Yes. That is my polemical reply to the titular question in Travis Norsens self-styled polemical response to Howard Wisemans recent paper. Less polemically, I am pleased to see that on two of my positions --- that Bells 1964 theorem is different from
Bells 1976 theorem, and that the former does not include Bells one-paragraph heuristic presentation of the EPR argument --- Norsen has made significant concessions. In his response, Norsen admits that Bells recapitulation of the EPR argument in [the relevant] paragraph leaves something to be desired, that it disappoints and is problematic. Moreover, Norsen makes other statements that imply, on the face of it, that he should have no objections to the title of my recent paper (The Two Bells Theorems of John Bell). My principle aim in writing that paper was to try to bridge the gap between two interpretational camps, whom I call operationalists and realists, by pointing out that they use the phrase Bells theorem to mean different things: his 1964 theorem (assuming locality and determinism) and his 1976 theorem (assuming local causality), respectively. Thus, it is heartening that at least one person from one side has taken one step on my bridge. That said, there are several issues of contention with Norsen, which we (the two authors) address after discussing the extent of our agreement with Norsen. The most significant issues are: the indefiniteness of the word locality prior to 1964; and the assumptions Einstein made in the paper quoted by Bell in 1964 and their relation to Bells theorem.
Bells theorem can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination. His 1976 theo
rem is their incompatibility with the single property of Local Causality. This is contrary to Bells own later assertions, that his 1964 theorem began with the assumption of Local Causality, even if not by that name. Although the two Bells theorems are logically equivalent, their assumptions are not. Hence, the earlier and later theorems suggest quite different conclusions, embraced by operationalists and realists, respectively. The key issue is whether Locality or Local Causality is the appropriate notion emanating from Relativistic Causality, and this rests on ones basic notion of causation. For operationalists the appropriate notion is what is here called the Principle of Agent-Causation, while for realists it is Reichenbachs Principle of common cause. By breaking down the latter into even more basic Postulates, it is possible to obtain a version of Bells theorem in which each camp could reject one assumption, happy that the remaining assumptions reflect its weltanschauung. Formulating Bells theorem in terms of causation is fruitful not just for attempting to reconcile the two camps, but also for better describing the ontology of different quantum interpretations and for more deeply understanding the implications of Bells marvellous work.
Many of the heated arguments about the meaning of Bells theorem arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomen
a with the dual assumptions of locality and determinism. His 1976 theorem is the incompatibility of quantum phenomena with the unitary property of local causality. This is contrary to Bells own later assertions, that his 1964 theorem began with that single, and indivisible, assumption of local causality (even if not by that name). While there are other forms of Bells theorems --- which I present to explain the relation between Jarrett-completeness, fragile locality, and EPR-completeness --- I maintain that Bells t
A common objective for quantum control is to force a quantum system, initially in an unknown state, into a particular target subspace. We show that if the subspace is required to be a decoherence-free subspace of dimension greater than 1, then such c
ontrol must be decoherent. That is, it will take almost any pure state to a mixed state. We make no assumptions about the control mechanism, but our result implies that for this purpose coherent control offers no advantage, in principle, over the obvious measurement-based feedback protocol.
By rigorously formalizing the Einstein-Podolsky-Rosen (EPR) argument, and Bohrs reply, one can appreciate that both arguments were technically correct. Their opposed conclusions about the completeness of quantum mechanics hinged upon an explicit diff
erence in their criteria for when a measurement on Alices system can be regarded as not disturbing Bobs system. The EPR criteria allow their conclusion (incompletness) to be reached by establishing the physical reality of just a single observable $q$ (not a conjugate pair $q$ and $p$), but I show that Bohrs definition of disturbance prevents the EPR chain of reasoning from establishing even this. Moreover, I show that Bohrs definition is intimately related to the asymmetric concept of quantum discord from quantum information theory: if and only if the joint state has no Alice-discord, she can measure any observable without disturbing (in Bohrs sense) Bobs system. Discord can be present even when systems are unentangled, and this has implications for our understanding of the historical development of notions of quantum nonlocality.
Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example: they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom bound; they
allow measurement of the phase of a quantum oscillator with accuracy approaching (or in some cases attaining) the Heisenberg limit; and they allow estimation of phase in interferometry with a variance scaling at the Heisenberg limit, using only single qubit measurement and control. Each of these examples has close links with quantum information, in particular experimental optical quantum information: the first is a basic quantum communication protocol; the second has potential application in linear optical quantum computing; the third uses an adaptive protocol inspired by the quantum phase estimation algorithm. We discuss each of these examples, and their implementation in the laboratory, but concentrate upon the last, which was published most recently [Higgins {em et al.}, Nature vol. 450, p. 393, 2007].
A which-way measurement in Youngs double-slit will destroy the interference pattern. Bohr claimed this complementarity between wave- and particle behaviour is enforced by Heisenbergs uncertainty principle: distinguishing two positions a distance s ap
art transfers a random momentum q sim hbar/s to the particle. This claim has been subject to debate: Scully et al. asserted that in some situations interference can be destroyed with no momentum transfer, while Storey et al. asserted that Bohrs stance is always valid. We address this issue using the experimental technique of weak measurement. We measure a distribution for q that spreads well beyond [-hbar/s, hbar/s], but nevertheless has a variance consistent with zero. This weakvalued momentum-transfer distribution P_{wv}(q) thus reflects both sides of the debate.
