The quantum coin toss-testing microphysical undecidability

Svozil, Karl

doi:10.1016/0375-9601(90)90408-g

Cited by 38 publications

(46 citation statements)

References 18 publications

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“…[15][16][17] How could anyone possibly see a difference with respect to their (non-)stochasticity? For all practical purposes, the sequences will appear structurally identically from a stochastic point of view, and heuristically random.…”

Section: Difficultiesmentioning

confidence: 99%

Quantum Randomness and Value Indefiniteness

Calude

Svozil

2008

adv sci lett

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Section: Difficultiesmentioning

confidence: 99%

Quantum Randomness and Value Indefiniteness

Calude

Svozil

2008

adv sci lett

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“…So, in principle, it is very simple to design a quantum device that outputs a sequence of independent unbiased bits. In fact, there have been several concrete proposals for implementing random generators based on quantum mechanics [8,9], and testing whether the outputs of the generators pass certain simple statistical tests [10,11], or even tests specifically designed towards detecting algorithmic randomness [12]. Of course, success in passing a handful of such tests in no way certifies that the output distribution of the generator is close to uniformly random-the best that one can hope to say is that failure to pass the tests certifies that the generator's output distribution is not uniform.…”

Section: Introductionmentioning

confidence: 99%

Certifiable quantum dice

Vazirani

Vidick

2012

Phil. Trans. R. Soc. A.

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We introduce a protocol through which a pair of quantum mechanical devices may be used to generate n random bits that are 3-close in statistical distance from n uniformly distributed bits, starting from a seed of O(log n log 1/3) uniform bits. The bits generated are certifiably random, based only on a simple statistical test that can be performed by the user, and on the assumption that the devices obey the no-signalling principle. No other assumptions are placed on the devices' inner workings: it is not necessary to even assume the validity of quantum mechanics.

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“…To be more precise: ac-cording to the 'creed' canonized by some 'quantum council,' the occurrence of certain individual quantum events are believed to be totally unpredictable, unlawful, acausal, and thus independent of past, present and future states of the system and of its surroundings, such as the measurement interface, in any algorithmically meaningful way 1 . As a consequence, with high probability, algorithmically incompressible sequences can be generated from quantum coin tosses [9,10]. Summing up, in terms of spin, electrons seem to specialize in two antithetical tasks, and in nothing else: being prepared to issue a deterministic answer when asked a proper question; and tossing more or less fair coins if asked improper questions.…”

Section: Amazing Single Particle Quantum Systemsmentioning

confidence: 99%

“…The first and second single particle states are drawn horizontally and vertically, respectively. Depicted are the first cases of equations (5)- (9).…”

Section: Inverse Problemsmentioning

confidence: 99%

“…In general, the permutations transform nonentangled states into entangled ones. Consider, for the sake of detail, the '(counter)diagonal' set of trits listed in equation (7), which is induced by the permutation whose cycle form is (1) (2,5,6,7,3,9,8,4). If the same two particle (3 × 3) product state space representation is used as in figure 1, then the trits just correspond to the completed diagonals and counterdiagonals; i.e., if the single particle states are labelled by a 1 , b 1 , c 1 and a 2 , b 2 , c 2 , respectively, then the new trit eigenstates {|ψ 1 , |ψ 2 , |ψ 3 } and {|ψ 4 , |ψ 5 , |ψ 6 } are…”

Section: Examples: Two Three-state Particle Cases and Entanglementmentioning

confidence: 99%

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Quantum information via state partitions and the context translation principle

Svozil

2004

Journal of Modern Optics

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For many-particle systems, quantum information in base n can be defined by partitioning the set of states according to the outcomes of n-ary (joint) observables. Thereby, k particles can carry k nits. With regards to the randomness of single outcomes, a context translation principle is proposed. Quantum randomness is related to the uncontrollable degrees of freedom of the measurement interface, thereby translating a mismatch between the state prepared and the state measured.1 Information in many-particle quantum systemsThe preparation of a single particle n-state quantum system in a single state constitutes the operationalization of a nit, or qunit. Likewise, the occurrence of an outcome of an observable with n possible outcomes can be associated with accessing a nit of information. For a single particle observable, this is associated with choosing a vector from an orthogonal basis of n-dimensional Hilbert space. In the many-particle case, nits may not only be localized at single particle observables, since due to entanglement, the nits may be distributed over the particles by representing joint particle properties.In what follows we shall review and extend formal generalizations [1, 2] of the single particle two-state case to an arbitrary finite number of particles with an arbitrary finite number of different measurement outcomes per particle. Thereby, we define a nit as a radix n measure of quantum information which is based on state partitions associated with the outcomes of n-ary observables. We shall demonstrate the following property: k particles specify k nits in such a way that k measurements of comeasurable observables with n possible outcomes are necessary to determine the information. Stated pointedly, k particles can carry k nits.

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The quantum coin toss-testing microphysical undecidability

Cited by 38 publications

References 18 publications

Quantum Randomness and Value Indefiniteness

Quantum Randomness and Value Indefiniteness

Certifiable quantum dice

Quantum information via state partitions and the context translation principle

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