Complete classification of trapping coins for quantum walks on the two-dimensional square lattice

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F20%3A10245747" target="_blank" >RIV/61989100:27240/20:10245747 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/20:00341853
Result on the web
<a href="https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.012207" target="_blank" >https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.012207</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1103/PhysRevA.102.012207" target="_blank" >10.1103/PhysRevA.102.012207</a>

Result language
angličtina
Original language name
Complete classification of trapping coins for quantum walks on the two-dimensional square lattice
Original language description
One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, although the system is translationally invariant. The effect is dependent on the dimension and the explicit form of the local coin. A four-state discrete-time quantum walk on a square lattice is defined by its unitary coin operator, acting on the four-dimensional coin Hilbert space. The well-known example of the Grover coin leads to a partial trapping, i.e., there exists some escaping initial state for which the probability of staying at the initial position vanishes. On the other hand, some other coins are known to exhibit strong trapping, where such an escaping state does not exist. We present a systematic study of coins leading to trapping, explicitly construct all such coins for discrete-time quantum walks on the two-dimensional square lattice, and classify them according to the structure of the operator and the manifestation of the trapping effect. We distinguish three types of trapping coins exhibiting distinct dynamical properties, as exemplified by the existence or nonexistence of the escaping state and the area covered by the spreading wave packet.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10300 - Physical sciences

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
S - Specificky vyzkum na vysokych skolach

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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