Determinism without causality

D’Ariano, Giacomo Mauro; Manessi, Franco; Perinotti, Paolo

doi:10.1088/0031-8949/2014/t163/014013

Cited by 24 publications

(34 citation statements)

References 12 publications

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“…However, it is clear that there is some nontrivial physical property that this condition expresses, i.e., it is regarded as an axiom for a reason. The fact that theories that allow signaling from the future are considered sensible [58] further shows that the causality axiom is not the implicit assumption that one makes about what an operation is supposed to mean.…”

Section: The Concept Of Operationmentioning

confidence: 99%

Operational formulation of time reversal in quantum theory

Oreshkov

Cerf

2015

Nature Phys

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The symmetry of quantum theory under time reversal has long been a subject of controversy because the transition probabilities given by Born's rule do not apply backward in time. Here, we resolve this problem within a rigorous operational probabilistic framework. We argue that reconciling time reversal with the probabilistic rules of the theory requires a notion of operation that permits realizations through both pre-and post-selection. We develop the generalized formulation of quantum theory that stems from this approach and give a precise definition of time-reversal symmetry, emphasizing a previously overlooked distinction between states and e ects. We prove an analogue of Wigner's theorem, which characterizes all allowed symmetry transformations in this operationally time-symmetric quantum theory. Remarkably, we find larger classes of symmetry transformations than previously assumed, suggesting a possible direction in the search for extensions of known physics.S ymmetries play a fundamental role in our understanding of physics. It is widely believed that the most general symmetry transformations in quantum theory correspond to unitary or anti-unitary transformations on the Hilbert space, with symmetries involving time reversal being anti-unitary 1 . This has profound implications for many phenomena, such as the classification of possible elementary particles 2 . The joint transformation of charge conjugation, parity inversion and time reversal, defined according to this principle, is considered an exact symmetry of all known physical laws 3-6 . However, it has been recognized that Born's rule, which describes the probabilities for the outcomes of future measurements conditional on past preparations, does not apply for events in the reverse order 7,8 . This is in conflict with the very definition of symmetry underlying the above assertions 9 . Moreover, because the operational interpretation of a quantum state is directly linked to Born's rule 10 , this raises doubts about whether the commonly accepted notion of time-reversed state makes physical sense.Here, we address this problem from a rigorous operational perspective 11-20 , using the circuit framework 14,15 for operational probabilistic theories (OPTs), which has been shown to successfully formalize the informational foundations of quantum theory 18,19 . We argue that reconciling time reversal with the probabilistic rules of the theory requires a generalized notion of operation, defined without assumptions on whether the implementation of an operation involves pre-or post-selection. In this approach, operations are not expected to be up to the 'free choices' of agents, but merely describe knowledge about the possible events taking place in different regions, conditional on information obtained locally. We develop the generalized formulation of quantum theory that stems from this approach and show that it has a new notion of state space that is not convex. We give a precise definition of time-reversal symmetry, taking into account the different nature of st...

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Section: The Concept Of Operationmentioning

confidence: 99%

Operational formulation of time reversal in quantum theory

Oreshkov

Cerf

2015

Nature Phys

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“…This is accomplished by using the rules governing the structure of operational devices, rules that are more empirical, albeit not completely, because they are given a mathematical representation or expression, as they must be, in accordance with the authors' and the present view, or principle. This principle entails the necessity of establishing a rigorous mathematical expression for the physical architecture 22 I think, that, in accordance with the definition given at the outset, "postulate" may be a better term, because one can hardly have self-evidence of "axioms," but this is a secondary matter, which, as I said, does not really affect the essence of the situation.…”

Section: Principles Of Information Processing Quantum Theory and DImentioning

confidence: 91%

“…6 As will be seen, D'Ariano et al adopt a principle of causality of that type [10, p. 3, 11]. See also [22] and [23] for further discussions of causality in quantum theory.…”

Section: Principle Thinking In Theoretical Physicsmentioning

confidence: 99%

A Matter of Principle: The Principles of Quantum Theory, Dirac’s Equation, and Quantum Information

Plotnitsky

2015

Found Phys

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Abstract. This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation of the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall also consider Heisenberg's earlier work leading him to the discovery of quantum mechanics, which inspired Dirac's work. I argue that Heisenberg's and Dirac's work was guided by their adherence to and their confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by G. M. D'Ariano and coworkers on the principles of quantum information theory, which extend quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equations from these principles alone, without using the principles of relativity.

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“…Quantum theory defined over real, rather than complex, Hilbert spaces supplies an example of a theory that does not satisfy tomographic locality. See also [19] for an explicit construction that does not satisfy the causality assumption.…”

Section: Examplesmentioning

confidence: 99%

Computation in generalised probabilisitic theories

2015

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From the general difficulty of simulating quantum systems using classical systems, and in particular the existence of an efficient quantum algorithm for factoring, it is likely that quantum computation is intrinsically more powerful than classical computation. At present, the best upper bound known for the power of quantum computation is that BQP AWPP ⊆ , where AWPP is a classical complexity class (known to be included in PP, hence PSPACE). This work investigates limits on computational power that are imposed by simple physical, or information theoretic, principles. To this end, we define a circuit-based model of computation in a class of operationally-defined theories more general than quantum theory, and ask: what is the minimal set of physical assumptions under which the above inclusions still hold? We show that given only an assumption of tomographic locality (roughly, that multipartite states and transformations can be characterized by local measurements), efficient computations are contained in AWPP. This inclusion still holds even without assuming a basic notion of causality (where the notion is, roughly, that probabilities for outcomes cannot depend on future measurement choices). Following Aaronson, we extend the computational model by allowing postselection on measurement outcomes. Aaronson showed that the corresponding quantum complexity class, PostBQP, is equal to PP. Given only the assumption of tomographic locality, the inclusion in PP still holds for post-selected computation in general theories. Hence in a world with post-selection, quantum theory is optimal for computation in the space of all operational theories. We then consider whether one can obtain relativized complexity results for general theories. It is not obvious how to define a sensible notion of a computational oracle in the general framework that reduces to the standard notion in the quantum case. Nevertheless, it is possible to define computation relative to a 'classical oracle'. Then, we show there exists a classical oracle relative to which efficient computation in any theory satisfying the causality assumption does not include NP.By comparison, relatively little has been learned about the connections between physical principles and computation. It was shown in [7] that a maximally non-local theory has no non-trivial reversible dynamics and, thus, any reversible computation in such a theory can be efficiently simulated on a classical computer. Aside from this result, most previous investigations into computation beyond the usual quantum formalism have centred around non-standard theories involving modifications of quantum theory. These theories often appear to have immense computational power and entail unreasonable physical consequences. For example, non-linear quantum theory appears to be able to solve NP-complete problems in polynomial time [8], as does quantum theory in the presence of closed timelike curves [9,40]. Aaronson has considered other modifications of quantum theory, such as a hidden variable model in which the hist...

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Determinism without causality

Cited by 24 publications

References 12 publications

Operational formulation of time reversal in quantum theory

Operational formulation of time reversal in quantum theory

A Matter of Principle: The Principles of Quantum Theory, Dirac’s Equation, and Quantum Information

Computation in generalised probabilisitic theories

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