### 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

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.

### 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.

### Operational Discord Measure for **Gaussian** States with **Gaussian** Measurements

www.archive.org/details/arxiv-1502.02331...

We introduce an operational discord-type measure for quantifying nonclassical correlations in bipartite

**Gaussian**states based on using**Gaussian**measurements. We refer to this measure as operational**Gaussian**discord (OGD). It is defined as the difference between the entropies of two conditional probability distributions associated to one subsystem, which are obtained by performing optimal local and joint**Gaussian**measurements. We demonstrate the operational significance of this measure in terms of a**Gaussian**quantum protocol for extracting maximal information about an encoded classical signal. As examples, we calculate OGD for several**Gaussian**states in the standard form.Published on 06/26/2018

Document details: 9 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: 48 downloads.

### 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.

### No-activation theorem for **Gaussian** nonclassical correlations by **Gaussian** operations

www.archive.org/details/arxiv-1405.6859...

We study general quantum correlations of continuous variable

**Gaussian**states and their interplay with entanglement. Specifically, we investigate the existence of a quantum protocol activating all nonclassical correlations between the subsystems of an input bipartite continuous variable system, into output entanglement between the system and a set of ancillae. For input**Gaussian**states, we prove that such an activation protocol cannot be accomplished with**Gaussian**operations, as the latter are unable to create any output entanglement from an initial separable yet nonclassical state in a worst-case scenario. We then construct a faithful non-**Gaussian**activation protocol, encompassing infinite-dimensional generalizations of controlled-NOT gates to generate entanglement between system and ancillae, in direct analogy with the finite-dimensional case. We finally calculate the negativity of quantumness, an operational measure of nonclassical correlations defined in terms of the performance of the activation protocol, for relevant classes of two-mode**Gaussian**states.Published on 06/29/2018

Document details: 3 downloads.

### Interconversion of pure **Gaussian** states using non-**Gaussian** operations

www.archive.org/details/arxiv-1409.8217...

We analyze the conditions under which local operations and classical communication enable entanglement transformations within the set of bipartite pure

**Gaussian**states. A set of necessary and sufficient conditions had been found in [Quant. Inf. Comp. 3, 211 (2003)] for the interconversion between such states that is restricted to**Gaussian**local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure**Gaussian**states that goes beyond**Gaussian**local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2 x 2**Gaussian**states that necessarily require non-**Gaussian**local operations to be transformed into each other.Published on 06/30/2018

Document details: 3 downloads.

### Driving non-**Gaussian** to **Gaussian** states with linear optics

www.archive.org/details/arxiv-quant-ph0211173...

We introduce a protocol that maps finite-dimensional pure input states onto approximately

**Gaussian**states in an iterative procedure. This protocol can be used to distill highly entangled bi-partite**Gaussian**states from a supply of weakly entangled pure**Gaussian**states. The entire procedure requires only the use of passive optical elements and photon detectors that solely distinguish between the presence and absence of photons.Published on 09/20/2013

Document details: 34 downloads.

**Gaussian** Process Regression with Heteroscedastic or Non-**Gaussian** Residuals

www.archive.org/details/arxiv-1212.6246...

**Gaussian**Process (GP) regression models typically assume that residuals are

**Gaussian**and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice, as do applications in which the residuals do not have a

**Gaussian**distribution. In this paper, we propose a GP Regression model with a latent variable that serves as an additional unobserved covariate for the regression. This model (which we call GPLC) allows for heteroscedasticity since it allows the function to have a changing partial derivative with respect to this unobserved covariate. With a suitable covariance function, our GPLC model can handle (a)

**Gaussian**residuals with input-dependent variance, or (b) non-

**Gaussian**residuals with input-dependent variance, or (c)

**Gaussian**residuals with constant variance. We compare our model, using synthetic datasets, with a model proposed by Goldberg, Williams and Bishop (1998), which we refer to as GPLV, which only deals with case (a), as well as a standard GP model which can handle only case (c). Markov Chain Monte Carlo methods are developed for both modelsl. Experiments show that when the data is heteroscedastic, both GPLC and GPLV give better results (smaller mean squared error and negative log-probability density) than standard GP regression. In addition, when the residual are

**Gaussian**, our GPLC model is generally nearly as good as GPLV, while when the residuals are non-

**Gaussian**, our GPLC model is better than GPLV.

Published on 09/22/2013

Document details: 42 downloads.