Characterizing Entanglement and Quantum Correlations Constrained by Symmetry

Alexander Streltsov

Leonardo A. Lessa, Meng Cheng, Chong Wang

Quantum entanglement measures of many-body states have been increasingly useful to characterize phases of matter. Here, we explore a surprising connection between mixed-state entanglement and ’t Hooft anomaly. More specifically, we consider lattice systems in d space dimensions with anomalous symmetry G where the anomaly is characterized by an invariant in the group cohomology H d + 2 [ G , U ( 1 ) ] . We show that any mixed state ρ that is strongly symmetric under G , in the sense that G ρ ∝ ρ is necessarily ( d + 2 )-nonseparable, i.e., is not the mixture of tensor products of d + 2 states in the Hilbert space. Furthermore, such states cannot be prepared from any ( d + 2 )-separable states using finite-depth local quantum channels, so the nonseparability is long-ranged in nature. We provide proof of these results in d ≤ 1 and plausibility arguments in d > 1 . The anomaly-nonseparability connection, thus, allows us to generate simple examples of mixed states with nontrivial long-ranged multipartite entanglement. In particular, in d = 1 we find an example of quantum phase, in the sense that states in this phase cannot be two-way connected to any pure state through finite-depth local quantum channels. We also analyze a mixed anomaly involving both strong and weak symmetries, including systems constrained by the Lieb-Schultz-Mattis type of anomaly. We find that, while strong-weak mixed anomaly, in general, does not constrain quantum entanglement, it does constrain long-range correlations of mixed states in nontrivial ways. Namely, such states are not symmetrically invertible and not gapped Markovian, generalizing familiar properties of anomalous pure states.

Alexander Streltsov

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.

Marek Kuś

Kiara Hansenne, Zhen‐Peng Xu, Tristan Kraft +1 more

Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress of the field, but so far only results for small basic network structures or pure quantum states are known. Here we show that symmetries provide a versatile tool for the analysis of correlations in quantum networks. We provide an analytical approach to characterize correlations in large network structures with arbitrary topologies. As examples, we show that entangled quantum states with a bosonic or fermionic symmetry can not be generated in networks; moreover, cluster and graph states are not accessible. Our methods can be used to design certification methods for the functionality of specific links in a network and have implications for the design of future network structures.