Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1403.7025 · Physical Review A

Nonexistence of entangled continuous-variable Werner states with positive partial transpose

Daniel McNulty, Richard Tatham, Ladislav Mišta

Published Mar 12, 2014• 4 citations
arXivHTMLPDF

Abstract

Analytical calculations show that positive-partial-transpose continuous-variable entangled Werner states do not to exist and sophisticated non-Gaussian measurements, distinct from photon counting, to optimally extract nonclassical correlations are constructed.
DOI
10.1103/physreva.89.032315

Related papers

Nonclassical correlations in continuous-variable non-Gaussian Werner states

Richard Tatham, Ladislav Mišta, Gerardo Adesso +1 more

We study nonclassical correlations beyond entanglement in a family of two-mode non-Gaussian states which represent the continuous-variable counterpart of two-qubit Werner states. We evaluate quantum discord and other quantumness measures obtaining exact analytical results in special instances, and upper and lower bounds in the general case. Non-Gaussian measurements such as photon counting are in general necessary to solve the optimization in the definition of quantum discord, whereas Gaussian measurements are strictly suboptimal for the considered states. The gap between Gaussian and optimal non-Gaussian conditional entropy is found to be proportional to a measure of non-Gaussianity in the regime of low squeezing, for a subclass of continuous-variable Werner states. We further study an example of a non-Gaussian state which is positive under partial transposition, and whose nonclassical correlations stay finite and small even for infinite squeezing. Our results pave the way to a systematic exploration of the interplay between nonclassicality and non-Gaussianity in continuous-variable systems, in order to gain a deeper understanding of---and to draw a bigger advantage from---these two important resources for quantum technology.

arXiv:1111.1101•Physical Review A•Feb 21, 2012•36 citations

Detecting strongly non-Gaussian entanglement

Serge Deside, Tobias Haas, Nicolas J. Cerf

Efficiently certifying non-Gaussian entanglement in continuous-variable quantum systems is a central challenge for advancing quantum information processing, photonic quantum computing, and metrology. Here, we put forward continuous-variable counterparts to the recently introduced entanglement criteria based on moments of the partially transposed state, together with simple readout schemes that require only a few replicas of the state, passive linear optics, and particle-number measurements. We develop a multicopy method that enables the detection of strongly non-Gaussian entanglement for various relevant state families overlooked by standard approaches, which include the entire class of NOON states. Further, it is robust against realistic experimental constraints (losses, noise, and finite statistics), which we demonstrate by extensive numerical simulations.

arXiv:2504.15831•Physical Review Research•Apr 2, 2026•0 citations

A problem of existence of bound entangled states with non-positive partial transpose and the Hilbert's 17th problem

Tohya Hiroshima

It is found that the problem of existence of bound entangled states with non-positive partial transpose (NPPT) has the intriguing relation to the Hilbert's 17th problem. More precisely, we compute the expectation value of the partially transposed Werner states by Schmidt rank-2 vectors for NPPT and 1-copy undistillable region. It is the positive polynomial but shown not to be expressed as the sum of squares of polynomials. A remedy for such pathological behavior as well as a similar but different approach to the problem is also mentioned.

arXiv:1007.1830•Jul 12, 2010•0 citations

A solution to 2-copy distillability of Werner states

Jinshi Fu, Li Gao, Sang-Jun Park

Entanglement distillation is a fundamental task in quantum information theory. In this work, we prove that Werner states in arbitrary dimension are $2$-copy distillable if and only if they are $1$-copy distillable. This answers the longstanding open question of the $2$-copy distillability of Werner states. This is an important step on determining whether every non-positive partial transpose (NPT) state is distillable, which remains one of the central open problems in the field of entanglement distillation.

quant-pharXiv:2607.21367•Jul 24, 2026•0 citations

Nonclassicality and entanglement: observable conditions

W. Vogel, Evgeny V Shchukin

A unified characterization of continuous-variable quantum states is presented that gives general insight in their nonclassical features and, in particular, in their entanglement properties. Nonclassicality is characterized in terms of observable characteristic functions. Equivalently, the nonclassicality conditions are reformulated in terms of moments. The latter approach turns out to be a powerful tool for deriving a complete set of entanglement conditions for bipartite quantum systems, which are fully equivalent to the nonpositivity of the partially transposed density operator. The possibilities of observing the needed moments by balanced homodyne correlation measurements are analyzed.

