253 research outputs found
Optimal cloning for two pairs of orthogonal states
We study the optimal cloning transformation for two pairs of orthogonal
states of two-dimensional quantum systems, and derive the corresponding optimal
fidelities.Comment: 4 pages, 3 figure
Multipartite entanglement in quantum algorithms
We investigate the entanglement features of the quantum states employed in
quantum algorithms. In particular, we analyse the multipartite entanglement
properties in the Deutsch-Jozsa, Grover and Simon algorithms. Our results show
that for these algorithms most instances involve multipartite entanglement
Multipartite entanglement in quantum algorithms
We investigate the entanglement features of the quantum states employed in
quantum algorithms. In particular, we analyse the multipartite entanglement
properties in the Deutsch-Jozsa, Grover and Simon algorithms. Our results show
that for these algorithms most instances involve multipartite entanglement
Experimental generation of pseudo bound entanglement
We use Nuclear Magnetic Resonance (NMR) to experimentally generate a bound
entangled (more precisely: pseudo bound entangled) state, i.e. a quantum state
which is non-distillable but nevertheless entangled. Our quantum system
consists of three qubits. We characterize the produced state via state
tomography to show that the created state has a positive partial transposition
with respect to any bipartite splitting, and we use a witness operator to prove
its entanglement.Comment: 5 page
Optimal eavesdropping in cryptography with three-dimensional quantum states
We study optimal eavesdropping in quantum cryptography with three-dimensional
systems, and show that this scheme is more secure than protocols using
two-dimensional states. We generalize the according eavesdropping
transformation to arbitrary dimensions, and discuss the connection with optimal
quantum cloning.Comment: 4 pages, 2 figure
Quantum Hypergraph States
We introduce a class of multiqubit quantum states which generalizes graph
states. These states correspond to an underlying mathematical hypergraph, i.e.
a graph where edges connecting more than two vertices are considered. We derive
a generalised stabilizer formalism to describe this class of states. We
introduce the notion of k-uniformity and show that this gives rise to classes
of states which are inequivalent under the action of the local Pauli group.
Finally we disclose a one-to-one correspondence with states employed in quantum
algorithms, such as Deutsch-Jozsa's and Grover's.Comment: 9+5 pages, 5 figures, 1 table, published versio
Quantum Cloning in dimensions
The quantum state space over a -dimensional Hilbert space is
represented as a convex subset of a -dimensional sphere , where Quantum tranformations (CP-maps) are then
associated with the affine transformations of and
{\it cloners} induce polynomial mappings. In this geometrical setting it is
shown that an optimal cloner can be chosen covariant and induces a map between
reduced density matrices given by a simple contraction of the associated
-dimensional Bloch vectors.Comment: 8 pages LaTeX, no figure
Quantum cloning machines for equatorial qubits
Quantum cloning machines for equatorial qubits are studied. For the case of 1
to 2 phase-covariant quantum cloning machine, we present the networks
consisting of quantum gates to realize the quantum cloning transformations. The
copied equatorial qubits are shown to be separable by using Peres-Horodecki
criterion. The optimal 1 to M phase-covariant quantum cloning transformations
are given.Comment: Revtex, 9 page
On the generalization of quantum state comparison
We investigate the unambiguous comparison of quantum states in a scenario
that is more general than the one that was originally suggested by Barnett et
al. First, we find the optimal solution for the comparison of two states taken
from a set of two pure states with arbitrary a priori probabilities. We show
that the optimal coherent measurement is always superior to the optimal
incoherent measurement. Second, we develop a strategy for the comparison of two
states from a set of N pure states, and find an optimal solution for some
parameter range when N=3. In both cases we use the reduction method for the
corresponding problem of mixed state discrimination, as introduced by Raynal et
al., which reduces the problem to the discrimination of two pure states only
for N=2. Finally, we provide a necessary and sufficient condition for
unambiguous comparison of mixed states to be possible.Comment: 8 pages, 4 figures, Proposition 1 corrected, appendix adde
Generalized self-testing and the security of the 6-state protocol
Self-tested quantum information processing provides a means for doing useful
information processing with untrusted quantum apparatus. Previous work was
limited to performing computations and protocols in real Hilbert spaces, which
is not a serious obstacle if one is only interested in final measurement
statistics being correct (for example, getting the correct factors of a large
number after running Shor's factoring algorithm). This limitation was shown by
McKague et al. to be fundamental, since there is no way to experimentally
distinguish any quantum experiment from a special simulation using states and
operators with only real coefficients.
In this paper, we show that one can still do a meaningful self-test of
quantum apparatus with complex amplitudes. In particular, we define a family of
simulations of quantum experiments, based on complex conjugation, with two
interesting properties. First, we are able to define a self-test which may be
passed only by states and operators that are equivalent to simulations within
the family. This extends work of Mayers and Yao and Magniez et al. in
self-testing of quantum apparatus, and includes a complex measurement. Second,
any of the simulations in the family may be used to implement a secure 6-state
QKD protocol, which was previously not known to be implementable in a
self-tested framework.Comment: To appear in proceedings of TQC 201
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