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

Physical Review A

Impossibility of cloning entangled states under stochastic local operation and classical communication

Xuan Wang

Published Mar 21, 2014• 2 citations
Publisher

Abstract

This paper shows that we cannot clone a given entangled state of a bipartite system with stochastic local operation and classical communication (SLOCC). It is well known that we cannot create entanglement from scratch under SLOCC; an interesting interpretation of our work implies that even with another entangled state being a catalyst, we cannot realize such a process either.

DOI
10.1103/physreva.89.034302

Related papers

Bound entangled states provide overall convertibility of pure entangled states

Satoshi Ishizaka

I show that two distant parties can transform a single copy of their pure entangled state to arbitrary pure state by stochastic local operations and classical communication (SLOCC), if they share a single copy of bound entangled states. It has been known that this entanglement processing is impossible by SLOCC alone. This is the first example of the effect of bound entangled states on the entanglement processing for bipartite pure states. Further, I obtain the optimal attainable probability for several classes of states.

•Mar 2, 2004•3 citations

Stochastic local operations with classical communication of absolutely maximally entangled states

Adam Burchardt, Zahra Raissi

Absolutely maximally entangled (AME) states are maximally entangled for every bipartition of the system. They are crucial resources for various quantum information protocols. We present techniques for verifying that two AME states are equivalent concerning stochastic local operations and classical communication (SLOCC). The conjecture that for a given multipartite quantum system all AME states are SLOCC equivalent is proven false. We also show that the existence of AME states with minimal support of six or more particles results in the existence of infinitely many such non-SLOCC-equivalent states. Moreover, we present AME states which are not SLOCC equivalent to the existing AME states with minimal support.

arXiv:2003.13639•Physical Review A•Aug 19, 2020•21 citations

Bound Entanglement Provides Convertibility of Pure Entangled States

Satoshi Ishizaka

I show that two distant parties can transform pure entangled states to arbitrary pure states by stochastic local operations and classical communication (SLOCC) at the single copy level, if they share bound entangled states. This is the effect of bound entanglement since this entanglement processing is impossible by SLOCC alone. A similar effect of bound entanglement exists in three qubits where two incomparable entangled states of GHZ (Greenberger, Horne, and Zeilinger) and W can be interconverted. In general, multipartite settings composed by N distant parties, all N-partite pure entangled states are interconvertible by SLOCC with the assistance of bound entangled states with positive partial transpose.

arXiv:quant-ph/0403016•Physical Review Letters•Nov 1, 2004•54 citations

Stochastic local operations and classical communication invariant and the residual entanglement for n qubits

Dafa Li, Xiangrong Li, Hongtao Huang +1 more

We find an invariant for $n$ qubits and propose residual entanglement for $n$ qubits by means of the invariant. Thus, we establish a relation between stochastic local operations and classical communication (SLOCC) entanglement and residual entanglement. Invariant and residual entanglement can be used for SLOCC entanglement classification of $n$ qubits.

arXiv:0704.2087•Physical Review A•Sep 5, 2007•31 citations

MULTIPARTITE ENTANGLEMENT UNDER STOCHASTIC LOCAL OPERATIONS AND CLASSICAL COMMUNICATION

Akimasa Miyake

Stochastic local operations and classical communication (SLOCC), also called local filtering operations, are a convenient, useful set of quantum operations in grasping essential properties of entanglement. We give a quick overview of the characteristics of multipartite entanglement in terms of SLOCC, illustrating the 2-qubit and the rest (2×2×n) quantum system. This not only includes celebrated results of 3-qubit pure states, but also has implications to 2-qubit mixed states.

arXiv:quant-ph/0401023•International Journal of Quantum Information•Mar 1, 2004•27 citations

Entanglement classification of four-partite states under the SLOCC

S. M. Zangi, Junli Li, Cong‐Feng Qiao

Abstract We present a practical classification scheme for the four-partite entangled states under stochastic local operations and classical communication (SLOCC). By transforming a four-partite state into a triple-state set composed of two tripartite states and a bipartite state, the entanglement classification is reduced to the classification of tripartite and bipartite entanglements. This reduction method has the merit of involving only the linear constrains, and meanwhile provides an insight into the entanglement character of the subsystems.

arXiv:1701.04155•Journal of Physics A Mathematical and Theoretical•Jun 19, 2017•19 citations
This paper shows that we cannot clone a given entangled state of a bipartite system with stochastic local operation and classical communication (SLOCC). It is well known that we cannot create entanglement from scratch under SLOCC; an interesting interpretation of our work implies that even with another entangled state being a catalyst, we cannot realize such a process either.
I show that two distant parties can transform a single copy of their pure entangled state to arbitrary pure state by stochastic local operations and classical communication (SLOCC), if they share a single copy of bound entangled states. It has been known that this entanglement processing is impossible by SLOCC alone. This is the first example of the effect of bound entangled states on the entanglement processing for bipartite pure states. Further, I obtain the optimal attainable probability for several classes of states.
Absolutely maximally entangled (AME) states are maximally entangled for every bipartition of the system. They are crucial resources for various quantum information protocols. We present techniques for verifying that two AME states are equivalent concerning stochastic local operations and classical communication (SLOCC). The conjecture that for a given multipartite quantum system all AME states are SLOCC equivalent is proven false. We also show that the existence of AME states with minimal support of six or more particles results in the existence of infinitely many such non-SLOCC-equivalent states. Moreover, we present AME states which are not SLOCC equivalent to the existing AME states with minimal support.
I show that two distant parties can transform pure entangled states to arbitrary pure states by stochastic local operations and classical communication (SLOCC) at the single copy level, if they share bound entangled states. This is the effect of bound entanglement since this entanglement processing is impossible by SLOCC alone. A similar effect of bound entanglement exists in three qubits where two incomparable entangled states of GHZ (Greenberger, Horne, and Zeilinger) and W can be interconverted. In general, multipartite settings composed by N distant parties, all N-partite pure entangled states are interconvertible by SLOCC with the assistance of bound entangled states with positive partial transpose.
We find an invariant for nnn qubits and propose residual entanglement for nnn qubits by means of the invariant. Thus, we establish a relation between stochastic local operations and classical communication (SLOCC) entanglement and residual entanglement. Invariant and residual entanglement can be used for SLOCC entanglement classification of nnn qubits.
Abstract We present a practical classification scheme for the four-partite entangled states under stochastic local operations and classical communication (SLOCC). By transforming a four-partite state into a triple-state set composed of two tripartite states and a bipartite state, the entanglement classification is reduced to the classification of tripartite and bipartite entanglements. This reduction method has the merit of involving only the linear constrains, and meanwhile provides an insight into the entanglement character of the subsystems.