We study Parrondo's paradox -- the phenomenon where combining losing strategies yields a winning one -- in a minimal discrete-time quantum walk. We introduce the transport vector, encoded in the coin's steady state, whose inner product with the initial coin state gives the walker's asymptotic velocity. More generally, the paradox emerges exactly when the transport vector of the combined strategy falls outside the cone spanned by the individual ones -- a geometric criterion valid for any combination of strategies. It explains, for instance, why composing two coin operators within a single step can produce the paradox while simple alternation between them cannot, since alternation keeps the combined vector confined to the cone. The paradoxical set has nonzero measure, and we compute its probability explicitly in representative cases. This casts the paradox as one instance of designing reachable transport in quantum walks.
How rapidly does order give way to randomness, and can quantum coherence accelerate this process? We address these questions through the paradigmatic problem of card shuffling, formulated as a random walk on the symmetric group $S_n$. We first recast the random-transposition walk studied by Diaconis and Shahshahani, as...
Feng He, Arthur Hutsalyuk, G. Mussardo et al.· 0 citations
We study the geometric spread of discrete-time quantum walks using Connes'distance formula. We introduce its discrete analogue by adapting the continuous spectral metric to the lattice, with the Dirac operator replaced by the unitary step operator. Focusing first on a (2+1)-dimensional quantum walk, we evaluate the dyn...
R. Trabelsi, A. Reyes-Lega, P. Arrighi· 0 citations
In this work, we extend the scattering quantum walk (SQW) framework to a lattice of energy-dependent point interactions. This yields, within the coined quantum walk (CQW) formalism, a coin operator that is directly related to the scattering matrix of zero-range potentials. The model thus provides a discrete-time quantu...
Alana Spak dos Santos, T. T. Tsutsui, F. M. Andrade· 0 citations
This is the first continuous-time quantum walk whose free dynamics coincides exactly with a Dirac equation on a hierarchical graph, and how the resulting construction can serve as the foundation of a quantum network with genuinely relativistic-type internal degrees of freedom, complementing earlier, non-relativistic p-...
Recent work quantified the notion of quantum counterfactual gain for an extended Elitzur-Vaidman bomb test style scenario, through a connection to the negativity of the Kirkwood-Dirac quasiprobability distribution. We here extend this work to identifying quantum advantage in a new scenario, which we term the ``Quantum...
Nicolas G. Underwood, Holger F. Hofmann, Jonte R Hance· 1 citation
We extend our description of the electron’s quaternion spin (Q–spin) as a geometric rotor. This follows from incorporating both the symmetric polarization and the antisymmetric coherence into the theory. Polarization is observed only through the local process we call contextual instantiation. For an EPR pair the observ...
B. Sanctuary· Quantum Reports· 0 citations
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