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.et al., 1996; Ekert and Macchiavello, 1996; Laflamme Decoherence and einselection are no exception.Theyet al., 1996) and codified into a mathematically appeal- have been investigated for about two decades.They areing formalism (Gottesman, 1996; Knill and Laflamme, the only explanation of classicality that does not require1997).Moreover, the first examples of successful imple- modifications of quantum theory, as do the alternativesmentation (see, for example, Cory et al., 1999) are al- (Bohm, 1952; Pearle, 1976, 1993; Leggett, 1980, 1998,ready at hand.2002; Ghirardi, Rimini, and Weber, 1986, 1987; Penrose,Error correction allows one, at least, in principle, to 1986, 1989; Gisin and Percival, 1992, 1993a, 1993b,compute forever, providing that the errors are suitably 1993c; Holland, 1993; Goldstein, 1998).Ideas based onsmall ( 10 4 per computational step seems to be the the immersion of the system in the environment haveerror-probability threshold sufficient for most error- recently gained enough support to be described (bycorrection schemes).Strategies that accomplish this en- skeptics) as the new orthodoxy (Bub, 1997).This is acode qubits in already encoded qubits (Aharonov and dangerous characterization, since it suggests that the in-Ben-Or, 1996; Knill, Laflamme, and Zurek, 1996, 1998a, terpretation based on the recognition of the role of the1998b; Kitaev, 1997c; Preskill, 1998).The number of lay- environment is both complete and widely accepted.Cer-ers of such concatenations necessary to achieve fault tainly neither is the case.tolerance the ability to carry out arbitrarily long Many conceptual and technical issues (such as whatcomputations depends on the size (and the character) constitutes a system) are still open.As for the breadth ofof the errors, and on the duration of the computation, acceptance, the new orthodoxy seems to be an opti-but when the error probability is smaller than the mistic (mis)characterization of decoherence and einse-threshold, that number of layers is finite.Overviews of lection, especially since this explanation of the transitionfault-tolerant computation are already at hand (Preskill, from quantum to classical has (with very few exceptions)1999; Nielsen and Chuang, 2000, and references not made it into the textbooks.This is intriguing, andtherein).may be as much a comment on the way in which quan-An interesting subject related to the above discussion tum physics has been taught, especially on the under-is quantum process tomography, anticipated by Jones graduate level, as on the status of the theory we have(1994), and described in the context of quantum infor- reviewed and its level of acceptance among physicists.mation processing by Chuang and Nielsen (1997) and by Quantum mechanics has been to date, by and large,Poyatos, Cirac, and Zoller (1997).The aim here is to presented in a manner that reflects its historical devel-completely characterize a process, such as a quantum opment.That is, Bohr s planetary model of the atom islogical gate, and not just a state.The first deliberate still often the point of departure, Hamilton-Jacobi equa-implementation of this procedure (Nielsen, Knill, and tions are used to derive the Schrödinger equation, andLaflamme, 1998) has also demonstrated experimentally an oversimplified version of the quantum-classical rela-that einselection is indeed equivalent to an unread mea- tionship (attributed to Bohr, but generally not doing jus-Rev.Mod.Phys., Vol.75, No.3, July 2003 770Wojciech Hubert Zurek: Decoherence, einselection, and the quantum origins of the classicaltice to his much more sophisticated views) with the cor- well, 1989; Barvinsky and Kamenshchik, 1990, 1995;Brandenberger, Laflamme, and Mijic, 1990; Paz andrespondence principle, kinship of commutators andSinha, 1991, 1992; Castagnino et al., 1993; Kiefer andPoisson brackets, the Ehrenfest theorem, some versionZeh, 1995; Mensky and Novikov, 1996) and even (quan-of the Copenhagen interpretation, and other evidencetum) robotics (Benioff, 1988).Given the limitations ofthat quantum theory is really not all that different fromspace we have not done justice to most of these subjects,classical especially when systems of interest becomefocusing instead on issues of principle.In some areasmacroscopic, and all one cares about are averages isreviews already exist.Thus Giulini et al.(1996) is a valu-presented.able collection of essays, where, for example, decoher-The message seems to be that there is really no prob-ence in field theories is addressed.The dissertation oflem and that quantum mechanics can be tamed andWallace (2002) offers a good (if somewhat philosophi-confined to the microscopic domain.Indeterminacy andcal) summary of the role of decoherence with a ratherthe double-slit experiment are of course discussed, butdifferent emphasis on similar field-theoretic issues.Con-to prove peaceful coexistence within the elbow roomference proceedings edited by Blanchard et al.