April 2021

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Author:
Otfried Gühne
Body:

The quantum marginal problem

Clarifying the relation between the whole and its parts
is crucial for many problems in science. In quantum
mechanics, this question manifests itself in the quantum
marginal problem, which asks whether there is a global pure
quantum state for some given marginals. This problem arises
in many contexts, ranging from quantum chemistry to entanglement
theory and quantum error correcting codes.

In this talk I will first present an introduction into
this problem and its applications. Then, I will discuss
the problem of absolutely maximally entangled states as
a special instance. Finally, I will prove a correspondence
of the marginal problem to the separability problem. Based
on this, I describe a sequence of semidefinite programs
which can decide whether some given marginals are compatible
with some pure global quantum state. As an application, I
prove that the existence of multi-particle absolutely
maximally entangled states for a given dimension is
equivalent to the separability of an explicitly given
two-party quantum state.

----------------------------
Reference:
X.-D. Yu, T. Simnacher, N. Wyderka, H. C. Nguyen, O. Gühne,
A complete hierarchy for the pure state marginal problem in
quantum mechanics
Nature Communications 12, 1012 (2021).

 
 
 
 
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Author:
Barbara Kraus
Body:

In this talk I will discuss several protocols designed for the verification and the characterization of quantum devices. In the first part of the talk I will focus on the purely classical verification of the output of a quantum computer and will present a minimal example for realizing such a verification protocol with current technology. In the second part I present experimentally accessible conditions for detecting entanglement
in mixed states. These conditions are based on the moments of the partial transposed density operator, which can be measured via local random measurements on single state copies (classical shadows).

Ref:

J. Carrasco, A. Elben, Ch. Kokail, B. K., and P. Zoller (PRX Quantum 2021)
J. Carrasco, A. Elben, A. Neven, R. Kueng, B. Vermesch, V. Vitale, P. Calabrese, M. Dalmonte, B. K., P. Zoller, (2021)
A. Elben, R. Kueng, H.-Y. Huang, R. van Bijnen, Ch. Kokail, M. Dalmonte, P. Calabrese, B.K., J. Preskill, P. Zoller, B. Vermersch, PRL (19)

 

 
 
 
 
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TBA
Author:
Sergio Boixo
Body:

TBA

 
 
 
 
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