2,364 research outputs found
How to share a quantum secret
We investigate the concept of quantum secret sharing. In a ((k,n)) threshold
scheme, a secret quantum state is divided into n shares such that any k of
those shares can be used to reconstruct the secret, but any set of k-1 or fewer
shares contains absolutely no information about the secret. We show that the
only constraint on the existence of threshold schemes comes from the quantum
"no-cloning theorem", which requires that n < 2k, and, in all such cases, we
give an efficient construction of a ((k,n)) threshold scheme. We also explore
similarities and differences between quantum secret sharing schemes and quantum
error-correcting codes. One remarkable difference is that, while most existing
quantum codes encode pure states as pure states, quantum secret sharing schemes
must use mixed states in some cases. For example, if k <= n < 2k-1 then any
((k,n)) threshold scheme must distribute information that is globally in a
mixed state.Comment: 5 pages, REVTeX, submitted to PR
Entanglement Polygon Inequality in Qubit Systems
We prove a set of tight entanglement inequalities for arbitrary -qubit
pure states. By focusing on all bi-partite marginal entanglements between each
single qubit and its remaining partners, we show that the inequalities provide
an upper bound for each marginal entanglement, while the known monogamy
relation establishes the lower bound. The restrictions and sharing properties
associated with the inequalities are further analyzed with a geometric polytope
approach, and examples of three-qubit GHZ-class and W-class entangled states
are presented to illustrate the results.Comment: 8 pages, 4 figure
Structural change in multipartite entanglement sharing: a random matrix approach
We study the typical entanglement properties of a system comprising two
independent qubit environments interacting via a shuttling ancilla. The initial
preparation of the environments is modeled using random-matrix techniques. The
entanglement measure used in our study is then averaged over many histories of
randomly prepared environmental states. Under a Heisenberg interaction model,
the average entanglement between the ancilla and one of the environments
remains constant, regardless of the preparation of the latter and the details
of the interaction. We also show that, upon suitable kinematic and dynamical
changes in the ancilla-environment subsystems, the entanglement-sharing
structure undergoes abrupt modifications associated with a change in the
multipartite entanglement class of the overall system's state. These results
are invariant with respect to the randomized initial state of the environments.Comment: 10 pages, RevTeX4 (Minor typo's corrected. Closer to published
version
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