6 research outputs found
Multi-output programmable quantum processor
By combining telecloning and programmable quantum gate array presented by
Nielsen and Chuang [Phys.Rev.Lett. 79 :321(1997)], we propose a programmable
quantum processor which can be programmed to implement restricted set of
operations with several identical data outputs. The outputs are
approximately-transformed versions of input data. The processor successes with
certain probability.Comment: 5 pages and 2 PDF figure
Non-negative Wigner functions in prime dimensions
According to a classical result due to Hudson, the Wigner function of a pure,
continuous variable quantum state is non-negative if and only if the state is
Gaussian. We have proven an analogous statement for finite-dimensional quantum
systems. In this context, the role of Gaussian states is taken on by stabilizer
states. The general results have been published in [D. Gross, J. Math. Phys.
47, 122107 (2006)]. For the case of systems of odd prime dimension, a greatly
simplified proof can be employed which still exhibits the main ideas. The
present paper gives a self-contained account of these methods.Comment: 5 pages. Special case of a result proved in quant-ph/0602001. The
proof is greatly simplified, making the general case more accessible. To
appear in Appl. Phys. B as part of the proceedings of the 2006 DPG Spring
Meeting (Quantum Optics and Photonics section
Multipartite Classical and Quantum Secrecy Monotones
In order to study multipartite quantum cryptography, we introduce quantities
which vanish on product probability distributions, and which can only decrease
if the parties carry out local operations or carry out public classical
communication. These ``secrecy monotones'' therefore measure how much secret
correlations are shared by the parties. In the bipartite case we show that the
mutual information is a secrecy monotone. In the multipartite case we describe
two different generalisations of the mutual information, both of which are
secrecy monotones. The existence of two distinct secrecy monotones allows us to
show that in multipartite quantum cryptography the parties must make
irreversible choices about which multipartite correlations they want to obtain.
Secrecy monotones can be extended to the quantum domain and are then defined on
density matrices. We illustrate this generalisation by considering tri-partite
quantum cryptography based on the Greenberger-Horne-Zeilinger (GHZ) state. We
show that before carrying out measurements on the state, the parties must make
an irreversible decision about what probability distribution they want to
obtain
Family of Zeilinger-Horne-Greenberger "W" states lead to stronger nonclassicality than family of Greenberger-Horne-Zeilinger "GHZ" states
The N-qubit states of the W class, for N>10, lead to more robust (against
noise admixture) violations of local realism, than the GHZ states. These
violations are most pronounced for correlations for a pair of qubits,
conditioned on specific measurement results for the remaining (N-2) qubits. The
considerations provide us with a qualitative difference between the W state and
GHZ state in the situation when they are separately sent via depolarizing
channels. For sufficiently high amount of noise in the depolarizing channel,
the GHZ states cannot produce a distillable state between two qubits, whereas
the W states can still produce a distillable state in a similar situation.Comment: v3: 7 pages, 2 figures, REVTeX4; v2: result on comparative yield of
singlets added, 1 new figur
Entanglement Properties of the Harmonic Chain
We study the entanglement properties of a closed chain of harmonic oscillators that are coupled via a translationally invariant Hamiltonian, where the coupling acts only on the position operators. We consider the ground state and thermal states of this system, which are Gaussian states. The entanglement properties of these states can be completely characterized analytically when one uses the logarithmic negativity as a measure of entanglement