619 research outputs found
Multipartite secure state distribution
We introduce the distribution of a secret multipartite entangled state in a
real-world scenario as a quantum primitive. We show that in the presence of
noisy quantum channels (and noisy control operations) any state chosen from the
set of two-colorable graph states (CSS codewords) can be created with high
fidelity while it remains unknown to all parties. This is accomplished by
either blind multipartite entanglement purification, which we introduce in this
paper, or by multipartite entanglement purification of enlarged states, which
offers advantages over an alternative scheme based on standard channel
purification and teleportation. The parties are thus provided with a secret
resource of their choice for distributed secure applications.Comment: V2: Replaced with published version: title changed, 2 figures added,
presentation improve
Entanglement purification protocols for all graph states
We present multiparty entanglement purification protocols that are capable of
purifying arbitrary graph states directly. We develop recurrence and breeding
protocols and compare our methods with strategies based on bipartite
entanglement purification in static and communication scenarios. We find that
direct multiparty purification is of advantage with respect to achievable
yields and minimal required fidelity in static scenarios, and with respect to
obtainable fidelity in the case of noisy operations in both scenarios.Comment: revtex 10 pages, 6 figure
Fast simulation of stabilizer circuits using a graph state representation
According to the Gottesman-Knill theorem, a class of quantum circuits, namely
the so-called stabilizer circuits, can be simulated efficiently on a classical
computer. We introduce a new algorithm for this task, which is based on the
graph-state formalism. It shows significant improvement in comparison to an
existing algorithm, given by Gottesman and Aaronson, in terms of speed and of
the number of qubits the simulator can handle. We also present an
implementation.Comment: v2: significantly improved presentation; accepted by PR
Entanglement Purification of Any Stabilizer State
We present a method for multipartite entanglement purification of any
stabilizer state shared by several parties. In our protocol each party measures
the stabilizer operators of a quantum error-correcting code on his or her
qubits. The parties exchange their measurement results, detect or correct
errors, and decode the desired purified state. We give sufficient conditions on
the stabilizer codes that may be used in this procedure and find that Steane's
seven-qubit code is the smallest error-correcting code sufficient to purify any
stabilizer state. An error-detecting code that encodes two qubits in six can
also be used to purify any stabilizer state. We further specify which classes
of stabilizer codes can purify which classes of stabilizer states.Comment: 11 pages, 0 figures, comments welcome, submitting to Physical Review
Multiparticle entanglement purification for two-colorable graph states
We investigate multiparticle entanglement purification schemes which allow
one to purify all two colorable graph states, a class of states which includes
e.g. cluster states, GHZ states and codewords of various error correction
codes. The schemes include both recurrence protocols and hashing protocols. We
analyze these schemes under realistic conditions and observe for a generic
error model that the threshold value for imperfect local operations depends on
the structure of the corresponding interaction graph, but is otherwise
independent of the number of parties. The qualitative behavior can be
understood from an analytically solvable model which deals only with a
restricted class of errors. We compare direct multiparticle entanglement
purification protocols with schemes based on bipartite entanglement
purification and show that the direct multiparticle entanglement purification
is more efficient and the achievable fidelity of the purified states is larger.
We also show that the purification protocol allows one to produce private
entanglement, an important aspect when using the produced entangled states for
secure applications. Finally we discuss an experimental realization of a
multiparty purification protocol in optical lattices which is issued to improve
the fidelity of cluster states created in such systems.Comment: 22 pages, 8 figures; replaced with published versio
Quantum states representing perfectly secure bits are always distillable
It is proven that recently introduced states with perfectly secure bits of
cryptographic key (private states representing secure bit) [K. Horodecki et
al., Phys. Rev. Lett. 94, 160502 (2005)] as well as its multipartite and higher
dimension generalizations always represent distillable entanglement. The
corresponding lower bounds on distillable entanglement are provided. We also
present a simple alternative proof that for any bipartite quantum state
entanglement cost is an upper bound on distillable cryptographic key in
bipartite scenario.Comment: RevTeX, 5 pages, published versio
Quantum communication cost of preparing multipartite entanglement
We study the preparation and distribution of high-fidelity multi-party
entangled states via noisy channels and operations. In the particular case of
GHZ and cluster states, we study different strategies using bipartite or
multipartite purification protocols. The most efficient strategy depends on the
target fidelity one wishes to achieve and on the quality of transmission
channel and local operations. We show the existence of a crossing point beyond
which the strategy making use of the purification of the state as a whole is
more efficient than a strategy in which pairs are purified before they are
connected to the final state. We also study the efficiency of intermediate
strategies, including sequences of purification and connection. We show that a
multipartite strategy is to be used if one wishes to achieve high fidelity,
whereas a bipartite strategy gives a better yield for low target fidelity.Comment: 21 pages, 17 figures; accepted for publication in Phys. Rev. A; v2:
corrections in figure
Entanglement Purification with Double Selection
We investigate efficient entanglement purification through double selection
process. This method works with higher noise thresholds for the communication
channels and local operations, and achieves higher fidelity of purified states.
Furthermore it provides a yield comparable to the usual protocol with single
selection. It is shown by general considerations that the double selection is
optimal to remove the first-order errors, achieving the upper bound on the
fidelity of purified states in the low noise regime. The double selection is
also applied to purification of multi-partite entanglement such as
two-colorable graph states.Comment: 10 pages, 10 figure
Optimal purification of thermal graph states
In this paper, a purification protocol is presented and its performance is
proven to be optimal when applied to a particular subset of graph states that
are subject to local Z-noise. Such mixed states can be produced by bringing a
system into thermal equilibrium, when it is described by a Hamiltonian which
has a particular graph state as its unique ground state. From this protocol, we
derive the exact value of the critical temperature above which purification is
impossible, as well as the related optimal purification rates. A possible
simulation of graph Hamiltonians is proposed, which requires only bipartite
interactions and local magnetic fields, enabling the tuning of the system
temperature.Comment: 5 pages, 4 figures v2: published versio
A Simultaneous Quantum Secure Direct Communication Scheme between the Central Party and Other M Parties
We propose a simultaneous quantum secure direct communication scheme between
one party and other three parties via four-particle GHZ states and swapping
quantum entanglement. In the scheme, three spatially separated senders, Alice,
Bob and Charlie, transmit their secret messages to a remote receiver Diana by
performing a series local operations on their respective particles according to
the quadripartite stipulation. From Alice, Bob, Charlie and Diana's Bell
measurement results, Diana can infer the secret messages. If a perfect quantum
channel is used, the secret messages are faithfully transmitted from Alice, Bob
and Charlie to Diana via initially shared pairs of four-particle GHZ states
without revealing any information to a potential eavesdropper. As there is no
transmission of the qubits carrying the secret message in the public channel,
it is completely secure for the direct secret communication. This scheme can be
considered as a network of communication parties where each party wants to
communicate secretly with a central party or server.Comment: 4 pages, no figur
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