observation’. In this respect, we will argue that the key to escape the anti-realist trap of interpretation is to recognize that —as Einstein told Heisenberg almost one century ago— it is only the theory which can tell you what can be observed.
    [Show full text]
  • CURRICULUM VITAE June, 2016 Hu, Bei-Lok Bernard Professor Of
    CURRICULUM VITAE June, 2016 Hu, Bei-Lok Bernard Professor of Physics, University of Maryland, College Park 胡悲樂 Founding Fellow, Joint Quantum Institute, Univ. Maryland and NIST Founding Member, Maryland Center for Fundamental Physics, UMD. I. PERSONAL DATA Date and Place of Birth: October 4, 1947, Chungking, China. Citizenship: U.S.A. Permanent Address: 3153 Physical Sciences Complex Department of Physics, University of Maryland, College Park, Maryland 20742-4111 Telephone: (301) 405-6029 E-mail: [email protected] Fax: MCFP: (301) 314-5649 Physics Dept: (301) 314-9525 UMd Physics webpage: http://umdphysics.umd.edu/people/faculty/153-hu.html Research Groups: - Gravitation Theory (GRT) Group: http://umdphysics.umd.edu/research/theoretical/87gravitationaltheory.html - Quantum Coherence and Information (QCI) Theory Group: http://www.physics.umd.edu/qcoh/index.html II. EDUCATION Date School Location Major Degree 1958-64 Pui Ching Middle School Hong Kong Science High School 1964-67 University of California Berkeley Physics A.B. 1967-69 Princeton University Princeton Physics M.A. 1969-72 Princeton University Princeton Physics Ph.D. III. ACADEMIC EXPERIENCE Date Institution Position June 1972- Princeton University Research Associate Jan. 1973 Princeton, N.J. 08540 Physics Department Jan. 1973- Institute for Advanced Study Member Aug. 1973 Princeton, N.J. 08540 School of Natural Science Sept.1973- Stanford University Research Associate Aug. 1974 Stanford, Calif. 94305 Physics Department Sept.1974- University of Maryland Postdoctoral Fellow Jan. 1975 College Park, Md. 20742 Physics & Astronomy Jan. 1975- University of California Research Mathematician Sept.1976 Berkeley, Calif. 94720 Mathematics Department Oct. 1976- Institute for Space Studies Research Associate May 1977 NASA, New York, N.Y.
    [Show full text]
  • Born's Rule and Measurement
    Born’s rule and measurement Arnold Neumaier Fakult¨at f¨ur Mathematik, Universit¨at Wien Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria email: [email protected] http://www.mat.univie.ac.at/~neum December 20, 2019 arXiv:1912.09906 Abstract. Born’s rule in its conventional textbook form applies to the small class of pro- jective measurements only. It is well-known that a generalization of Born’s rule to realistic experiments must be phrased in terms of positive operator valued measures (POVMs). This generalization accounts for things like losses, imperfect measurements, limited detec- tion accuracy, dark detector counts, and the simultaneous measurement of position and momentum. Starting from first principles, this paper gives a self-contained, deductive introduction to quantum measurement and Born’s rule, in its generalized form that applies to the results of measurements described by POVMs. It is based on a suggestive definition of what constitutes a detector, assuming an intuitive informal notion of response. The formal exposition is embedded into the context of a variaety of quotes from the litera- ture illuminating historical aspects of the subject. The material presented suggests a new approach to introductory courses on quantum mechanics. For the discussion of questions related to this paper, please use the discussion forum https://www.physicsoverflow.org. MSC Classification (2010): primary: 81P15, secondary: 81-01 1 Contents 1 The measurement process 3 1.1 Statesandtheirproperties . .... 5 1.2 Detectors,scales,andPOVMs . .. 8 1.3 Whatismeasured? ................................ 9 1.4 InformationallycompletePOVMs . ... 11 2 Examples 12 2.1 Polarizationstatemeasurements. ...... 13 2.2 Joint measurements of noncommuting quantities .
