Einstein-Podolsky-Rosen steering: Its geometric quantification and witness

Huan Yu Ku, Shin Liang Chen, Costantino Budroni, Adam Miranowicz, Yueh Nan Chen, Franco Nori

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We propose a measure of quantum steerability, namely, a convex steering monotone, based on the trace distance between a given assemblage and its corresponding closest assemblage admitting a local-hidden-state (LHS) model. We provide methods to estimate such a quantity, via lower and upper bounds, based on semidefinite programming. One of these upper bounds has a clear geometrical interpretation as a linear function of rescaled Euclidean distances in the Bloch sphere between the normalized quantum states of (i) a given assemblage and (ii) an LHS assemblage. For a qubit-qubit quantum state, these ideas also allow us to visualize various steerability properties of the state in the Bloch sphere via the so-called LHS surface. In particular, some steerability properties can be obtained by comparing such an LHS surface with a corresponding quantum steering ellipsoid. Thus, we propose a witness of steerability corresponding to the difference of the volumes enclosed by these two surfaces. This witness (which reveals the steerability of a quantum state) enables one to find an optimal measurement basis, which can then be used to determine the proposed steering monotone (which describes the steerability of an assemblage) optimized over all mutually unbiased bases.

Original languageEnglish
Article number022338
JournalPhysical Review A
Volume97
Issue number2
DOIs
Publication statusPublished - 2018 Feb 27

Fingerprint

ellipsoids
programming
estimates

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

Cite this

Ku, Huan Yu ; Chen, Shin Liang ; Budroni, Costantino ; Miranowicz, Adam ; Chen, Yueh Nan ; Nori, Franco. / Einstein-Podolsky-Rosen steering : Its geometric quantification and witness. In: Physical Review A. 2018 ; Vol. 97, No. 2.
@article{c817975b310b4b3a905f9e98ae69efb7,
title = "Einstein-Podolsky-Rosen steering: Its geometric quantification and witness",
abstract = "We propose a measure of quantum steerability, namely, a convex steering monotone, based on the trace distance between a given assemblage and its corresponding closest assemblage admitting a local-hidden-state (LHS) model. We provide methods to estimate such a quantity, via lower and upper bounds, based on semidefinite programming. One of these upper bounds has a clear geometrical interpretation as a linear function of rescaled Euclidean distances in the Bloch sphere between the normalized quantum states of (i) a given assemblage and (ii) an LHS assemblage. For a qubit-qubit quantum state, these ideas also allow us to visualize various steerability properties of the state in the Bloch sphere via the so-called LHS surface. In particular, some steerability properties can be obtained by comparing such an LHS surface with a corresponding quantum steering ellipsoid. Thus, we propose a witness of steerability corresponding to the difference of the volumes enclosed by these two surfaces. This witness (which reveals the steerability of a quantum state) enables one to find an optimal measurement basis, which can then be used to determine the proposed steering monotone (which describes the steerability of an assemblage) optimized over all mutually unbiased bases.",
author = "Ku, {Huan Yu} and Chen, {Shin Liang} and Costantino Budroni and Adam Miranowicz and Chen, {Yueh Nan} and Franco Nori",
year = "2018",
month = "2",
day = "27",
doi = "10.1103/PhysRevA.97.022338",
language = "English",
volume = "97",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "2",

}

Einstein-Podolsky-Rosen steering : Its geometric quantification and witness. / Ku, Huan Yu; Chen, Shin Liang; Budroni, Costantino; Miranowicz, Adam; Chen, Yueh Nan; Nori, Franco.

In: Physical Review A, Vol. 97, No. 2, 022338, 27.02.2018.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Einstein-Podolsky-Rosen steering

T2 - Its geometric quantification and witness

AU - Ku, Huan Yu

AU - Chen, Shin Liang

AU - Budroni, Costantino

AU - Miranowicz, Adam

AU - Chen, Yueh Nan

AU - Nori, Franco

PY - 2018/2/27

Y1 - 2018/2/27

N2 - We propose a measure of quantum steerability, namely, a convex steering monotone, based on the trace distance between a given assemblage and its corresponding closest assemblage admitting a local-hidden-state (LHS) model. We provide methods to estimate such a quantity, via lower and upper bounds, based on semidefinite programming. One of these upper bounds has a clear geometrical interpretation as a linear function of rescaled Euclidean distances in the Bloch sphere between the normalized quantum states of (i) a given assemblage and (ii) an LHS assemblage. For a qubit-qubit quantum state, these ideas also allow us to visualize various steerability properties of the state in the Bloch sphere via the so-called LHS surface. In particular, some steerability properties can be obtained by comparing such an LHS surface with a corresponding quantum steering ellipsoid. Thus, we propose a witness of steerability corresponding to the difference of the volumes enclosed by these two surfaces. This witness (which reveals the steerability of a quantum state) enables one to find an optimal measurement basis, which can then be used to determine the proposed steering monotone (which describes the steerability of an assemblage) optimized over all mutually unbiased bases.

AB - We propose a measure of quantum steerability, namely, a convex steering monotone, based on the trace distance between a given assemblage and its corresponding closest assemblage admitting a local-hidden-state (LHS) model. We provide methods to estimate such a quantity, via lower and upper bounds, based on semidefinite programming. One of these upper bounds has a clear geometrical interpretation as a linear function of rescaled Euclidean distances in the Bloch sphere between the normalized quantum states of (i) a given assemblage and (ii) an LHS assemblage. For a qubit-qubit quantum state, these ideas also allow us to visualize various steerability properties of the state in the Bloch sphere via the so-called LHS surface. In particular, some steerability properties can be obtained by comparing such an LHS surface with a corresponding quantum steering ellipsoid. Thus, we propose a witness of steerability corresponding to the difference of the volumes enclosed by these two surfaces. This witness (which reveals the steerability of a quantum state) enables one to find an optimal measurement basis, which can then be used to determine the proposed steering monotone (which describes the steerability of an assemblage) optimized over all mutually unbiased bases.

UR - http://www.scopus.com/inward/record.url?scp=85043255963&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043255963&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.97.022338

DO - 10.1103/PhysRevA.97.022338

M3 - Article

AN - SCOPUS:85043255963

VL - 97

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

M1 - 022338

ER -