Abstract
In the space of mixed states the Schrödinger-Robertson uncertainty relation holds though it can never be saturated. Two tight extensions of this relation in the space of mixed states exist; one proposed by Dodonov and Man'ko, where the lower limit on the uncertainty depends on the purity of the state, and another where the uncertainty is bounded by the von Neumann entropy of the state proposed by Bastiaans. Driven by the needs that have emerged in the field of quantum information, in a recent work we have extended the purity-bounded uncertainty relation by adding an additional parameter characterizing the state, namely its degree of non-Gaussianity. In this work we alternatively present a extension of the entropy-bounded uncertainty relation. The common points and differences between the two extensions of the uncertainty relation help us to draw more general conclusions concerning the bounds on the non-Gaussianity of mixed states.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |
| Volume | 7727 |
| DOIs | |
| Publication status | Published - 2010 |
| Externally published | Yes |
| Event | Quantum Optics - Brussels, Belgium Duration: Apr 13 2010 → Apr 14 2010 |
Other
| Other | Quantum Optics |
|---|---|
| Country | Belgium |
| City | Brussels |
| Period | 4/13/10 → 4/14/10 |
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Keywords
- Mixed states
- Non-Gaussian states
- Uncertainty principle
ASJC Scopus subject areas
- Applied Mathematics
- Computer Science Applications
- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
Cite this
Uncertainty, entropy and non-Gaussianity for mixed states. / Mandilara, Aikaterini; Karpov, Evgueni; Cerf, Nicolas J.
Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7727 2010. 77270H.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Uncertainty, entropy and non-Gaussianity for mixed states
AU - Mandilara, Aikaterini
AU - Karpov, Evgueni
AU - Cerf, Nicolas J.
PY - 2010
Y1 - 2010
N2 - In the space of mixed states the Schrödinger-Robertson uncertainty relation holds though it can never be saturated. Two tight extensions of this relation in the space of mixed states exist; one proposed by Dodonov and Man'ko, where the lower limit on the uncertainty depends on the purity of the state, and another where the uncertainty is bounded by the von Neumann entropy of the state proposed by Bastiaans. Driven by the needs that have emerged in the field of quantum information, in a recent work we have extended the purity-bounded uncertainty relation by adding an additional parameter characterizing the state, namely its degree of non-Gaussianity. In this work we alternatively present a extension of the entropy-bounded uncertainty relation. The common points and differences between the two extensions of the uncertainty relation help us to draw more general conclusions concerning the bounds on the non-Gaussianity of mixed states.
AB - In the space of mixed states the Schrödinger-Robertson uncertainty relation holds though it can never be saturated. Two tight extensions of this relation in the space of mixed states exist; one proposed by Dodonov and Man'ko, where the lower limit on the uncertainty depends on the purity of the state, and another where the uncertainty is bounded by the von Neumann entropy of the state proposed by Bastiaans. Driven by the needs that have emerged in the field of quantum information, in a recent work we have extended the purity-bounded uncertainty relation by adding an additional parameter characterizing the state, namely its degree of non-Gaussianity. In this work we alternatively present a extension of the entropy-bounded uncertainty relation. The common points and differences between the two extensions of the uncertainty relation help us to draw more general conclusions concerning the bounds on the non-Gaussianity of mixed states.
KW - Mixed states
KW - Non-Gaussian states
KW - Uncertainty principle
UR - http://www.scopus.com/inward/record.url?scp=77954584470&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77954584470&partnerID=8YFLogxK
U2 - 10.1117/12.854750
DO - 10.1117/12.854750
M3 - Conference contribution
SN - 9780819482006
VL - 7727
BT - Proceedings of SPIE - The International Society for Optical Engineering
ER -