The paper is a Chapter of a book. In it an exhaustive review of the proposals to send faster than light signals resorting to quantum nonlocality and the reduction process is presented, together with a critical analysis and rebuttal of all proposals. The most interesting part of the Chapter is the one in which the problem of quantum cloning is discussed. Actually, a proposal of superluminal signaling based on an hypothetical cloning machine has been presented by N. Herbert. The proposal does not work just because of the assumption that one can clone nonorthogonal states. The fact that such a machine is incompatible with quantum theory (i.e., the so-called No-Cloning Theorem) has been proved, for the first time, by the author of the present chapter in his referee's report to Herbert's paper. In the final part of the paper some recent (different but similarly not correct) proposals are analyzed and the reasons for which they are basically wrong are presented.
The paper is a Chapter of a book. In it an exhaustive review of the proposals to send faster than light signals resorting to quantum nonlocality and the reduction process is presented, together with a critical analysis and rebuttal of all proposals. The most interesting part of the Chapter is the one in which the problem of quantum cloning is discussed. Actually, a proposal of superluminal signaling based on an hypothetical cloning machine has been presented by N. Herbert. The proposal does not work just because of the assumption that one can clone nonorthogonal states. The fact that such a machine is incompatible with quantum theory (i.e., the so-called No-Cloning Theorem) has been proved, for the first time, by the author of the present chapter in his referee's report to Herbert's paper. In the final part of the paper some recent (different but similarly not correct) proposals are analyzed and the reasons for which they are basically wrong are presented.
After a brief introduction to the quantum no-cloning theorem and its link with the linearity and causality of quantum mechanics, the concept of quantum cloning machines is sketched, following, whenever possible, the chronology of the main results. The important classes of quantum cloning machines are reviewed, in particular state-independent and state-dependent cloning machines. The 1-to-2 cloning problem is then studied from a formal point of view, using the isomorphism between completely positive maps and operators, which leads to the so-called double-Bell ansatz. This also yields an efficient numerical approach to quantum cloning, based on semidefinite programming methods. The derivation of the optimal N-to-M universal cloning machine in d dimensions is then detailed, as well as the notion of asymmetric cloning machines. In the second part of this review, the optical implementation of cloning machines is considered. It is shown that the universal cloning of photons can be achieved by parametric amplification of light or by symmetrization via the Hong-Ou-Mandel effect. The various experimental demonstrations of quantum cloning machines are reviewed. The cloning of orthogonally polarized photons is also considered, as well as the asymmetric and phase-covariant cloning of photons. Finally, the extension of quantum cloning to continuous variables is analyzed. The optimal cloning of coherent states of light by phase-insensitive amplification is explained, as well as the experimental realization of continuous-variable quantum cloning with linear optics, measurement, and feed-forward operations.
We show that non-local resources cannot be used for probabilistic signalling even if one can produce exact clones with the help of a probabilistic quantum cloning machine (PQCM). We show that PQCM cannot help to distinguish two statistical mixtures at a remote location. Thus quantum theory rules out the possibility of sending superluminal signals not only deterministically but also probabilistically. We give a bound on the success probability of producing multiple clones in an entangled system. All the useful information that can be transmitted has a universal speed limit, namely, the speed of light. In quantum mechanics the situation seems to be changed when Einstein, Podolsky and Rosen put forward their famous thought experiment on two systems that had interacted in the past but are no longer in direct contact [1]. These kind of systems are described by entangled states which show non-local correlations that cannot be explained by any local hidden variable theory [2]. In [1] they proved that the measurement outcome of one system can instantaneously affect the result of the other. This suggested that one can
