Most applications in quantum information processing make either explicit or implicit use of entanglement. It is thus important to have a good understanding of entanglement and the role it plays in these protocols. However, especially when it comes to multipartite entanglement, there still remain a lot of mysteries. This thesis is devoted to getting a better understanding of multipartite entanglement, and its role in various quantum information protocols.\n\nFirst, we investigate transformations between multipartite entangled states that only use local operations and classical communication (LOCC). We mostly focus on three qubit states in the GHZ class, and derive upper and lower bounds for the successful transformation probability between two states.\n\nWe then focus on absolutely maximally entangled (AME) states, which are highly entangled multipartite states that have the property that they are maximally entangled for any bipartition. With them as a resource, we develop new parallel teleportation protocols, which can then be used to implement quantum secret sharing (QSS) schemes. We further prove the existence of AME states for any number of parties, if the dimension of the involved quantum systems is chosen appropriately. An equivalence between threshold QSS schemes and AME states shared between an even number of parties is established, and further protocols are designed, such as constructing ramp QSS schemes and open-destination teleportation protocols with AME states as a resource.\n\nAs a framework to work with AME states, graph states are explored. They allow for efficient bipartite entanglement verification, which makes them a promising candidate for the description of AME states. We show that for all currently known AME states, absolutely maximally entangled graph states can be found, and we were even able to use graph states to find a new AME state for seven three-dimensional systems (qutrits). In addition, the implementation of QSS schemes from AME states can be conveniently described within the graph state formalism.\n\nFinally, we use the insight gained from entanglement in QSS schemes to derive necessary and sufficient conditions for quantum erasure channel and quantum error correction codes that satisfy the quantum Singleton bound, as these codes are closely related to ramp QSS schemes. This provides us with a very intuitive approach to codes for the quantum erasure channel, purely based on the entanglement required to protect information against losses by use of the parallel teleportation protocol.Most applications in quantum information processing make either explicit or implicit use of entanglement. It is thus important to have a good understanding of entanglement and the role it plays in these protocols. However, especially when it comes to multipartite entanglement, there still remain a lot of mysteries. This thesis is devoted to getting a better understanding of multipartite entanglement, and its role in various quantum information protocols.\n\nFirst, we investigate transformations between multipartite entangled states that only use local operations and classical communication (LOCC). We mostly focus on three qubit states in the GHZ class, and derive upper and lower bounds for the successful transformation probability between two states.\n\nWe then focus on absolutely maximally entangled (AME) states, which are highly entangled multipartite states that have the property that they are maximally entangled for any bipartition. With them as a resource, we develop new parallel teleportation protocols, which can then be used to implement quantum secret sharing (QSS) schemes. We further prove the existence of AME states for any number of parties, if the dimension of the involved quantum systems is chosen appropriately. An equivalence between threshold QSS schemes and AME states shared between an even number of parties is established, and further protocols are designed, such as constructing ramp QSS schemes and open-destination teleportation protocols with AME states as a resource.\n\nAs a framework to work with AME states, graph states are explored. They allow for efficient bipartite entanglement verification, which makes them a promising candidate for the description of AME states. We show that for all currently known AME states, absolutely maximally entangled graph states can be found, and we were even able to use graph states to find a new AME state for seven three-dimensional systems (qutrits). In addition, the implementation of QSS schemes from AME states can be conveniently described within the graph state formalism.\n\nFinally, we use the insight gained from entanglement in QSS schemes to derive necessary and sufficient conditions for quantum erasure channel and quantum error correction codes that satisfy the quantum Singleton bound, as these codes are closely related to ramp QSS schemes. This provides us with a very intuitive approach to codes for the quantum erasure channel, purely based on the entanglement required to protect information against losses by use of the parallel teleportation protocol.

Mar 27, 20143 citations

Access structure in graphs in high dimension and application to secret sharing

Anne Marin, Damian Markham, Simon Perdrix

We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension $q$ , as well as explicit decoding operations for quantum secret sharing based on graph state protocols. We give a lower bound on $k$ for the existence of a $((k,n))_q$ scheme and prove, using probabilistic methods, that there exists $α$ such that a random multigraph has an accessing parameter $k\leq αn$ with high probability.We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension $q$, as well as explicit decoding operations for quantum secret sharing based on graph state protocols. We give a lower bound on $k$ for the existence of a $((k,n))_q$ scheme and prove, using probabilistic methods, that there exists $α$ such that a random multigraph has an accessing parameter $k\leq αn$ with high probability.

arXiv:1304.7105Apr 26, 20136 citations

Experimental demonstration of graph-state quantum secret sharing

Bryn A. Bell, Damian Markham, David A. Herrera-Martí +4 more

arXiv:1411.5827Nature CommunicationsNov 21, 2014165 citations

Access Structure in Graphs in High Dimension and Application to Secret Sharing

Anne Marin, Damian Markham, Simon Perdrix

We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension q, as well as explicit decoding operations for quantum secret sharing based on graph state protocols. We give a lower bound on $k$ for the existence of a ((k,n))_q scheme and prove, using probabilistic methods, that there exists alpha such that a random multigraph has an accessing parameter k => alpha*n with high probability.We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension q, as well as explicit decoding operations for quantum secret sharing based on graph state protocols. We give a lower bound on $k$ for the existence of a ((k,n))_q scheme and prove, using probabilistic methods, that there exists alpha such that a random multigraph has an accessing parameter k => alpha*n with high probability.

Leibniz international proceedings in informaticsJan 1, 20130 citations

Quantum secret sharing with continuous variable graph state

Yadong Wu, Runze Cai, Guangqiang He +1 more

arXiv:1304.4477Quantum Information ProcessingDec 16, 201316 citations

We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension

q

, as well as explicit decoding operations for quantum secret sharing based on graph state protocols. We give a lower bound on

k

for the existence of a

((k,n))_q

scheme and prove, using probabilistic methods, that there exists

α

such that a random multigraph has an accessing parameter

k\leq αn

with high probability.

k

for the existence of a ((k,n))_q scheme and prove, using probabilistic methods, that there exists alpha such that a random multigraph has an accessing parameter k => alpha*n with high probability.