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arXiv:quant-ph/9810050 · Applicable Algebra in Engineering Communication and Computing

Shifts on a Finite Qubit String: A Class of Quantum Baker's Maps

Rüdiger Schack, Carlton M. Caves

Published May 1, 2000• 40 citations
arXivHTMLPDF
DOI
10.1007/s002000050133

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We investigate entanglement production in a class of quantum baker's maps. The dynamics of these maps is constructed using strings of qubits, providing a natural tensor-product structure for application of various entanglement measures. We find that, in general, the quantum baker's maps are good at generating entanglement, producing multipartite entanglement amongst the qubits close to that expected in random states. We investigate the evolution of several entanglement measures: the subsystem linear entropy, the concurrence to characterize entanglement between pairs of qubits, and two proposals for a measure of multipartite entanglement. Also derived are some new analytical formulae describing the levels of entanglement expected in random pure states.
We show that the coarse-grained quantum baker's map exhibits a linear entropy increase at an asymptotic rate given by the Kolmogorov-Sinai entropy of the classical chaotic baker's map. The starting point of our analysis is a symbolic representation of the map on a string of N qubits, i.e., an N-bit register of a quantum computer. To coarse grain the quantum evolution, we make use of the decoherent histories formalism. As a by-product, we show that the condition of medium decoherence holds asymptotically for the coarse-grained quantum baker's map.