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Minimal port-based teleportation

Published version
Peer-reviewed

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Abstract

jats:titleAbstract</jats:title> jats:pThere are two types of port-based teleportation (PBT) protocols: deterministic—when the state always arrives to the receiver but is imperfectly transmitted and probabilistic—when the state reaches the receiver intact with high probability. We introduce the minimal set of requirements that define a feasible PBT protocol and construct a simple PBT protocol that satisfies these requirements: it teleports an unknown state of a qubit with success probability jats:inline-formula jats:tex-math</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:msub mml:mip</mml:mi> mml:mrow mml:mrow mml:mtextsucc</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> mml:mo=</mml:mo> mml:mn1</mml:mn> mml:mo−</mml:mo> mml:mfrac mml:mrow mml:miN</mml:mi> mml:mo+</mml:mo> mml:mn2</mml:mn> </mml:mrow> mml:msup mml:mn2</mml:mn> mml:mrow mml:miN</mml:mi> mml:mo+</mml:mo> mml:mn1</mml:mn> </mml:mrow> </mml:msup> </mml:mfrac> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njpacdab4ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> and fidelity jats:inline-formula jats:tex-math</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mn1</mml:mn> mml:mo−</mml:mo> mml:miO</mml:mi> <mml:mo stretchy="false">(</mml:mo> mml:mfrac mml:mn1</mml:mn> mml:miN</mml:mi> </mml:mfrac> <mml:mo stretchy="false">)</mml:mo> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="njpacdab4ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> with the resource state consisting of jats:italicN</jats:italic> maximally entangled states. This protocol is not reducible from either the deterministic or probabilistic PBT protocol. We define the corresponding efficient superdense coding protocols which transmit more classical bits with fewer maximally entangled states. Furthermore, we introduce rigorous methods for comparing and converting between different PBT protocols.</jats:p>

Description

Keywords

quantum teleportation, port-based teleportation, representation theory

Journal Title

New Journal of Physics

Conference Name

Journal ISSN

1367-2630
1367-2630

Volume Title

Publisher

IOP Publishing
Sponsorship
Narodowe Centrum Nauki (Sonatina 2, UMO-2018/28/C/ST2/00004)
The Royal Society (University Research Fellowship URF\R1\191617)