arXiv subjects

Ritabrata Sengupta

Publications and source records attributed to Ritabrata Sengupta.

25 records · Page 2Linked to original sources

arXiv2015

Exchangeable, stationary and entangled chains of Gaussian states

We explore conditions on the covariance matrices of a consistent chain of mean zero finite mode Gaussian states in order that the chain may be exchangeable or stationary. For an exchangeable chain our conditions are necessary and sufficient. Every stationary Gaussian chain admits an asymptotic entropy rate. Whereas an exchangeable chain admits a simple expression for its entropy rate, in our examples of stationary chains the same admits an integral formula based on the asymptotic eigenvalue distribution for Toeplitz matrices. An example of a stationary entangled Gaussian chain is given.

quant-ph↗

arXiv2015

From particle counting to Gaussian tomography

All the $n(2n+3)$ mean and covariance parameters of an $n$-mode Gaussian states are expressed in terms of the expectation values of the same number of conjugates of the total number observable. This permits a complete tomography of the state. The same is applied to outputs of a Gaussian channel corresponding to selected coherent states to perform the complete tomography of the channel. This leads to some interesting problems concerning the distribution of the number operator and also tomographic complexity.

quant-ph↗

arXiv2015

Measurement-based local quantum filters and their ability to transform quantum entanglement

We introduce local filters as a means to detect the entanglement of bound entangled states which do not yield to detection by witnesses based on positive (P) maps which are not completely positive (CP). We demonstrate how such non-detectable bound entangled states can be locally filtered into detectable bound entangled states. Specifically, we show that a bound entangled state in the orthogonal complement of the unextendible product bases (UPB), can be locally filtered into a another bound entangled state that is detectable by the Choi map. We reinterpret these filters as local measurements on locally extended Hilbert spaces. We give explicit constructions of a measurement-based implementation of these filters for $2 \otimes 2$ and $3 \otimes 3$ systems. This provides us with a physical mechanism to implement such local filters.

quant-ph↗

arXiv2014

Witnessing genuine multipartite entanglement with positive maps

We derive a general framework that connects every positive map with a corresponding witness for partial separability in multipartite quantum systems. We show that many previous approaches were intimately connected to the witnesses derived from partial transposition and that such criteria can easily be outperformed in higher dimensions by non-decomposable maps. As an exemplary case we present a witness that is capable of detecting genuine multipartite entanglement in bound entangled states.

quant-ph↗

arXiv2009

Application of Generalised sequential crossover of languages to generalised splicing

This paper outlines an application of iterated version of generalised sequential crossover of two languages (which in some sense, an abstraction of the crossover of chromosomes in living organisms) in studying some classes of the newly proposed generalised splicing ($GS$) over two languages. It is proved that, for $X,Y \in \{FIN, REG, LIN, CF, CS, RE \}, \sg \in FIN$, the subclass of generalized splicing languages namely $GS(X,Y,\sg)$, (which is a subclass of the class $GS(X,Y,FIN)$) is always regular.

cs.DM↗

arXiv2009

Generalised sequential crossover of words and languages

In this paper, we propose a new operation, Generalised Sequential Crossover (GSCO) of words, which in some sense an abstract model of crossing over of the chromosomes in the living organisms. We extend GSCO over language $L$ iteratively ($GSCO^*(L)$ as well as iterated GSCO over two languages $GSCO^*(L_1,L_2)$). Our study reveals that $GSCO^*(L)$ is subclass of regular languages for any $L$. We compare the different classes of GSCO languages with the prominent sub-regular classes.

cs.DM↗

arXiv2008

A proposal to a generalised splicing with a self assembly approach

Theory of splicing is an abstract model of the recombinant behaviour of DNAs. In a splicing system, two strings to be spliced are taken from the same set and the splicing rule is from another set. Here we propose a generalised splicing (GS) model with three components, two strings from two languages and a splicing rule from third component. We propose a generalised self assembly (GSA) of strings. Two strings $u_1xv_1$ and $u_2xv_2$ self assemble over $x$ and generate $u_1xv_2$ and $u_2xv_1$. We study the relationship between GS and GSA. We study some classes of generalised splicing languages with the help of generalised self assembly.

cs.DM↗