scholarly journals Continuous Variable Quantum Information: Gaussian States and Beyond

2014 ◽  
Vol 21 (01n02) ◽  
pp. 1440001 ◽  
Author(s):  
Gerardo Adesso ◽  
Sammy Ragy ◽  
Antony R. Lee
Keyword(s):  
Quantum Information ◽  
Symplectic Geometry ◽  
Quantum Information Processing ◽  
Mathematical Structure ◽  
Continuous Variable ◽  
Gaussian State ◽  
Mathematical Framework ◽  
Gaussian States ◽  
Subject Material ◽  
Selection Of

The study of Gaussian states has arisen to a privileged position in continuous variable quantum information in recent years. This is due to vehemently pursued experimental realisations and a magnificently elegant mathematical framework. In this paper, we provide a brief, and hopefully didactic, exposition of Gaussian state quantum information and its contemporary uses, including sometimes omitted crucial details. After introducing the subject material and outlining the essential toolbox of continuous variable systems, we define the basic notions needed to understand Gaussian states and Gaussian operations. In particular, emphasis is placed on the mathematical structure combining notions of algebra and symplectic geometry fundamental to a complete understanding of Gaussian informatics. Furthermore, we discuss the quantification of different forms of correlations (including entanglement and quantum discord) for Gaussian states, paying special attention to recently developed measures. The paper is concluded by succinctly expressing the main Gaussian state limitations and outlining a selection of possible future lines for quantum information processing with continuous variable systems.

scholarly journals Generating superposition of up-to three photons for continuous variable quantum information processing

2013 ◽  
Vol 21 (5) ◽  
pp. 5529 ◽  
Author(s):  
Mitsuyoshi Yukawa ◽  
Kazunori Miyata ◽  
Takahiro Mizuta ◽  
Hidehiro Yonezawa ◽  
Petr Marek ◽  
...  
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Continuous Variable

Quantum non-gaussianity from an indefnite causal order of Gaussian operations

2021 ◽  
Author(s):  
Seid Koudia ◽  
Abdelhakim Gharbi
Keyword(s):  
Quantum Information ◽  
Quantum Key Distribution ◽  
Degrees Of Freedom ◽  
Quantum Communication ◽  
Quantum Information Processing ◽  
Quantum Metrology ◽  
Causal Order ◽  
Gaussian States ◽  
Control Qubit ◽  
Non Gaussian

Quantum non-Gaussian states are considered a useful resource for many tasks in quantum information processing, from quantum metrology and quantum sensing to quantum communication and quantum key distribution. Another useful tool that is gaining attention is the newly constructed quantum switch. Its applications in many tasks in quantum information have been proved to outperform many existing schemes in quantum communication and quantum thermometry. In this contribution, we demonstrate this to be very useful for engineering highly non-Gaussian states from Gaussian operations whose order is controlled by degrees of freedom of a control qubit. The nonconvexity of the set of Gaussian states and the set of Gaussian operations guarantees the emergence of non-Gaussianity after post-selection on the control qubit deterministically, in contrast to existing protocols in the literature. The nonclassicality of the resulting states is discussed accordingly.

scholarly journals ENTANGLEMENT SHARING: FROM QUBITS TO GAUSSIAN STATES

2006 ◽  
Vol 04 (03) ◽  
pp. 383-393 ◽  
Author(s):  
GERARDO ADESSO ◽  
FABRIZIO ILLUMINATI
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Continuous Variable ◽  
Quantum Systems ◽  
Tripartite Entanglement ◽  
Gaussian States ◽  
Trade Off ◽  
Entanglement Sharing

It is a central trait of quantum information theory that there exist limitations to the free sharing of quantum correlations among multiple parties. Such monogamy constraints have been introduced in a landmark paper by Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a trade-off between the couplewise and the genuine tripartite entanglement for states of three qubits. Since then, a lot of efforts have been devoted to the investigation of distributed entanglement in multipartite quantum systems. In this paper we report, in a unifying framework, a bird's eye view of the most relevant results that have been established so far on entanglement sharing in quantum systems. We will take off from the domain of N qubits, graze qudits, and finally land in the almost unexplored territory of multimode Gaussian states of continuous variable systems.

scholarly journals Quantum mode filtering of non-Gaussian states for teleportation-based quantum information processing

2012 ◽  
Vol 85 (5) ◽  
Author(s):  
Shuntaro Takeda ◽  
Hugo Benichi ◽  
Takahiro Mizuta ◽  
Noriyuki Lee ◽  
Jun-ichi Yoshikawa ◽  
...  
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Gaussian States ◽  
Non Gaussian

Pre-selection of optical transitions in rare-earth ions in crystals perspective for quantum information processing

2012 ◽  
Vol 59 (2) ◽  
pp. 166-178 ◽  
Author(s):  
T.T. Basiev ◽  
I.T. Basieva ◽  
A.A. Kornienko ◽  
V.V. Osiko ◽  
K.K. Pukhov ◽  
...  
Keyword(s):  
Rare Earth ◽  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Rare Earth Ions ◽  
Optical Transitions ◽  
Selection Of

scholarly journals A Computable Gaussian Quantum Correlation for Continuous-Variable Systems

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1190
Author(s):  
Liang Liu ◽  
Jinchuan Hou ◽  
Xiaofei Qi
Keyword(s):  
Quantum Correlation ◽  
Quantum Discord ◽  
Continuous Variable ◽  
Gaussian State ◽  
Product State ◽  
Gaussian States ◽  
System A ◽  
Gaussian Channels ◽  
The Mean ◽  
Gaussian Quantum Discord

Generally speaking, it is difficult to compute the values of the Gaussian quantum discord and Gaussian geometric discord for Gaussian states, which limits their application. In the present paper, for any (n+m)-mode continuous-variable system, a computable Gaussian quantum correlation M is proposed. For any state ρAB of the system, M(ρAB) depends only on the covariant matrix of ρAB without any measurements performed on a subsystem or any optimization procedures, and thus is easily computed. Furthermore, M has the following attractive properties: (1) M is independent of the mean of states, is symmetric about the subsystems and has no ancilla problem; (2) M is locally Gaussian unitary invariant; (3) for a Gaussian state ρAB, M(ρAB)=0 if and only if ρAB is a product state; and (4) 0≤M((ΦA⊗ΦB)ρAB)≤M(ρAB) holds for any Gaussian state ρAB and any Gaussian channels ΦA and ΦB performed on the subsystem A and B, respectively. Therefore, M is a nice Gaussian correlation which describes the same Gaussian correlation as Gaussian quantum discord and Gaussian geometric discord when restricted on Gaussian states. As an application of M, a noninvasive quantum method for detecting intracellular temperature is proposed.

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