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:1808.00294 · Physics Letters A

Construction of noisy bound entangled states and the range criterion

Saronath Halder, Ritabrata Sengupta

Published Apr 4, 2019• 20 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2019.04.003

Related papers

Unextendible product bases, bound entangled states, and the range criterion

Pratapaditya Bej, Saronath Halder

arXiv:2005.02108•Physics Letters A•Nov 5, 2020•14 citations

Non-full-rank bound entangled states satisfying the range criterion (6 pages)

Somshubhro Bandyopadhyay

Physical Review A•Jan 1, 2005•0 citations

Noisy bound entangled states: construction and their detection

Saronath Halder, Ritabrata Sengupta

It is known that bound entangled states are mixed entangled states from which no pure entanglement can be distilled by local operations and classical communication. This holds true even if large number of identical copies of the state are shared between spatially separated parties. In this work we consider bipartite {\it noisy} bound entangled states with positive partial transpose, that is, such a state can be written as a convex combination of a so-called edge state and a separable state ({\it noise}). Starting from a particular class of unextendible product bases (UPBs) we first show a systematic method to construct low-rank noisy bound entangled states which satisfy the range criterion. Next, we consider different classes of uncompletable product bases (UCPBs) to construct noisy bound entangled states. A subset of these bound entangled states has the property that they satisfy the range criterion. However, UCPBs are important to produce noisy bound entangled states and thus, the problem of constructing UCPBs from different classes of UPBs is also considered in this work. In each case explicit examples are constructed. In fact, present bound entangled states help us to learn about the robustness of edge states. We also discuss about the detection these states.

•Aug 1, 2018•0 citations

Maximally entangled states and the Bell inequality

Jose Luis Cereceda

arXiv:quant-ph/9812012•Physics Letters A•Mar 1, 1996•8 citations

Non-full-rank bound entangled states satisfying the range criterion

Somshubhro Bandyopadhyay, Sibasish Ghosh A, Vwani Roychowdhury

A systematic method for generating bound entangled states in any bipartite system, with ranks ranging from five to full rank, is presented. These states are constructed by mixing separable states with unextendable product basis--generated bound entangled states that are positive under partial transposition (PPT). A subset of this class of PPT bound entangled states, having less than full rank, is shown to satisfy the range criterion [P. Horodecki, Phys. Lett. A 232, 333 (1997)].

arXiv:quant-ph/0406023•Physical Review A•Jan 12, 2005•29 citations

Bound entangled states invariant underUx

Zhen Wang, Zhi‐Xi Wang

This paper obtains an entangled condition for isotropic-like states by using an atomic map. It constructs a class of bound entangled states from the entangled condition and shows that the partial transposition of the state from the constructed bound entangled class is an edge bound entangled state by using range criterion.

Chinese Physics B•Aug 1, 2008•0 citations
It is known that bound entangled states are mixed entangled states from which no pure entanglement can be distilled by local operations and classical communication. This holds true even if large number of identical copies of the state are shared between spatially separated parties. In this work we consider bipartite {\it noisy} bound entangled states with positive partial transpose, that is, such a state can be written as a convex combination of a so-called edge state and a separable state ({\it noise}). Starting from a particular class of unextendible product bases (UPBs) we first show a systematic method to construct low-rank noisy bound entangled states which satisfy the range criterion. Next, we consider different classes of uncompletable product bases (UCPBs) to construct noisy bound entangled states. A subset of these bound entangled states has the property that they satisfy the range criterion. However, UCPBs are important to produce noisy bound entangled states and thus, the problem of constructing UCPBs from different classes of UPBs is also considered in this work. In each case explicit examples are constructed. In fact, present bound entangled states help us to learn about the robustness of edge states. We also discuss about the detection these states.