Entanglement suppression, quantum statistics, and symmetries in spin-3/2 baryon scatterings

We explore the interplay among entanglement suppression, quantum statistics, and enhanced symmetries in the nonrelativistic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>S</a:mi> </a:math> -wave scattering involving the lowest-lying spin-3/2 baryons, which can be considered as four-dimensional qudits. These baryons form a ten-dimensional representation (decuplet) under the SU(3) light-flavor symmetry and, in this limit, are considered indistinguishable under strong interactions. Treating the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>S</b:mi> </b:math> matrix in the spin-3/2 baryon-baryon scattering as a quantum logic gate in the spin space, we study the consequence of entanglement suppression and compute the entanglement power of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>S</c:mi> </c:math> matrix. When the entanglement power vanishes, the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>S</d:mi> </d:math> matrix is either an Identity or a SWAP gate and spin-flavor symmetries and/or nonrelativistic conformal invariance emerge, as previously observed in spin-1/2 baryons. In the case of scattering identical particles, the entanglement power never vanishes due to constraints from spin statistics, which we interpret as projection-valued measurements onto symmetric or antisymmetric Hilbert space and define the entanglement power accordingly. When the entanglement power is nonvanishing but sits at a global or local minimum, enhanced symmetries still emerge and the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>S</e:mi> </e:math> matrix can be interpreted as an Identity or a SWAP gate acting on the restricted Hilbert space allowed by quantum statistics. In general, when scattering identical spin- <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>s</f:mi> </f:math> particles, we identify an enhanced <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>SU</g:mi> <g:msub> <g:mrow> <g:mo>(</g:mo> <g:mn>2</g:mn> <g:mi>s</g:mi> <g:mo>+</g:mo> <g:mn>1</g:mn> <g:mo>)</g:mo> </g:mrow> <g:mi>spin</g:mi> </g:msub> </g:mrow> </g:math> symmetry for the Identity gate.