    [Show full text]
  • Quantum Computation: a Short Course
    Quantum Computation: A Short Course Frank Rioux Emeritus Professor of Chemistry College of St. Benedict | St. John’s University The reason I was keen to include at least some mathematical descriptions was simply that in my own study of quantum computation the only time I really felt that I understood what was happening in a quantum program was when I examined some typical quantum circuits and followed through the equations. Julian Brown, The Quest for the Quantum Computer, page 6. My reason for beginning with Julian Brown’s statement is that I accept it wholeheartedly. I learn the same way. So in what follows I will present mathematical analyses of some relatively simple and representative quantum circuits that are designed to carry out important contemporary processes such as parallel computation, teleportation, data-base searches, prime factorization, quantum encryption and quantum simulation. I will conclude with a foray into the related area of Bell’s theorem and the battle between local realism and quantum mechanics. Quantum computers use superpositions, entanglement and interference to carry out calculations that are impossible with a classical computer. The following link contains insightful descriptions of the non-classical character of superpositions and entangled superpositions from a variety of sources. http://www.users.csbsju.edu/~frioux/q-intro/EntangledSuperposition.pdf To illuminate the difference between classical and quantum computation we begin with a review of the fundamental principles of quantum theory using the computational methods of matrix mechanics. http://www.users.csbsju.edu/~frioux/matmech/RudimentaryMatrixMechanics.pdf The following is an archive of photon and spin vector states and their matrix operators.
    [Show full text]
  • QUANTUM NONLOCALITY and INSEPARABILITY Asher Peres
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server QUANTUM NONLOCALITY AND INSEPARABILITY Asher Peres Department of Physics Technion—Israel Institute of Technology 32 000 Haifa, Israel A quantum system consisting of two subsystems is separable if its den- 0 00 0 00 sity matrix can be written as ρ = wK ρK ⊗ ρK,whereρK and ρK are density matrices for the two subsytems,P and the positive weights wK satisfy wK = 1. A necessary condition for separability is derived and is shownP to be more sensitive than Bell’s inequality for detecting quantum inseparability. Moreover, collective tests of Bell’s inequality (namely, tests that involve several composite systems simultaneously) may sometimes lead to a violation of Bell’s inequality, even if the latter is satisfied when each composite system is tested separately. 1. INTRODUCTION From the early days of quantum mechanics, the question has often been raised whether an underlying “subquantum” theory, that would be deterministic or even stochastic, was viable. Such a theory would presumably involve additional “hidden” variables, and the statistical 1 predictions of quantum theory would be reproduced by performing suit- able averages over these hidden variables. A fundamental theorem was proved by Bell [1], who showed that if the constraint of locality was imposed on the hidden variables (namely, if the hidden variables of two distant quantum systems were themselves be separable into two distinct subsets), then there was an upper bound to the correlations of results of measurements that could be performed on the two distant systems.
    [Show full text]
  • Continuous Groups of Transversal Gates for Quantum Error Correcting Codes from finite Clock Reference Frames
    Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames Mischa P. Woods1 and Alvaro´ M. Alhambra2 1Institute for Theoretical Physics, ETH Zurich, Switzerland 2Perimeter Institute for Theoretical Physics, Waterloo, Canada Following the introduction of the task of ref- ply logical gates transversally, which one can imple- erence frame error correction [1], we show ment while still being able to correct for local errors. how, by using reference frame alignment with The framework for error correction is based on con- clocks, one can add a continuous Abelian sidering three spaces | a logical HL, physical HP 1 group of transversal logical gates to any error- and a code HCo ⊆ HP space. Logical states ρL correcting code. With this we further explore containing quantum information are encoded via an a way of circumventing the no-go theorem of encoding map E : B(HL) → B(HCo) onto the code Eastin and Knill, which states that if local er- space, which is a subspace of some larger physical rors are correctable, the group of transversal space where errors | represented via error maps gates must be of finite order. We are able to {Ej}j : B(HCo) → B(HP) | can occur. Decoding do this by introducing a small error on the de- maps {Dj}j : B(HP) → B(HL) can then retrieve the coding procedure that decreases with the di- information while correcting for errors; outputting the mension of the frames used. Furthermore, we logical state ρL. That is: show that there is a direct relationship be- tween how small this error can be and how ρL E Ej Dj ρL, (1) accurate quantum clocks can be: the more ac- for all j and for all states ρ ∈ S (H ).
