Theory Seminar: What parts of a quantum state tell about the whole

Nikolai Wyderka (Uni Siegen)
Correlations in quantum states have to obey restrictions from the underlying quantum theory, such as positivity or purity

July 16, 2019

Nikolai Wyderka (Uni Siegen)
Special Theory Group Seminar, Herbert-Walther Lecture Hall G0.25
Tue, 16. July 2019, 11:30 am

Abstract:

Correlations in quantum states have to obey restrictions from the underlying quantum theory, such as positivity or purity. These restrictions give rise to an abundance of interesting quantum features, like monogamy of entanglement or the existence of absolutely maximally entangled states. On the other hand, they allow to infer many properties of the whole state from knowledge of subsets of the correlations only. For example, whether or not a state is uniquely determined by its low-body correlations is directly connected to the question of whether or not it is the unique ground state of a local Hamiltonian.

In this talk I will discuss some instances of this uniqueness problem, more formally known as the marginal problem, in the case of multi-qubit systems. Furthermore, I will formulate positivity constraints for a certain type of LU-invariants, known as sector lengths, and will discuss their relation to entanglement and entropic strong subadditivity.


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