### 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

### 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.

### 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: 29 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: 54 downloads.

**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: 47 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: 2 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.

### Key distillation from **Gaussian** states by **Gaussian** operations

www.archive.org/details/arxiv-quant-ph0405047...

We study the secrecy properties of

**Gaussian**states under**Gaussian**operations. Although such operations are useless for quantum distillation, we prove that it is possible to distill a secret key secure against any attack from sufficiently entangled**Gaussian**states with non-positive partial transposition. Moreover, all such states allow for key distillation, when Eve is assumed to perform finite-size coherent attacks before the reconciliation process.Published on 09/19/2013

Document details: 43 downloads.

### On the impossibility of distilling **Gaussian** states with **Gaussian** operations

www.archive.org/details/arxiv-quant-ph0204052...

We show that no distillation protocol for

**Gaussian**quantum states exists that relies on (i) arbitrary local unitary operations that preserve the**Gaussian**character of the state and (ii) homodyne detection together with classical communication and postprocessing by means of local**Gaussian**unitary operations on two symmetric identically prepared copies. This is in contrast to the finite-dimensional case, where entanglement can be distilled in an iterative protocol using two copies at a time. The ramifications for the distribution of**Gaussian**states over large distances will be outlined. We also comment on the generality of the approach and sketch the most general form of a**Gaussian**local operation with classical communication in a bipartite setting.Published on 09/19/2013

Document details: 48 downloads.

### Non-**Gaussian** Spectra

www.archive.org/details/arxiv-astro-ph9610174...

**Gaussian**cosmic microwave background skies are fully specified by the power spectrum. The conventional method of characterizing non-

**Gaussian**skies is to evaluate higher order moments, the n-point functions and their Fourier transforms. We argue that this method is inefficient, due to the redundancy of information existing in the complete set of moments. In this paper we propose a set of new statistics or non-

**Gaussian**spectra to be extracted out of the angular distribution of the Fourier transform of the temperature anisotropies in the small field limit. These statistics complement the power spectrum and act as localization, shape, and connectedness statistics. They quantify generic non-

**Gaussian**structure, and may be used in more general image processing tasks. We concentrate on a subset of these statistics and argue that while they carry no information in

**Gaussian**theories they may be the best arena for making predictions in some non-

**Gaussian**theories. As examples of applications we consider superposed

**Gaussian**and non-

**Gaussian**signals, such as point sources in

**Gaussian**theories or the realistic Kaiser-Stebbins effect. We show that in these theories non-

**Gaussian**ity is only present in a ring in Fourier space, which is best isolated in our formalism. Subtle but strongly non-

**Gaussian**theories are also written down for which only non-

**Gaussian**spectra may accuse non-

**Gaussian**ity.

Published on 09/20/2013

Document details: 26 downloads.