### Symplectic Dilations, **Gaussian** States and **Gaussian** Channels

www.archive.org/details/arxiv-1405.6476...

By elementary matrix algebra we show that every real $2n \times 2n$ matrix admits a dilation to an element of the real symplectic group $Sp (2(n+m))$ for some nonnegative integer $m.$ Our methods do not yield the minimum value of $m,$ for which such a dilation is possible. After listing some of the main properties of

**Gaussian**states in $L^2 (\mathbb{R}^n),$ we analyse the implications of symplectic dilations in the study of quantum**Gaussian**channels which lead to some interesting open problems, particularly, in the context of the work of Heinosaari, Holevo and Wolf \cite{3}.Published on 06/29/2018

### Quantum steering of **Gaussian** states via non-**Gaussian** measurements

www.archive.org/details/arxiv-1511.02649...

Quantum steering---a strong correlation to be verified even when one party or its measuring device is fully untrusted---not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems,

**Gaussian**states among others have been extensively studied, however, mostly confined to**Gaussian**measurements. While the fulfillment of**Gaussian**criterion is sufficient to detect CV steering, whether it is also necessary for**Gaussian**states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under**Gaussian**measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-**Gaussian**measurements, which is shown to manifest quantum steering of some**Gaussian**states that**Gaussian**criterion fails to detect. To this aim, we look into**Gaussian**states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying**Gaussian**channel. Our finding significantly modifies the characteristics of**Gaussian**-state steering so far established such as monogamy relations and one-way steering under**Gaussian**measurements, thus opening a new direction for critical studies beyond**Gaussian**regime.Published on 06/28/2018

Document details: 1 download.

**Gaussian** transformations and distillation of entangled **Gaussian** states

www.archive.org/details/arxiv-quant-ph0204069...

We prove that it is impossible to distill more entanglement from a single copy of a two-mode bipartite entangled

**Gaussian**state via LOCC**Gaussian**operations. More generally, we show that any hypothetical distillation protocol for**Gaussian**states involving only**Gaussian**operations would be a deterministic protocol. Finally, we argue that the protocol considered by Eisert et al. [quant-ph/0204052] is the optimum**Gaussian**distillation protocol for two copies of entangled**Gaussian**states.Published on 09/19/2013

Document details: 34 downloads.

### Elasticity of **Gaussian** and nearly-**Gaussian** phantom networks

www.archive.org/details/arxiv-cond-mat0006004...

We study the elastic properties of phantom networks of

**Gaussian**and nearly-**Gaussian**springs. We show that the stress tensor of a**Gaussian**network coincides with the conductivity tensor of an equivalent resistor network, while its elastic constants vanish. We use a perturbation theory to analyze the elastic behavior of networks of slightly non-**Gaussian**springs. We show that the elastic constants of phantom percolation networks of nearly-**Gaussian**springs have a power low dependence on the distance of the system from the percolation threshold, and derive bounds on the exponents.Published on 09/18/2013

Document details: 34 downloads.

**Gaussian** fields and **Gaussian** sheets with generalized Cauchy covariance structure

www.archive.org/details/arxiv-0807.0022...

Two types of

**Gaussian**processes, namely the**Gaussian**field with generalized Cauchy covariance (GFGCC) and the**Gaussian**sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transformation to GFGCC and GSGCC are studied.Published on 07/22/2013

Document details: 27 downloads.

### The characterization of **Gaussian** operations and Distillation of **Gaussian** States

www.archive.org/details/arxiv-quant-ph0204085...

We characterize the class of all physical operations that transform

**Gaussian**states to**Gaussian**states. We show that this class coincides with that of all operations which can be performed on**Gaussian**states using linear optical elements and homodyne measurements. For bipartite systems we characterize the processes which can be implemented by local operations and classical communication, as well as those that can be implemented using positive partial transpose preserving maps. As an application, we show that**Gaussian**states cannot be distilled by local**Gaussian**operations and classical communication. We also define and characterize positive (but not completely positive)**Gaussian**maps.Published on 09/19/2013

Document details: 21 downloads.

### One-mode quantum-limited **Gaussian** channels have **Gaussian** maximizers

www.archive.org/details/arxiv-1610.09967...

We prove that

**Gaussian**states saturate the p->q norms of the one-mode quantum-limited attenuator and amplifier. The proof starts from the majorization result of De Palma et al., IEEE Trans. Inf. Theory 62, 2895 (2016), and is based on a new logarithmic Sobolev inequality. Our result extends to noncommutative probability the seminal theorem "**Gaussian**kernels have only**Gaussian**maximizers" (Lieb, Invent. Math. 102, 179 (1990)), stating that**Gaussian**operators saturate the p->q norms of**Gaussian**integral kernels. Our result also implies that the p->q norms of the thinning are saturated by geometric probability distributions. Moreover, the multimode extension of our result would imply the multiplicativity of the p->q norms of quantum-limited**Gaussian**channels.Published on 06/29/2018

Document details: 21 downloads.

### Hybrid Coding for **Gaussian** Broadcast Channels with **Gaussian** Sources

www.archive.org/details/arxiv-0906.2603...

This paper considers a degraded

**Gaussian**broadcast channel over which**Gaussian**sources are to be communicated. When the sources are independent, this paper shows that hybrid coding achieves the optimal distortion region, the same as that of separate source and channel coding. It also shows that uncoded transmission is not optimal for this setting. For correlated sources, the paper shows that a hybrid coding strategy has a better distortion region than separate source-channel coding below a certain signal to noise ratio threshold. Thus, hybrid coding is a good choice for**Gaussian**broadcast channels with correlated**Gaussian**sources.Published on 09/22/2013

Document details: 20 downloads.

### Non-**Gaussian** states from continuous-wave **Gaussian** light sources

www.archive.org/details/arxiv-quant-ph0602202...

We present a general analysis of the state obtained by subjecting the output from a continuous-wave (cw)

**Gaussian**field to non-**Gaussian**measurements. The generic multimode state of cw**Gaussian**fields is characterized by an infinite dimensional covariance matrix involving the noise correlations of the source. Our theory extracts the information relevant for detection within specific temporal output modes from these correlation functions . The formalism is applied to schemes for production of non-classical light states from a squeezed beam of light.Published on 09/21/2013

Document details: 32 downloads.

**Gaussian** entanglement of symmetric two-mode **Gaussian** states

www.archive.org/details/arxiv-0711.3477...

A

**Gaussian**degree of entanglement for a symmetric two-mode**Gaussian**state can be defined as its distance to the set of all separable two-mode**Gaussian**states. The principal property that enables us to evaluate both Bures distance and relative entropy between symmetric two-mode**Gaussian**states is the diagonalization of their covariance matrices under the same beam-splitter transformation. The multiplicativity property of the Uhlmann fidelity and the additivity of the relative entropy allow one to finally deal with a single-mode optimization problem in both cases. We find that only the Bures-distance**Gaussian**entanglement is consistent with the exact entanglement of formation.Published on 09/17/2013

Document details: 49 downloads.