Entanglement suppression and emergent symmetry

Tao-Ran Hu, Katsuyoshi Sone, Feng-Kun Guo +2 more

We explore the interplay among entanglement suppression, quantum statistics, and enhanced symmetries in the nonrelativistic S -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 S 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 S matrix. When the entanglement power vanishes, the S 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 S 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- s particles, we identify an enhanced SU ( 2 s + 1 ) spin symmetry for the Identity gate.

Navin McGinnis

We present a general framework connecting global symmetries to the relativistic $S$-matrix through the lens of quantum information theory. Analyzing the 2-to-2 scattering of particles of any helicity, we systematically characterize relativistic scattering amplitudes as quantum gates in the bipartite space of states with a discrete quantum number. This formalism naturally recovers and significantly extends previous results on entanglement suppression of the $S$-matrix, providing a comprehensive approach for studying the emergence of symmetries from an information-theoretic perspective. As a central result, we show that constraining the $S$-matrix to the span of minimally entangling operators is equivalent to realizing an emergent $SU(N)$ global symmetry.

Luis de la Peña, Ana Marı́a Cetto, Andrea Valdés Hernández

Sooryansh Asthana, Sai Vinjanampathy

Quantum illumination provides a quantum advantage in detecting weakly reflecting objects embedded in a noisy environment, even when environmental noise destroys most of the initial entanglement. We investigate this advantage using Haar-random probe states constrained to symmetry-resolved subspaces. Employing tools from quantum channel discrimination and asymptotic hypothesis testing, we derive the discrimination exponents associated with Haar-random probe ensembles and identify the role of symmetry in determining their performance. We show that typical states drawn from fixed-charge sectors achieve the same asymptotic quantum-illumination advantage as maximally entangled probes. In particular, we show that the effective thermal-noise suppression and the corresponding Chernoff exponent are governed by the dimension of the accessible symmetry sector. Our results reveal that the operational resource underlying quantum illumination can be generalized from fine-tuned structure of a specific probe state to the existence of a large symmetry-protected correlation subspace. These findings establish a direct connection between quantum illumination, symmetry-resolved typicality, and quantum channel discrimination, and demonstrate that near-optimal quantum hypothesis testing resources can emerge naturally from generic many-body quantum states constrained by conservation laws.

Katsuyoshi Sone, Tao-Ran Hu, Feng-Kun Guo +2 more

We study entanglement suppression in $s$-wave $ΩΩ$ scattering, where each baryon has spin $3/2$. By treating the $S$-matrix as a quantum operator acting on the spin states, we quantify its ability to generate entanglement and identify the conditions on the phase shifts of the spin channels that minimize entanglement generation in the system. In $ΩΩ$ scattering, only antisymmetric spin channels are allowed due to Fermi-Dirac statistics. Applying the entanglement-suppression framework to $ΩΩ$ scattering, we find two solutions for the phase shifts: one leading to a spin SU(4) symmetry and the other to a nonrelativistic conformal symmetry. We show that the solution associated with the nonrelativistic conformal symmetry originates from the specific structure of the Clebsch-Gordan coefficients in the $3/2 \otimes 3/2$ system.