3 research outputs found
How to hide a secret direction
We present a procedure to share a secret spatial direction in the absence of
a common reference frame using a multipartite quantum state. The procedure
guarantees that the parties can determine the direction if they perform joint
measurements on the state, but fail to do so if they restrict themselves to
local operations and classical communication (LOCC). We calculate the fidelity
for joint measurements, give bounds on the fidelity achievable by LOCC, and
prove that there is a non-vanishing gap between the two of them, even in the
limit of infinitely many copies. The robustness of the procedure under particle
loss is also studied. As a by-product we find bounds on the probability of
discriminating by LOCC between the invariant subspaces of total angular
momentum N/2 and N/2-1 in a system of N elementary spins.Comment: 4 pages, 1 figur
Symmetric coupling of four spin-1/2 systems
We address the non-binary coupling of identical angular momenta based upon
the representation theory for the symmetric group. A correspondence is pointed
out between the complete set of commuting operators and the
reference-frame-free subsystems. We provide a detailed analysis of the coupling
of three and four spin-1/2 systems and discuss a symmetric coupling of four
spin-1/2 systems.Comment: 20 pages, no figure
Compatible Transformations for a Qudit Decoherence-free/Noiseless Encoding
The interest in decoherence-free, or noiseless subsystems (DFS/NSs) of
quantum systems is both of fundamental and practical interest. Understanding
the invariance of a set of states under certain transformations is mutually
associated with a better understanding of some fundamental aspects of quantum
mechanics as well as the practical utility of invariant subsystems. For
example, DFS/NSs are potentially useful for protecting quantum information in
quantum cryptography and quantum computing as well as enabling universal
computation. Here we discuss transformations which are compatible with a DFS/NS
that is composed of d-state systems which protect against collective noise.
They are compatible in the sense that they do not take the logical (encoded)
states outside of the DFS/NS during the transformation. Furthermore, it is
shown that the Hamiltonian evolutions derived here can be used to perform
universal quantum computation on a three qudit DFS/NS. Many of the methods used
in our derivations are directly applicable to a large variety of DFS/NSs. More
generally, we may also state that these transformations are compatible with
collective motions.Comment: 30 pages, replaced with published versio