Quantum dating market

Zabaleta, Omar Gustavo; Arizmendi, C. M.

doi:10.1016/j.physa.2010.03.010

Cited by 14 publications

(13 citation statements)

References 32 publications

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“…Starting from the maps Eqs. (3), (28), (29), (30) the corresponding dynamical equations for the GCD are built. More explicitly, following the procedure in Ref.…”

Section: Gcd Dynamics With Broken Linksmentioning

confidence: 99%

“…combining the two components of each map of Eqs. (3), (28), (29), (30), the maps for their respective probability distributions are obtained P k,L (t + 1) = P k+1,L (t) cos 2 θ + P k+1,R (t) sin 2 θ + β k+1 (t, θ ),…”

Section: Gcd Dynamics With Broken Linksmentioning

confidence: 99%

“…(3) and for the right half-line it is determined by the set of equations Eqs. (3), (28), (29), (30), weighted with the values r 0 , r 1 , r 2 , r 3 respectively. The stochastic behavior of the GCD, for an ensemble of these QWs, will depend, for the left side, on the usual QW and, for the right side, on the QW with broken links.…”

Section: Gcd Dynamics With Broken Linksmentioning

confidence: 99%

“…We have performed this calculation, as a function of the probability r with θ = π /4 using the original maps Eqs. (3), (28), (29), (30) with an ensemble of 100 dynamical trajectories and 2000 time steps. Fig.…”

Section: Gcd Dynamics With Broken Linksmentioning

confidence: 99%

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Quantum walks: Decoherence and coin-flipping games

Romanelli

Hernández

2011

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tWe investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first mechanism drives the system towards a classical diffusive behavior. This is used to build new quantum games, similar to the spin-flip game. The second mechanism involves two different possibilities: (a) All the quantum walk links have the same probability of being broken. (b) Only the quantum walk links on a half-line are affected by random breakage. In case (a) the decoherence drives the system to a classical Markov process, whose master equation is equivalent to the dynamical equation of the quantum density matrix. This is not the case in (b) where the asymptotic global chirality distribution unexpectedly maintains some dependence with the initial condition. Explicit analytical equations are obtained for all cases.

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“…Starting from the maps Eqs. (3), (28), (29), (30) the corresponding dynamical equations for the GCD are built. More explicitly, following the procedure in Ref.…”

Section: Gcd Dynamics With Broken Linksmentioning

confidence: 99%

Section: Gcd Dynamics With Broken Linksmentioning

confidence: 99%

Section: Gcd Dynamics With Broken Linksmentioning

confidence: 99%

Section: Gcd Dynamics With Broken Linksmentioning

confidence: 99%

See 2 more Smart Citations

Quantum walks: Decoherence and coin-flipping games

Romanelli

Hernández

2011

Physica A: Statistical Mechanics and its Applications

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“…Orthodox opinion would have the label of quantum biology applied to only those bioprocesses which exhibit physical or chemical quantum mechanical behavior. This uncompromising a priori decision to reject the possibility of other kinds of quantum phenomena can lead to Type I inferential errors, since bioprocesses become excluded that obey quantum statistical mechanics, quantum information theory, and quantum game theory without necessarily manifesting physical or chemical quantum traits (e.g., Clark, 2010a-d;Flitney and Abbott, 2002;Khrennikov, 2009;Meyer, 1999;Pascual-Leone, 1970;Pothos and Busemeyer, 2009;Turner and Cho, 1999;Zabaleta and Arizmendi, 2010). Tests of the boundary conditions for quantum biological phenomena have been introduced for many systems (cf.…”

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confidence: 99%

Bioreaction Quantum Computing without Quantum Diffusion

Clark¹

2012

Neuroquantology

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Debate exists over whether or not adherence to quantum statistical mechanics and emulation of quantum information properties are sufficient criteria for biocomputations to be classified as quantum processes. A noteworthy example at the scale of intact life forms making social decisions can be found in "lower" eukaryotes. Ciliates learn to group Ca 2+ -dependent behavioral strategies into heuristics which they then use to signal mating status after physical contacts from presumed suitors and rivals. The time taken by ciliates to find appropriate strategies stored within behavioral repertoires diminishes with experience. Improvements in strategy search speeds by experts resemble the root-rate performance of Grover's quantum search algorithm over classical processes. Ciliates putatively implement fast strategy search algorithms by learning to change the reaction kinetics of mechanically activated Ca 2+ -induced Ca 2+ waves that travel through different cellular compartments to preferentially trigger over-learned behavioral sequences. Fire-diffuse-fire models demonstrate wave-conduction velocities most suited for quadratic increases in strategy search speeds are sensitive to limitations imposed by Ca 2+ release times and distances between Ca 2+ storage sites. These reaction-diffusion computations provide an interesting contrast to physicochemical quantum events described by equations containing quantum diffusion terms, as a modifiable classical diffusion coefficient solely accounts for root-rate processing efficiency. Fast chemical events underlying quantum information processing schemes in live biological systems can thus counter-intuitively exert their effects via thermodynamically vulnerable reaction parameters. The ubiquity and biological importance of intracellular Ca 2+ -induced Ca 2+ cascades across taxa suggests bacteria to mammals might likewise learn to use quantum-level processing when planning and executing behavioral strategies.

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Quantum prisoners’ dilemma under enhanced interrogation

Siopsis

Balu

Solmeyer

2018

Quantum Inf Process

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In the quantum version of prisoners' dilemma, each prisoner is equipped with a single qubit that the interrogator can entangle. We enlarge the available Hilbert space by introducing a third qubit that the interrogator can entangle with the other two. We discuss an enhanced interrogation technique based on tripartite entanglement and analyze Nash equilibria. We show that for tripartite entanglement approaching a W-state, there exist Nash equilibria that coincide with the Pareto optimal choice where both prisoners cooperate. Upon continuous variation between a W-state and a pure bipartite entangled state, the game is shown to have a surprisingly rich structure. The role of bipartite and tripartite entanglement is explored to explain that structure.Quantum games as a field received a lot of attention from the early works of Meyer [1], and has grown steadily ever since. Connections exist between quantum games and various other fields, such as Bell non-locality [3] and quantum logic [2], to name a few. Various aspects of quantum games, including the role of entanglement and multiple player extensions, explored by different authors can be found in references [4][5][6]. A solution to the quantum prisoners' dilemma in which players have a Nash equilibrium that is Pareto optimal ignited interest in quantum games [7]. However, this initial formulation drew criticism because it dramatically restricted the strategy space of the players and did not persist under maximal entanglement if arbitrary quantum strategies were allowed [8].In this work, we enlarge the Hilbert space in a minimal way in order to arrive at a Nash equilibrium (NE) that is Pareto-optimal with maximal entanglement. In addition to the two player qubits, we consider a resource qubit that the referee, or interrogator, has access to. In the three-qubit Hilbert space, one can introduce tripartite entanglement which will lead to a much richer Nash equilibrium structure. Interestingly, for tripartite entanglement close to maximum (approaching a W-state), we obtain Nash equilibria that coincide with Pareto optimal points. The bipartite entanglement between the players' qubits partially explains the structure. In addition, it is shown that there is no NE for a GHZ state, which has a fundamentally different type of entanglement [9].We briefly review the standard formulation of the prisoners' dilemma.

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Quantum dating market

Cited by 14 publications

References 32 publications

Quantum walks: Decoherence and coin-flipping games

Quantum walks: Decoherence and coin-flipping games

Bioreaction Quantum Computing without Quantum Diffusion

Quantum prisoners’ dilemma under enhanced interrogation

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