Construction of PPT entangled state and its detection by using second-order moment of the partial transposition

Fuente: arXiv
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Main Authors: Kumar, Rohit, Adhikari, Satyabrata
Format: Preprint
Published: 2025
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author Kumar, Rohit
Adhikari, Satyabrata
author_facet Kumar, Rohit
Adhikari, Satyabrata
contents We adopt a formalism by which we construct and detect a new family of positive partial transpose entangled states in $d_1\otimes d_2$ dimensional system. Our detection method is based on the second order moment $p_2(ρ^{T_B})$ as it is very easy to calculate and may be realizable in laboratory. We show that if the second order moment $p_2(ρ^{T_B})$ in $d_1\otimes d_2$ dimensional system satisfy $p_2(ρ^{T_B})\leq\frac{1}{d_1 d_2-1}$, then the state is a PPT state. We also derive an equivalent condition on the bloch vector. Then, we construct a quantum state by considering the mixture of a separable and an entangled state and obtain a condition on the mixing parameter for which the mixture represents a PPTES. Finally, applying our results, we have shown that the distillable key rate of the private state, prepared through our prescription, is positive. It suggests that our result also has potential applications in quantum cryptography.
format Preprint
id arxiv_https___arxiv_org_abs_2509_06565
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Construction of PPT entangled state and its detection by using second-order moment of the partial transposition
Kumar, Rohit
Adhikari, Satyabrata
Quantum Physics
We adopt a formalism by which we construct and detect a new family of positive partial transpose entangled states in $d_1\otimes d_2$ dimensional system. Our detection method is based on the second order moment $p_2(ρ^{T_B})$ as it is very easy to calculate and may be realizable in laboratory. We show that if the second order moment $p_2(ρ^{T_B})$ in $d_1\otimes d_2$ dimensional system satisfy $p_2(ρ^{T_B})\leq\frac{1}{d_1 d_2-1}$, then the state is a PPT state. We also derive an equivalent condition on the bloch vector. Then, we construct a quantum state by considering the mixture of a separable and an entangled state and obtain a condition on the mixing parameter for which the mixture represents a PPTES. Finally, applying our results, we have shown that the distillable key rate of the private state, prepared through our prescription, is positive. It suggests that our result also has potential applications in quantum cryptography.
title Construction of PPT entangled state and its detection by using second-order moment of the partial transposition
topic Quantum Physics
url https://arxiv.org/abs/2509.06565