    [Show full text]
  • Obituary by Graduate Students
    Quantum information science lost one of its founding fathers. Asher Peres died on Sunday, January 1, 2005. He was 70 years old. A distinguished professor at the Department of Physics, Technion - Israel Institute of Technology, Asher described himself as "the cat who walks by himself". His well-known independence in thought and research is the best demonstration of this attitude. Asher will be missed by all of us not only as a great scientist but especially as a wonderful person. He was a surprisingly warm and unpretentious man of stubborn integrity, with old-world grace and a pungent sense of humor. He was a loving husband to his wife Aviva, a father to his two daughters Lydia and Naomi, and a proud grandfather of six. Asher was a demanding but inspiring teacher. Many physicists considered him not only a valued colleague but also a dear friend and a mentor. Asher's scientific work is too vast to review, while its highlights are well-known. One of the six fathers of quantum teleportation, he made fundamental contributions to the definition and characterization of quantum entanglement, helping to promote it from the realm of philosophy to the world of physics. The importance of his contributions to other research areas cannot be overestimated. Starting his career as a graduate student of Nathan Rosen, he established the physicality of gravitational waves and provided a textbook example of a strong gravitational wave with his PP-wave. Asher was also able to point out some of the signatures of quantum chaos, paving the way to many more developments.
    [Show full text]
  • A Phenomenological Ontology for Physics Michel Bitbol
    A Phenomenological Ontology For Physics Michel Bitbol To cite this version: Michel Bitbol. A Phenomenological Ontology For Physics. H. Wiltsche & P. Berghofer (eds.) Phe- nomenological approaches to physics Springer, 2020. hal-03039509 HAL Id: hal-03039509 https://hal.archives-ouvertes.fr/hal-03039509 Submitted on 3 Dec 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. A PHENOMENOLOGICAL ONTOLOGY FOR PHYSICS Merleau-Ponty and QBism1 Michel Bitbol Archives Husserl, CNRS/ENS, 45, rue d’Ulm, 75005 Paris, France in: H. Wiltsche & P. Berghofer, (eds.), Phenomenological approaches to physics, Springer, 2020 Foreword Let’s imagine that, despite the lack of any all-encompassing picture, an abstract mathematical structure guides our (technological) activities more efficiently than ever, possibly assisted by a set of clumsy, incomplete, ancillary pictures. In this new situation, the usual hierarchy of knowledge would be put upside down. Unlike the standard order of priorities, situation-centered practical knowledge would be given precedence over theoretical knowledge associated with elaborate unified representations; in the same way as, in Husserl’s Crisis of the European Science, the life-world is given precedence over theoretical “substructions”. Here, instead of construing representation as an accomplished phase of knowledge beyond the primitive embodied adaptation to a changing pattern of phenomena, one would see representation as an optional instrument that is sometimes used in highly advanced forms of embodied fitness.
    [Show full text]
  • Spooky Action … Or Entanglement Tales
    Spooky action … or Entanglement tales Gunnar Björk Department of Applied Phusics AlbaNova University center, Royal institute of Technology, Stockholm, Sweden Brief outline • There is something fishy about quantum mechanics • Classical and quantum correlations • Bell inequalities (for two particles) • FLASH — a proposal for superluminal communication • A funny (and highly original) review • Tying the knot ADOPT winter school, Romme, 2012 There is something fishy with quantum mecanics ̶ circa 1928-1935 Albert Einstein Boris Podolsky Nathan Rosen Erwin Schrödinger The EPR-“paradox” In their1935 paper Einstein, Podolsky, and Rosen showed that particles that intrinsically possess certain properties even before these properties are measured, is violated by quantum mechanics. They did not like what they found. In particular, for two entangled particles, one particle appears to acquire certain definite properties the very instant the other particle is measured, irrespective of their separation – Einstein, in a letter to max Born, called this “spooky action at a distance”. Polarization Measurement of State of other photon entangled photon one photon pair 1 2 Polarization correlations Entangled photons ”Classically” correlated photons ˆ 2 Polarizer Polarizer For a = b’= 0 a Atom a b’ P b’ 1 0 0,5 1 1 0 1 0 1 0,5 2 0 0 0 Photodetector Forbidden Photodetector transition Correlation coefficient 1 Polarization correlations, continued For a = b’= 45 degrees Entangled photons ”Classically” correlated photons a b’ P a b’ P 1 0 0,5 1 0 0,25 1 1 0 1 1 0,25 0 1 0,5 0 1 0,25 0 0 0 0 0 0,25 Correlation coefficient 1 Correlation coefficient 0 Many years pass ̶ come John Bell John Bell Bell claimed that quantum mechanics was at odds with locality ― and proposed an experiment to test locality v.s.
