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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/68407700:21340/20:00341853

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Physical Review A

ISSN

2469-9926

e-ISSN

—

Svazek periodika

102

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

"012207(1)"-"012207(14)"

Kód UT WoS článku

000564912400006

EID výsledku v databázi Scopus

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