PLQP &amp; Company: Decidable Logics for Quantum Algorithms

Baltag, Alexandru; Bergfeld, Jort M.; Kishida, Kohei; Sack, Joshua; Smets, Sonja; Zhong, Shengyang

doi:10.1007/s10773-013-1987-3

Cited by 10 publications

(19 citation statements)

References 14 publications

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“…In quantum computing, however, entanglement is viewed as a computational resource, that allows us to go beyond the world of classical computing. Among the papers that address this part of the gap between quantum logic and quantum computation are [3,8], and [9,Chapter 17]. Our work strengthens the connection further.…”

supporting

confidence: 69%

Quantum Probabilistic Dyadic Second-Order Logic

Baltag

Bergfeld

Kishida

et al. 2013

Logic, Language, Information, and Computation

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Abstract. We propose an expressive but decidable logic for reasoning about quantum systems. The logic is endowed with tensor operators to capture properties of composite systems, and with probabilistic predication formulas P ≥r (s), saying that a quantum system in state s will yield the answer 'yes' (i.e. it will collapse to a state satisfying property P ) with a probability at least r whenever a binary measurement of property P is performed. Besides first-order quantifiers ranging over quantum states, we have two second-order quantifiers, one ranging over quantum-testable properties, the other over quantum "actions". We use this formalism to express the correctness of some quantum programs. We prove decidability, via translation into the first-order logic of real numbers.

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supporting

confidence: 69%

Quantum Probabilistic Dyadic Second-Order Logic

Baltag

Bergfeld

Kishida

et al. 2013

Logic, Language, Information, and Computation

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“…This view equips quantum logic with an operational dimension, linking every physical property or proposition about a physical system to the experimental procedures that can be performed on those systems. Inspired by the work of C. Piron, [33,34], the operational view has lead to new axiomatic systems that are now studied in the context of Dynamic Quantum Logic [7][8][9][12][13][14]. In contrast to the traditional work on quantum logic (following [24,39]), the dynamic logical approach has several advantages.…”

Section: Dynamic Quantum Logicmentioning

confidence: 99%

Logics of Informational Interactions

Baltag

Smets

2015

J Philos Logic

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The pre-eminence of logical dynamics, over a static and purely propositional view of Logic, lies at the core of a new understanding of both formal epistemology and the logical foundations of quantum mechanics. Both areas appear at first sight to be based on purely static propositional formalisms, but in our view their fundamental operators are essentially dynamic in nature. Quantum logic can be best understood as the logic of physically-constrained informational interactions (in the form of measurements and entanglement) between subsystems of a global physical system. Similarly, (multi-agent) epistemic logic is the logic of sociallyconstrained informational interactions (in the form of direct observations, learning, various forms of communication and testimony) between "subsystems" of a social system. Dynamic Epistemic Logic (DEL) provides us with a unifying setting in which these informational interactions, coming from seemingly very different areas of research, can be fully compared and analyzed. The DEL formalism comes with a powerful set of tools that allows us to make the underlying dynamic/interactive mechanisms fully transparent.

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“…Recent work toward the development of quantum logics for computation yielded probabilistic dynamic quantum logics that are decidable, such as Baltag et al (2013Baltag et al ( , 2014, and the correctness of many quantum protocols can be expressed in these languages. However, an axiomatization of these probabilistic systems is lacking.…”

Section: Introductionmentioning

confidence: 99%

“…The language involves dynamic modalities for quantum programs as well as probabilistic modalities, and is similar to the decidable logic in Baltag et al (2014), and hence we give it the same name: the Probabilistic Logic of Quantum Programs. Among the differences between our language here and the one in Baltag et al (2014) is that our language here simplifies the formulas for locality to describing full separability with respect to a given set of components. This simplification of the language allows us to highlight basic properties in the proof system that are essential to properties of bases of a finite-dimensional Hilbert space.…”

Section: Introductionmentioning

confidence: 99%

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Deriving the correctness of quantum protocols in the probabilistic logic for quantum programs

Bergfeld

Sack

2015

Soft Comput

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This paper presents a sound axiomatization for a probabilistic modal dynamic logic of quantum programs. The logic can express whether a state is separable or entangled, information that is local to a subsystem of the whole quantum system, and the probability of positive answers to quantum tests of certain properties. The power of this axiomatization is demonstrated with proofs of properties concerning bases of a finite-dimensional Hilbert space, composite systems, entangled and separable states, and with proofs of the correctness of two probabilistic quantum protocols (the quantum leader election protocol and the BB84 quantum key distribution protocol).

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PLQP & Company: Decidable Logics for Quantum Algorithms

Cited by 10 publications

References 14 publications

Quantum Probabilistic Dyadic Second-Order Logic

Quantum Probabilistic Dyadic Second-Order Logic

Logics of Informational Interactions

Deriving the correctness of quantum protocols in the probabilistic logic for quantum programs

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