(2000)assured by Heisenberg s principle and complementarity.and, especially, an extensive historical overview of theEntanglement is rarely explored.This is quite consistentfoundation of quantum theory from the modern per-with the aim of introductory quantum-mechanicsspective by Auletta (2000) are also recommended.Morecourses, which has been (only slightly unfairly) summedspecific technical issues with implications for decoher-up by the memorable phrase shut up and calculate. ence and einselection have also been reviewed.For ex-Discussion of measurement is either dealt with throughample, on the subject of master equations there are sev-models based on the Copenhagen interpretation old or- eral reviews with very different emphases includingthodoxy or not at all.An implicit (and sometimes ex- Alicki and Lendi (1987); Grabert, Schramm, and Ingoldplicit) message is that those who ask questions that do(1988); Namiki and Pascazio (1993); as well as morenot lend themselves to an answer through laborious,recently Paz and Zurek (2001).In some areas, such aspreferably perturbative calculations are philosophers atomic Bose-Einstein condensation, the study of deco-and should be avoided.herence has only started (Anglin, 1997; Dalvit, Dziar-The above description is of course a caricature.Butmaga, and Zurek, 2001).In many situations (e.g., quan-given that the calculational techniques of quantumtum optics) a useful supplement to the decoherencetheory needed in atomic, nuclear, particle, or condensed- view of the quantum-classical interface is afforded bymatter physics are indeed difficult to master, and givenquantum trajectories a study of the state of the systemthat, to date, most of the applications had nothing to doinferred from the intercepted state of the environmentwith the nature of quantum states, entanglement, and(see Carmichael, 1993; Gisin and Percival, 1993a, 1993b,such, the attitude of avoiding the most flagrantly quan- 1993c; Wiseman and Milburn, 1993).This approach un-tum aspects of quantum theory is easy to understand [ Pobierz caÅ‚ość w formacie PDF ]
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.et al., 1996; Ekert and Macchiavello, 1996; Laflamme Decoherence and einselection are no exception.Theyet al., 1996) and codified into a mathematically appeal- have been investigated for about two decades.They areing formalism (Gottesman, 1996; Knill and Laflamme, the only explanation of classicality that does not require1997).Moreover, the first examples of successful imple- modifications of quantum theory, as do the alternativesmentation (see, for example, Cory et al., 1999) are al- (Bohm, 1952; Pearle, 1976, 1993; Leggett, 1980, 1998,ready at hand.2002; Ghirardi, Rimini, and Weber, 1986, 1987; Penrose,Error correction allows one, at least, in principle, to 1986, 1989; Gisin and Percival, 1992, 1993a, 1993b,compute forever, providing that the errors are suitably 1993c; Holland, 1993; Goldstein, 1998).Ideas based onsmall ( 10 4 per computational step seems to be the the immersion of the system in the environment haveerror-probability threshold sufficient for most error- recently gained enough support to be described (bycorrection schemes).Strategies that accomplish this en- skeptics) as the new orthodoxy (Bub, 1997).This is acode qubits in already encoded qubits (Aharonov and dangerous characterization, since it suggests that the in-Ben-Or, 1996; Knill, Laflamme, and Zurek, 1996, 1998a, terpretation based on the recognition of the role of the1998b; Kitaev, 1997c; Preskill, 1998).The number of lay- environment is both complete and widely accepted.Cer-ers of such concatenations necessary to achieve fault tainly neither is the case.tolerance the ability to carry out arbitrarily long Many conceptual and technical issues (such as whatcomputations depends on the size (and the character) constitutes a system) are still open.As for the breadth ofof the errors, and on the duration of the computation, acceptance, the new orthodoxy seems to be an opti-but when the error probability is smaller than the mistic (mis)characterization of decoherence and einse-threshold, that number of layers is finite.Overviews of lection, especially since this explanation of the transitionfault-tolerant computation are already at hand (Preskill, from quantum to classical has (with very few exceptions)1999; Nielsen and Chuang, 2000, and references not made it into the textbooks.This is intriguing, andtherein).may