Abstract
For a generic n-qubit system, local invariants under the action of 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.
Highlights
Entanglement, perhaps the most bizarre feature of the quantum world [1, 2], plays a crucial role in quantum information processing and quantum computation [3, 4]
We consider two-qubit Yang–Baxter operators and show that their eigenvalues completely determine the non-local properties of the system
In this work we explore the possibility of simplifying this task by ‘creating’ quantum systems with braid operators built from Yang–Baxter operators (YBOs), i.e. operators that solve the Yang–Baxter equation
Summary
Entanglement, perhaps the most bizarre feature of the quantum world [1, 2], plays a crucial role in quantum information processing and quantum computation [3, 4]. When considering the action of the full generators, more constraints for the invariants may arise and the number could possibly decrease Combining this with the previous assertion that six is the lower bound of the number of invariants, we conclude that there are precisely six SL(2, C)⊗2 invariants (3.4) that one can construct out of the X-type operators. These six independent local invariants are spanned by the single linear invariant (I1) and the five quadratic invariants (I2,4, I2,5, I2,8, I2,9, I2,10) of (3.3). The relation between the two classifications is detailed in appendix A
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
