Quick Navigation

Overview Topics Abstract Importance Paper Tools References Reactions Discussion Publication Related

Topics

Open Quantum Systems Decoherence Quantum Simulation Entanglement Theory Quantum Correlations

Unextendible Product Basis for Fermionic Systems

arXiv
Authors: Jianxin Chen, Lin Chen, Bei Zeng

Year

2013

Paper ID

31410

Status

Preprint

Abstract Read

~2 min

Abstract Words

133

Citations

N/A

Abstract

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 antisymmetric subspace wedge^ N bCM. We construct an explicit example of generalized fermionic unextendible product basis (FUPB) of minimum cardinality N(M-N)+1 for any Nge2,Mge4. We also show that any bipartite antisymmetric space wedge^ 2 bCM of codimension two is spanned by Slater determinants, and the spaces of higher codimension may not be spanned by Slater determinants. Furthermore, we construct an example of complex FUPB of N=2,M=4 with minimum cardinality 5. In contrast, we show that a real FUPB does not exist for N=2,M=4 . Finally we provide a systematic construction for FUPBs of higher dimensions using FUPBs and UPBs of lower dimensions.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2013 reference point for readers tracking recent quantum research.
  • 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...

Paper Tools

Become a member to use research tools

Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.

Become a member Sign in
Show Paper arXiv Publisher Share Cite This Paper Copy URL Compare Copy DOI Add to Reading List Category Correction Request

References & Citation Signals

[1] DOI https://doi.org/arXiv:1312.4218 [2] arXiv https://arxiv.org/abs/1312.4218 [3] Publisher https://arxiv.org/abs/1312.4218

Local Citation Graph (Related-Paper Links)

Current Paper #31410 #73579 QR-SPPS: Quantum-Native Retail ... #73578 Intelligence-Guided Adaptive Pu... #73576 Number Fluctuations and Entangl... #73571 Gaussian Reformulation of the F...

External citation index: OpenAlex citation signal

Community Reactions

Quick sentiment from readers on this paper.

Score: 0
Likes: 0 Dislikes: 0

Sign in to react to this paper.

Discussion & Reviews (Moderated)

Average Rating: 0.0 / 5 (0 ratings)

No written reviews yet.