10,505 research outputs found
Approximate reconstructability of quantum states and noisy quantum secret sharing schemes
We introduce and analyse approximate quantum secret sharing in a formal
cryptographic setting, wherein a dealer encodes and distributes a quantum
secret to players such that authorized structures (sets of subsets of players)
can approximately reconstruct the quantum secret and omnipotent adversarial
agents controlling non-authorized subsets of players are approximately denied
the quantum secret. In particular, viewing the map encoding the quantum secret
to shares for players in an authorized structure as a quantum channel, we show
that approximate reconstructability of the quantum secret by these players is
possible if and only if the information leakage, given in terms of a certain
entanglement-assisted capacity of the complementary quantum channel to the
players outside the structure and the environment, is small.Comment: 6 pages, 1 figur
Some Directions beyond Traditional Quantum Secret Sharing
We investigate two directions beyond the traditional quantum secret sharing
(QSS). First, a restriction on QSS that comes from the no-cloning theorem is
that any pair of authorized sets in an access structure should overlap. From
the viewpoint of application, this places an unnatural constraint on secret
sharing. We present a generalization, called assisted QSS (AQSS), where access
structures without pairwise overlap of authorized sets is permissible, provided
some shares are withheld by the share dealer. We show that no more than
withheld shares are required, where is the minimum number
of {\em partially linked classes} among the authorized sets for the QSS. Our
result means that such applications of QSS need not be thwarted by the
no-cloning theorem. Secondly, we point out a way of combining the features of
QSS and quantum key distribution (QKD) for applications where a classical
information is shared by quantum means. We observe that in such case, it is
often possible to reduce the security proof of QSS to that of QKD.Comment: To appear in Physica Scripta, 7 pages, 1 figure, subsumes
arXiv:quant-ph/040720
Quantum network communication -- the butterfly and beyond
We study the k-pair communication problem for quantum information in networks
of quantum channels. We consider the asymptotic rates of high fidelity quantum
communication between specific sender-receiver pairs. Four scenarios of
classical communication assistance (none, forward, backward, and two-way) are
considered. (i) We obtain outer and inner bounds of the achievable rate regions
in the most general directed networks. (ii) For two particular networks
(including the butterfly network) routing is proved optimal, and the free
assisting classical communication can at best be used to modify the directions
of quantum channels in the network. Consequently, the achievable rate regions
are given by counting edge avoiding paths, and precise achievable rate regions
in all four assisting scenarios can be obtained. (iii) Optimality of routing
can also be proved in classes of networks. The first class consists of directed
unassisted networks in which (1) the receivers are information sinks, (2) the
maximum distance from senders to receivers is small, and (3) a certain type of
4-cycles are absent, but without further constraints (such as on the number of
communicating and intermediate parties). The second class consists of arbitrary
backward-assisted networks with 2 sender-receiver pairs. (iv) Beyond the k-pair
communication problem, observations are made on quantum multicasting and a
static version of network communication related to the entanglement of
assistance.Comment: 15 pages, 17 figures. Final versio
Teleportation and Secret Sharing with Pure Entangled States
We present two optimal methods of teleporting an unknown qubit using any pure
entangled state. We also discuss how such methods can also have succesful
application in quantum secret sharing with pure multipartite entangled states.Comment: Latex, 13 pages, submitted to PRA. One sub section already appeared
in the archive: quant-ph /990701
Unconstrained Capacities of Quantum Key Distribution and Entanglement Distillation for Pure-Loss Bosonic Broadcast Channels
We consider quantum key distribution (QKD) and entanglement distribution
using a single-sender multiple-receiver pure-loss bosonic broadcast channel. We
determine the unconstrained capacity region for the distillation of bipartite
entanglement and secret key between the sender and each receiver, whenever they
are allowed arbitrary public classical communication. A practical implication
of our result is that the capacity region demonstrated drastically improves
upon rates achievable using a naive time-sharing strategy, which has been
employed in previously demonstrated network QKD systems. We show a simple
example of the broadcast QKD protocol overcoming the limit of the
point-to-point strategy. Our result is thus an important step toward opening a
new framework of network channel-based quantum communication technology.Comment: 9 pages, 5 figure
Trade-off coding for universal qudit cloners motivated by the Unruh effect
A "triple trade-off" capacity region of a noisy quantum channel provides a
more complete description of its capabilities than does a single capacity
formula. However, few full descriptions of a channel's ability have been given
due to the difficult nature of the calculation of such regions---it may demand
an optimization of information-theoretic quantities over an infinite number of
channel uses. This work analyzes the d-dimensional Unruh channel, a noisy
quantum channel which emerges in relativistic quantum information theory. We
show that this channel belongs to the class of quantum channels whose capacity
region requires an optimization over a single channel use, and as such is
tractable. We determine two triple-trade off regions, the quantum dynamic
capacity region and the private dynamic capacity region, of the d-dimensional
Unruh channel. Our results show that the set of achievable rate triples using
this coding strategy is larger than the set achieved using a time-sharing
strategy. Furthermore, we prove that the Unruh channel has a distinct structure
made up of universal qudit cloning channels, thus providing a clear
relationship between this relativistic channel and the process of stimulated
emission present in quantum optical amplifiers.Comment: 26 pages, 4 figures; v2 has minor corrections to Definition 2.
Definition 4 and Remark 5 have been adde
Single-photon-assisted entanglement concentration of a multi-photon system in a partially entangled W state with weak cross-Kerr nonlinearity
We propose a nonlocal entanglement concentration protocol (ECP) for
-photon systems in a partially entangled W state, resorting to some
ancillary single photons and the parity-check measurement based on cross-Kerr
nonlinearity. One party in quantum communication first performs a parity-check
measurement on her photon in an -photon system and an ancillary photon, and
then she picks up the even-parity instance for obtaining the standard W state.
When she obtains an odd-parity instance, the system is in a less-entanglement
state and it is the resource in the next round of entanglement concentration.
By iterating the entanglement concentration process several times, the present
ECP has the total success probability approaching to the limit in theory. The
present ECP has the advantage of a high success probability. Moreover, the
present ECP requires only the -photon system itself and some ancillary
single photons, not two copies of the systems, which decreases the difficulty
of its implementation largely in experiment. It maybe have good applications in
quantum communication in future.Comment: 7 pages, 3 figure
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