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FM: Fall Meeting

FM 11: Entanglement: Many-Body States I

FM 11.1: Invited Talk

Montag, 23. September 2019, 14:00–14:30, 2004

Correlations in many-body states: The simplest constraints for their distribution — •Jens Siewert — University of the Basque Country UPV/EHU, 48080 Bilbao, Spain — IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain

It has long been known that correlations in many-body systems cannot be freely distributed. Correspondingly, not all choices of reduced states (the marginals) are compatible with a joint global state of the system. This difficulty is known as the quantum marginal problem. In solid-state physics and quantum chemistry problems of this kind were discussed in the context of ‘N-representability’, whereas in quantum information the term ‘monogamy of entanglement’ (and other correlations) was coined.

Surprisingly, this problem is not completely solved even in the simplest of its variants, the existence of so-called absolutely maximally entangled states of N distinguishible quantum systems, each of which has d levels. However, substantial progress in this field was achieved recently by analyzing the Bloch representation of quantum states: This representation corresponds to an expansion of an N-party density matrix into all its k-particle correlations (k N). The simplest correlation quantifiers based on this are the k-sector lengths. By using these tools, constraints for the distribution of correlations viz. sector lengths can be derived systematically and transparently. They may also be viewed as monogamy relations for entanglement as well as, e.g., inequalities for the linear entropy or conditions for the existence of quantum error correcting codes.