Strong quantum nonlocality for unextendible product bases in heterogeneous systems

@article{Shi2021StrongQN,
  title={Strong quantum nonlocality for unextendible product bases in heterogeneous systems},
  author={Fei Shi and Mao-Sheng Li and Lin Chen and Xiande Zhang},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={55}
}
A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. It is known that unextendible product bases (UPBs) can show the phenomenon of quantum nonlocality without entanglement. Thus it is interesting to investigate the strong quantum nonlocality for UPBs. Most of the UPBs with the minimum size cannot demonstrate strong quantum nonlocality. In this paper… 
Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
A set of orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement [Phys. Rev.
Strong quantum nonlocality in general multipartite quantum systems
The concept of strong quantum nonlocality is introduced by Halder et. al. in [Phys. Rev. Lett. 122, 040403 (2019)]. An orthogonal set of states in multipartite systems is called to be strong quantum
Strongly nonlocal unextendible product bases do exist
A set of multipartite orthogonal product states is locally irreducible, if it is not possible to eliminate one or more states from the set by orthogonality-preserving local measurements. An effective
Bounds on the smallest strong nonlocality set of multipartite quantum states
An orthogonal set of states in multipartite systems is called to be strong quantum nonlocality if it is locally irreducible under every bipartition of the subsystems [Phys. Rev. Lett. 122 , 040403
Unextendible and uncompletable product bases in every bipartition
Unextendible product basis is an important object in quantum information theory and features a broad spectrum of applications, ranging bound entangled states, quantum nonlocality without
Constructing unextendible product bases from multiqubit ones
The construction of multipartite unextendible product bases (UPBs) is a basic problem in quantum information. We respectively construct two families of 2× 2× 4 and 2× 2× 2× 4 UPBs of size eight by
Strong quantum nonlocality in $N$-partite systems
Fei Shi, ∗ Zuo Ye, † Lin Chen, 4, ‡ and Xiande Zhang § School of Cyber Security, University of Science and Technology of China, Hefei, 230026, People’s Republic of China School of Mathematical

References

SHOWING 1-10 OF 65 REFERENCES
Strong quantum nonlocality with entanglement
Strong quantum nonlocality was introduced recently as a stronger manifestation of nonlocality in multipartite systems through the notion of local irreducibility in all bipartitions. Known existing
Local distinguishability based genuinely quantum nonlocality without entanglement
Recently, Halder et al (2019 Phys. Rev. Lett. 122 040403) proposed the concept of strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems
Strongly nonlocal unextendible product bases do exist
A set of multipartite orthogonal product states is locally irreducible, if it is not possible to eliminate one or more states from the set by orthogonality-preserving local measurements. An effective
Strong Quantum Nonlocality without Entanglement.
TLDR
The first examples of orthogonal product bases on C=3, 4 that are locally irreducible in all bipartitions are provided, where the construction for d=3 achieves the minimum dimension necessary for such product states to exist.
Multipartite nonlocality without entanglement in many dimensions
TLDR
This is the first method to construct a product basis exhibiting nonlocality without entanglement with n parties each holding a system of dimension at least n-1 via a quantum circuit made of controlled discrete Fourier transform gates acting on the computational basis.
Several nonlocal sets of multipartite pure orthogonal product states
It is known that there exist sets of pure orthogonal product states which cannot be perfectly distinguished by local operations and classical communication (LOCC). Such sets are nonlocal sets which
Tight Bell inequalities with no quantum violation from qubit unextendible product bases
We investigate the relation between unextendible product bases (UPB) and Bell inequalities found recently in [R. Augusiak et al., Phys. Rev. Lett. 107, 070401 (2011)]. We first review the procedure
Unextendible product basis for fermionic systems
We discuss the concept of unextendible product basis (UPB) and generalized UPB for fermionic systems, using Slater determinants as an analogue of product states, in the anti-symmetric subspace ∧NCM.
Unextendible product bases and bound entanglement
An unextendible product basis( UPB) for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state. We give examples of UPBs, and
...
...