2020/10/31 by Pramod Padmanabhan, Fumihiko Sugino, Diego Trancanelli
Computer Science · Mathematics · Physics and Astronomy · #Action (physics) #Algebra over a field #Eigenvalues and eigenvectors #Link (geometry) #Power (physics) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum system #Spectral Theory in Mathematical Physics #Spectral properties #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8121/abdfe9
published as J. Phys. A: Math. Theor. 54 135301 2021 · 43 pages, Published version
openalex created_date 2020/10/08 · openalex publication_date 2021/01/26 · arxiv created 2021/03/15 · arxiv updated 2021/03/16 · openalex updated_date 2026/08/05
Abstract For a generic n -qubit system, local invariants under the action of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>S</mml:mi> <mml:mi>L</mml:mi> <mml:msup> <mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mo>⊗</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> </mml:math> characterize non-local properties of entanglement. In general, such properties are not immediately apparent and hard to construct. Here we consider two-qubit Yang–Baxter operators and show that their eigenvalues completely determine the non-local properties of the system. Moreover, we apply the Turaev procedure to these operators and obtain their associated link/knot polynomials. We also compute their entangling power and compare it with that of a generic two-qubit operator.