be as much a comment on the way in which quan-An interesting subject related to the above discussion tum physics has been taught, especially on the under-is quantum process tomography, anticipated by Jones graduate level, as on the status of the theory we have(1994), and described in the context of quantum infor- reviewed and its level of acceptance among physicists.mation processing by Chuang and Nielsen (1997) and by Quantum mechanics has been to date, by and large,Poyatos, Cirac, and Zoller (1997).The aim here is to presented in a manner that reflects its historical devel-completely characterize a process, such as a quantum opment.That is, Bohr s planetary model of the atom islogical gate, and not just a state.The first deliberate still often the point of departure, Hamilton-Jacobi equa-implementation of this procedure (Nielsen, Knill, and tions are used to derive the Schrödinger equation, andLaflamme, 1998) has also demonstrated experimentally an oversimplified version of the quantum-classical rela-that einselection is indeed equivalent to an unread mea- tionship (attributed to Bohr, but generally not doing jus-Rev.Mod.Phys., Vol.75, No.3, July 2003 770Wojciech Hubert Zurek: Decoherence, einselection, and the quantum origins of the classicaltice to his much more sophisticated views) with the cor- well, 1989; Barvinsky and Kamenshchik, 1990, 1995;Brandenberger, Laflamme, and Mijic, 1990; Paz andrespondence principle, kinship of commutators andSinha, 1991, 1992; Castagnino et al., 1993; Kiefer andPoisson brackets, the Ehrenfest theorem, some versionZeh, 1995; Mensky and Novikov, 1996) and even (quan-of the Copenhagen interpretation, and other evidencetum) robotics (Benioff, 1988).Given the limitations ofthat quantum theory is really not all that different fromspace we have not done justice to most of these subjects,classical especially when systems of interest becomefocusing instead on issues of principle.In some areasmacroscopic, and all one cares about are averages isreviews already exist.Thus Giulini et al.(1996) is a valu-presented.able collection of essays, where, for example, decoher-The message seems to be that there is really no prob-ence in field theories is addressed.The dissertation oflem and that quantum mechanics can be tamed andWallace (2002) offers a good (if somewhat philosophi-confined to the microscopic domain.Indeterminacy andcal) summary of the role of decoherence with a ratherthe double-slit experiment are of course discussed, butdifferent emphasis on similar field-theoretic issues.Con-to prove peaceful coexistence within the elbow roomference proceedings edited by Blanchard et al.(2000)assured by Heisenberg s principle and complementarity.and, especially, an extensive historical overview of theEntanglement is rarely explored.This is quite consistentfoundation of quantum theory from the modern per-with the aim of introductory quantum-mechanicsspective by Auletta (2000) are also recommended.Morecourses, which has been (only slightly unfairly) summedspecific technical issues with implications for decoher-up by the memorable phrase shut up and calculate. ence and einselection have also been reviewed.For ex-Discussion of measurement is either dealt with throughample, on the subject of master equations there are sev-models based on the Copenhagen interpretation old or- eral reviews with very different emphases includingthodoxy or not at all.An implicit (and sometimes ex- Alicki and Lendi (1987); Grabert, Schramm, and Ingoldplicit) message is that those who ask questions that do(1988); Namiki and Pascazio (1993); as well as morenot lend themselves to an answer through laborious,recently Paz and Zurek (2001).In some areas, such aspreferably perturbative calculations are philosophers atomic Bose-Einstein condensation, the study of deco-and should be avoided.herence has only started (Anglin, 1997; Dalvit, Dziar-The above description is of course a caricature.Butmaga, and Zurek, 2001).In many situations (e.g., quan-given that the calculational techniques of quantumtum optics) a useful supplement to the decoherencetheory needed in atomic, nuclear, particle, or condensed- view of the quantum-classical interface is afforded bymatter physics are indeed difficult to master, and givenquantum trajectories a study of the state of the systemthat, to date, most of the applications had nothing to doinferred from the intercepted state of the environmentwith the nature of quantum states, entanglement, and(see Carmichael, 1993; Gisin and Percival, 1993a, 1993b,such, the attitude of avoiding the most flagrantly quan- 1993c; Wiseman and Milburn, 1993).This approach un-tum aspects of quantum theory is easy to understand [ Pobierz caÅ‚ość w formacie PDF ]