Journal of Physics Conference Series•Oct 1, 2007•2 citations

Non-Gaussian Entanglement and Wigner Function

Mustapha Ziane, M. El Baz

A measure of non-Gaussian entanglement in continuous variable (CV) systems based on the volume of the negative part of the Wigner function is proposed. We analyze comparatively this quantity with a numerical evaluation of the negativity of the partial transpose (NPT) considering a system of Bell states formed in the coherent state basis (quasi-Bell states).

IntechOpen eBooks•Oct 30, 2019•1 citation
We study nonclassical correlations beyond entanglement in a family of two-mode non-Gaussian states which represent the continuous-variable counterpart of two-qubit Werner states. We evaluate quantum discord and other quantumness measures obtaining exact analytical results in special instances, and upper and lower bounds in the general case. Non-Gaussian measurements such as photon counting are in general necessary to solve the optimization in the definition of quantum discord, whereas Gaussian measurements are strictly suboptimal for the considered states. The gap between Gaussian and optimal non-Gaussian conditional entropy is found to be proportional to a measure of non-Gaussianity in the regime of low squeezing, for a subclass of continuous-variable Werner states. We further study an example of a non-Gaussian state which is positive under partial transposition, and whose nonclassical correlations stay finite and small even for infinite squeezing. Our results pave the way to a systematic exploration of the interplay between nonclassicality and non-Gaussianity in continuous-variable systems, in order to gain a deeper understanding of---and to draw a bigger advantage from---these two important resources for quantum technology.
Efficiently certifying non-Gaussian entanglement in continuous-variable quantum systems is a central challenge for advancing quantum information processing, photonic quantum computing, and metrology. Here, we put forward continuous-variable counterparts to the recently introduced entanglement criteria based on moments of the partially transposed state, together with simple readout schemes that require only a few replicas of the state, passive linear optics, and particle-number measurements. We develop a multicopy method that enables the detection of strongly non-Gaussian entanglement for various relevant state families overlooked by standard approaches, which include the entire class of NOON states. Further, it is robust against realistic experimental constraints (losses, noise, and finite statistics), which we demonstrate by extensive numerical simulations.
It is found that the problem of existence of bound entangled states with non-positive partial transpose (NPPT) has the intriguing relation to the Hilbert's 17th problem. More precisely, we compute the expectation value of the partially transposed Werner states by Schmidt rank-2 vectors for NPPT and 1-copy undistillable region. It is the positive polynomial but shown not to be expressed as the sum of squares of polynomials. A remedy for such pathological behavior as well as a similar but different approach to the problem is also mentioned.
Entanglement distillation is a fundamental task in quantum information theory. In this work, we prove that Werner states in arbitrary dimension are 222-copy distillable if and only if they are 111-copy distillable. This answers the longstanding open question of the 222-copy distillability of Werner states. This is an important step on determining whether every non-positive partial transpose (NPT) state is distillable, which remains one of the central open problems in the field of entanglement distillation.
A unified characterization of continuous-variable quantum states is presented that gives general insight in their nonclassical features and, in particular, in their entanglement properties. Nonclassicality is characterized in terms of observable characteristic functions. Equivalently, the nonclassicality conditions are reformulated in terms of moments. The latter approach turns out to be a powerful tool for deriving a complete set of entanglement conditions for bipartite quantum systems, which are fully equivalent to the nonpositivity of the partially transposed density operator. The possibilities of observing the needed moments by balanced homodyne correlation measurements are analyzed.