scholarly journals Weak measurement-based state estimation of Gaussian states of one-variable quantum systems

2017 ◽  
Vol 50 (14) ◽  
pp. 145307 ◽  
Author(s):  
Debmalya Das ◽  
Arvind
Keyword(s):  
State Estimation ◽  
Quantum Systems ◽  
Weak Measurement ◽  
Gaussian States

scholarly journals Geometry of variational methods: dynamics of closed quantum systems

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Lucas Hackl ◽  
Tommaso Guaita ◽  
Tao Shi ◽  
Jutho Haegeman ◽  
Eugene Demler ◽  
...  
Keyword(s):  
Variational Methods ◽  
Time Evolution ◽  
Coherent States ◽  
Geometric Approach ◽  
Quantum Systems ◽  
Imaginary Time ◽  
Excitation Spectra ◽  
Spectral Functions ◽  
Geometric Framework ◽  
Gaussian States

We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: Kähler and non-Kähler. Traditional variational methods typically require the variational family to be a Kähler manifold, where multiplication by the imaginary unit preserves the tangent spaces. This covers the vast majority of cases studied in the literature. However, recently proposed classes of generalized Gaussian states make it necessary to also include the non-Kähler case, which has already been encountered occasionally. We illustrate our approach in detail with a range of concrete examples where the geometric structures of the considered manifolds are particularly relevant. These go from Gaussian states and group theoretic coherent states to generalized Gaussian states.

Relativistic motion on Gaussian quantum steering for two-mode localized Gaussian states

2021 ◽  
Author(s):  
Gong Xiao-long ◽  
Cao Shuo ◽  
Yue Fang ◽  
Liu Tong-Hua
Keyword(s):  
Single Mode ◽  
Quantum Systems ◽  
Unruh Effect ◽  
Gaussian States ◽  
The Earth ◽  
Single Mode Approximation ◽  
Quantum Steering ◽  
The One ◽  
Interesting Behavior ◽  
Monotonically Decrease

Abstract Realistic quantum systems always exhibit gravitational and relativistic features. In this paper, we investigate the properties of Gaussian steering and its asymmetry by the localized two-mode Gaussian quantum states, instead of the traditional single-mode approximation method in the relativistic setting. We find that the one-side Gaussian quantum steering will monotonically decrease with increasing observers of acceleration. Meanwhile, our results also reveal the interesting behavior of the Gaussian steering asymmetry, which increases for a specific range of accelerated parameter and then gradually approaches to a finite value. Such findings is well consistent and explained by the well-known Unruh effect, which could significantly destroy the one-side Gaussian quantum steering. Finally, our results could also be applied to the dynamical studies of Gaussian steering between the Earth and satellites, since the effects of acceleration is equal to the effects of gravity according to the equivalence principle.

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 Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Johannes Nokkala ◽  
Rodrigo Martínez-Peña ◽  
Gian Luca Giorgi ◽  
Valentina Parigi ◽  
Miguel C. Soriano ◽  
...  
Keyword(s):  
Thermal Fluctuations ◽  
Continuous Variable ◽  
Quantum Systems ◽  
Full Potential ◽  
Reservoir Computing ◽  
Linear Dynamical Systems ◽  
Gaussian States ◽  
Proposed Model ◽  
Training Cost ◽  
The Rich

AbstractQuantum reservoir computing aims at harnessing the rich dynamics of quantum systems for machine-learning purposes. It can be used for online time series processing while having a remarkably low training cost. Here, we establish the potential of continuous-variable Gaussian states of linear dynamical systems for quantum reservoir computing. We prove that Gaussian resources are enough for universal reservoir computing. We find that encoding the input into Gaussian states is both a source and a means to tune the nonlinearity of the overall input-output map. We further show that the full potential of the proposed model can be reached by encoding to quantum fluctuations, such as squeezed vacuum, instead of classical fields or thermal fluctuations. Our results introduce a research paradigm for reservoir computing harnessing quantum systems and engineered Gaussian quantum states.

scholarly journals ENTANGLEMENT FRUSTRATION IN MULTIMODE GAUSSIAN STATES

2012 ◽  
Vol 09 (02) ◽  
pp. 1260022 ◽  
Author(s):  
COSMO LUPO ◽  
STEFANO MANCINI ◽  
PAOLO FACCHI ◽  
GIUSEPPE FLORIO ◽  
SAVERIO PASCAZIO
Keyword(s):  
Pure State ◽  
High Energy ◽  
Quantum Systems ◽  
Entangled States ◽  
Multipartite Entanglement ◽  
Total System ◽  
Continuous Variables ◽  
Bipartite Entanglement ◽  
Gaussian States ◽  
Composite Quantum System

Bipartite entanglement between two parties of a composite quantum system can be quantified in terms of the purity of one party and there always exists a pure state of the total system that maximizes it (and minimizes purity). When many different bipartitions are considered, the requirement that purity be minimal for all bipartitions gives rise to the phenomenon of entanglement frustration. This feature, observed in quantum systems with both discrete and continuous variables, can be studied by means of a suitable cost function whose minimizers are the maximally multipartite-entangled states (MMES). In this paper we extend the analysis of multipartite entanglement frustration of Gaussian states in multimode bosonic systems. We derive bounds on the frustration, under the constraint of finite mean energy, in the low- and high-energy limits.

OPTIMAL STATE ESTIMATION AND CLONING FOR EQUATORIAL QUANTUM SYSTEMS WITH ARBITRARY DIMENSION

2005 ◽  
Vol 03 (01) ◽  
pp. 57-63
Author(s):  
C. MACCHIAVELLO
Keyword(s):  
State Estimation ◽  
Finite Dimension ◽  
Arbitrary Dimension ◽  
Optimal Estimation ◽  
Estimation Procedure ◽  
Quantum Systems ◽  
Optimal State ◽  
Optimal State Estimation

We review the problem of optimal estimation of multiple phases for systems with arbitrary finite dimension and derive the optimal estimation fidelity for equatorial states. We present optimal phase covariant cloning transformations for d-dimensional systems, relating these results to the optimal estimation procedure.

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