Bell's Theorem demonstrates that factorizable theories for the EPR experiment (EPR) cannot reproduce the quantum correlations. Factorizability is motivated by various locality conditions. So to understand the nature of nonlocality in EPR, we first need to understand the conceptual relations between factorizability, these various locality conditions and the nature of the quantum correlations. That is the main focus of my thesis. My main conclusion is that these conceptual relations are more subtle than the literature has usually suggested. Chapter 1 is a general introduction. In Chapter 2, I review the general framework of factorizable stochastic theories for EPR. I argue that factorizability can be motivated by various locality conditions, even in theories that admit time-dependent states and take the measurement interactions to be neither instantaneous, nor simultaneous. In Chapter 3, I focus on Cartwright' s (1989) and Humphreys' (1989) theories of probabilistic causation for singular events, which are based on modifications of traditional causal linear modelling. I argue (against Cartwright) that local models for EPR in the framework of these theories are committed to factorizability; and so they cannot reproduce the EPR correlations. In Chapter 4, I turn to Stochastic-Einstein Locality (SEL). Hellman (1982) proposed that SEL with some provisos characterizes the No-Superluminal-Action (NSA) of the Special Theory of Relativity (STR), and he argued that SEL is not violated in EPR. Butterfield (1994) proposed that SEL (without Hellman's provisos) characterizes the lack of superluminal Lewisian causation, and he argued that SEL is violated in EPR. I argue that SEL (without Hellman's provisos) is motivated by NSA and spatiotemporal separability. Thus, the violation of SEL might arise from the failure of spatiotemporal separability. And this failure is compatible with NSA and superluminal Lewisian causation. Accordingly, Hellman's and Butterfield's views need not be in tension. In Chapter 5, I focus on the implications for nonlocality of Jarrett's (1984) analysis of factorizability into "locality" and "completeness". I argue that although this analysis cannot distinguish between failures of factorizability which are compatible with STR and those which are not, it is significant for clarifying the implications of Bell's theorem for nonlocality. In Chapter 6, I qmsider three arguments that are intended to deny superluminal causal propagation in EPR, and a fourth argument that is intended to establish the opposite conclusion. I argue that in various ways these arguments have gone wrong. Three of these argument rely on implicit assumptions that have been overlooked. Accordingly, two of them reached a reasonable conclusion, i.e. the failure of separability, for the wrong reasons; whereas the third reached a wrong conclusion, i.e. that the failure of the contiguity of causal processes explains the failure of factorizability in EPR. The fourth relies on a wrong assumption, and thus it reaches a too strong conclusion, that the EPR correlations require superluminal action. My main conclusion is that the quantum correlations require nonseparability . In Chapter 7, I focus on decision theory in the context of EPR. In both EPR and the famous Newcomb's problem (NewProb), there are unscreenable-off correlations. I argue that NewProb can be related to EPR, in the sense that a NewProb can be realized by that experiment.
If YES, then we can look forward to physical realization of superluminal communication, as the original considerations of the ``no-cloning'' theorem were motivated in part as an explanation of why certain schemes for superluminal signaling cannot work. If NO, then it would seem that some aspects of the ``hidden'' variables must be ``intrinsically hidden'', i.e., ``unknowable'', such that ``hidden-variable'' theories belong more to the ``idealist'' than to the ``realist'' school of thought. I pose this question without proposing a definite answer. I am unaware of any commentary on this topic during these 23 years since the formulation of the ``no-cloning'' theorem, but I would be pleased to be enlightened by more knowledgeable readers.
We understand emergent quantum mechanics in the sense that quantum mechanics describes processes of physical emergence relating an assumed sub-quantum physics to macroscopic boundary conditions. The latter can be shown to entail top-down causation, in addition to usual bottom-up scenarios. With this example it is demonstrated that definitions of "realism" in the literature are simply too restrictive. A prevailing manner to define realism in quantum mechanics is in terms of pre-determination independent of the measurement. With our counter-example, which actually is ubiquitous in emergent, or self-organizing, systems, we argue for realism without pre-determination . We refer to earlier results of our group showing how the guiding equation of the de Broglie-Bohm interpretation can be derived from a theory with classical ingredients only. Essentially, this corresponds to a "quantum mechanics without wave functions" in ordinary 3-space, albeit with nonlocal correlations. This, then, leads to the central question of how to deal with the nonlocality problem in a relativistic setting. We here show that a basic argument discussing the allegedly paradox time ordering of events in EPR-type two-particle experiments falls short of taking into account the contextuality of the experimental setup. Consequently, we then discuss under which circumstances (i.e. physical premises) superluminal information transfer (but not signaling) may be compatible with a Lorentz-invariant theory. Finally, we argue that the impossibility of superluminal signaling - despite the presence of superluminal information transfer - is not the result of some sort of conspiracy (á la "Nature likes to hide"), but the consequence of the impossibility to exactly reproduce in repeated experimental runs a state's preparation, or of the no-cloning theorem, respectively.