    [Show full text]
  • Quantum Probability 1982-2017
    Quantum Probability 1982-2017 Hans Maassen, Universities of Nijmegen and Amsterdam Nijmegen, June 23, 2017. 1582: Pope Gregory XIII audaciously replaces the old-fashioned Julian calender by the new Gregorian calender, which still prevails. 1982: A bunch of mathematicians and physicists replaces the old-fashioned Kolmogorovian probability axioms by new ones: quantum probability, which still prevail. Two historic events 1982: A bunch of mathematicians and physicists replaces the old-fashioned Kolmogorovian probability axioms by new ones: quantum probability, which still prevail. Two historic events 1582: Pope Gregory XIII audaciously replaces the old-fashioned Julian calender by the new Gregorian calender, which still prevails. Two historic events 1582: Pope Gregory XIII audaciously replaces the old-fashioned Julian calender by the new Gregorian calender, which still prevails. 1982: A bunch of mathematicians and physicists replaces the old-fashioned Kolmogorovian probability axioms by new ones: quantum probability, which still prevail. Two historic events 1582: Pope Gregory XIII audaciously replaces the old-fashioned Julian calender by the new Gregorian calender, which still prevails. 1982: A bunch of mathematicians and physicists replaces the old-fashioned Kolmogorovian probability axioms by new ones: quantum probability, which still prevail. ∗ 400 years time difference; ∗ They happened in the same hall, in Villa Mondragone, 30 km south-west of Rome, in the Frascati hills. Villa Mondragone First conference in quantum probability, 1982 How are these two events related? ∗ They happened in the same hall, in Villa Mondragone, 30 km south-west of Rome, in the Frascati hills. Villa Mondragone First conference in quantum probability, 1982 How are these two events related? ∗ 400 years time difference; Villa Mondragone First conference in quantum probability, 1982 How are these two events related? ∗ 400 years time difference; ∗ They happened in the same hall, in Villa Mondragone, 30 km south-west of Rome, in the Frascati hills.
    [Show full text]
  • Classical Interventions in Quantum Systems. I. the Measuring Process
    Classical interventions in quantum systems. I. The measuring process Asher Peres∗ Department of Physics, Technion—Israel Institute of Technology, 32 000 Haifa, Israel Abstract The measuring process is an external intervention in the dynamics of a quantum system. It involves a unitary interaction of that system with a measuring apparatus, a further interaction of both with an unknown environment causing decoherence, and then the deletion of a subsystem. This description of the measuring process is a substantial generalization of current models in quantum measurement theory. In particular, no ancilla is needed. The final result is represented by a completely positive map of the quantum state ρ (possibly with a change of the dimensions of ρ). A continuous limit of the above process leads to Lindblad’s equation for the quantum dynamical semigroup. arXiv:quant-ph/9906023v3 7 Feb 2000 PACS numbers: 03.65.Bz, 03.67.* Physical Review A 61, 022116 (2000) ∗E-mail: [email protected] 1 I. INTRODUCTION The measuring process [1, 2] is the interface of the classical and quantum worlds. The classical world has a description which may be probabilistic, but in a way that is compatible with Boolean logic. In the quantum world, probabilities result from complex amplitudes that interfere in a non-classical way. In this article, the notion of measurement is extended to a more general one: an intervention. An intervention has two consequences. One is the acquisition of information by means of an apparatus that produces a record. This step is called a measurement. Its outcome, which is in general unpredictable, is the output of the intervention.
    [Show full text]
  • I Am the Cat Who Walks by Himself
    I am the cat who walks by himself Asher Peres∗ Abstract The city of lions. Beaulieu-sur-Dordogne. The war starts. Drˆole de guerre. Going to work. Going to school. Fleeing from village to village. Playing cat and mouse. The second landing. Return to Beaulieu. Return to Paris. Joining the boyscouts. Learning languages. Israel becomes independent. Arrival in Haifa. Kalay high school. Military training. The Hebrew Technion in Haifa. Relativity. Asher Peres. Metallurgy. Return to France. Escape from jail. Aviva. I am the cat who walks by himself, and all places are alike to me. Rudyard Kipling1 I am grateful to all those who contributed to this Festschrift which celebrates my 70th birthday and therefore the beginning of my eighth decade. In the Jewish religion, there is a prayer, “she-hehhyanu” to thank the Lord for having kept us alive and let us reach this day. I am an atheist and I have no Lord to thank, but I wish to thank many other people who are no longer alive and who helped me reach this point. The city of lions First, I thank my parents, Salomon and Salomea Pressman, for leaving Poland before World War II and going to live temporarily in France, so that we remained alive. Other- wise, I would not have been able to celebrate my seventh birthday. My family originated in a city which was called Lemberg when my parents were born in the Austrian empire, Lw´ow when I was born, Lviv (Ukraine) today. It also has a French name (L´eopol) and other names too.
    [Show full text]