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LOCATION:ICFO Auditorium and Online (Teams)
SUMMARY:ICFO | ZAHRA RAISSI
CLASS:PUBLIC
DESCRIPTION:PhD Thesis Defense\nZAHRA RAISSI\nQuantum Information TheoryICF
 O-The Institute of Photonic Sciences\n&nbsp\;\nStudying entanglement is es
 sential for our understanding of such diverse areas as quantum optics\, co
 ndensed matter physics and even high energy physics. Moreover\, entangleme
 nt allows us to surpass classical physics and technologies enabling better
  information processing\, computation\, and improved metrology. It was rec
 ently discovered that entanglement plays a prominent role in characterizin
 g and simulating quantum many-body states and in this way deepened our und
 erstanding of quantum matter. While bipartite pure entangled states are we
 ll understood\, multipartite entanglement is much richer and leads to stro
 nger contradictions with classical physics. Among all possible entangled s
 tates\, a special class of states has attracted attention for a wide range
  of tasks. These states are called k-uniform states and are pure multipart
 ite quantum states of n parties and local dimension q with the property th
 at all of their reductions to k parties are maximally mixed. Operationally
 \, in a k-uniform state any subset of at most k parties is maximally entan
 gled with the rest. The k = [n/2]-uniform states are called absolutely max
 imally entangled because they are maximally entangled along any splitting 
 of the n parties into two groups. These states find applications in severa
 l protocols and\, in particular\, are the building blocks of quantum error
  correcting codes with a holographic geometry\, which has provided valuabl
 e insight into the connections between quantum information theory and conf
 ormal field theory. Their properties and the applications are\, however\, 
 intriguing\, as we know little about them: when they exist\, how to constr
 uct them\, how they relate to other multipartite entangled states\, such a
 s graph states\, or how they connect under local operations and classical 
 communication.\nWith this motivation in mind\, in this thesis we first stu
 dy the properties of k-uniform states and then present systematic methods 
 to construct closed-form expressions of them. The nature of our methods pr
 oves to be particularly fruitful in understanding the structure of these q
 uantum states\, their graph-state representation and classification under 
 local operations and classical communication. We also construct several ex
 amples of absolutely maximally entangled states\, whose existence was a su
 bject of an open question. Finally\, we explore a new family of quantum er
 ror correcting codes that generalize and improve the link between classica
 l error correcting codes\, multipartite entangled states\, and the stabili
 zer formalism.\nThe results of this thesis can have a role in characterizi
 ng and studying the following three topics: multipartite entanglement\, cl
 assical error correcting codes and quantum error correcting codes. The mul
 tipartite entangled states can provide a link to find different resources 
 for quantum information processing tasks and quantify entanglement. Constr
 ucting two sets of highly entangled multipartite states\, it is important 
 to know if they are equivalent under local operations and classical commun
 ication. By understanding which states belong to the same class of quantum
  resource\, one may discuss the role they play in some certain quantum inf
 ormation tasks like quantum key distribution\, teleportation and construct
 ing optimum quantum error correcting codes. They can also be used to explo
 re the connection between the Antide Sitter/Conformal Field Theory hologra
 phic correspondence and quantum error correction\, which will then allow u
 s to construct better quantum error correcting codes. At the same time the
 ir roles in the characterization of quantum networks will be essential to 
 design functional networks\, robust against losses and local noise.
DTSTAMP:20260429T163848Z
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