Are right angles special? The optimal primitive reference frame

Abstract

We consider the smallest possible directional reference frames allowed and determine the best one can ever do in preserving quantum information in various scenarios. We find that for the preservation of a single spin state, two orthogonal spins are optimal primitive reference frames, and in a product state do approximately 22% as well as an infinite-sized classical frame. By adding a small amount of entanglement to the reference frame this can be raised to 2(2/3)^5 = 26%. Under the different criterion of entanglement-preservation a very similar optimal reference frame is found, however this time for spins aligned at an optimal angle of 87 degrees. In this case 24% of the negativity is preserved. The classical limit is considered numerically, and indicates under the criterion of entanglement preservation, that 90 degrees is selected out non-monotonically, with a peak optimal angle of 96.5 degrees for L = 3 spins.

9 pages, 3 figures, v2 has minor corrections and elaborations, including an extra appendix. Published version

References in corpus (5)

• Reference frames, superselection rules, and quantum information
• Quantum communication using a bounded-size quantum reference frame
• Dynamics of a Quantum Reference Frame
• Optimal measurements for relative quantum information
• Dynamics of a quantum reference frame undergoing selective measurements and coherent interactions