1,853 research outputs found
GHZ extraction yield for multipartite stabilizer states
Let be an arbitrary stabilizer state distributed between three
remote parties, such that each party holds several qubits. Let be a
stabilizer group of . We show that can be converted by local
unitaries into a collection of singlets, GHZ states, and local one-qubit
states. The numbers of singlets and GHZs are determined by dimensions of
certain subgroups of . For an arbitrary number of parties we find a
formula for the maximal number of -partite GHZ states that can be extracted
from by local unitaries. A connection with earlier introduced measures
of multipartite correlations is made. An example of an undecomposable
four-party stabilizer state with more than one qubit per party is given. These
results are derived from a general theoretical framework that allows one to
study interconversion of multipartite stabilizer states by local Clifford group
operators. As a simple application, we study three-party entanglement in
two-dimensional lattice models that can be exactly solved by the stabilizer
formalism.Comment: 12 pages, 1 figur
Multi-party entanglement in graph states
Graph states are multi-particle entangled states that correspond to
mathematical graphs, where the vertices of the graph take the role of quantum
spin systems and edges represent Ising interactions. They are many-body spin
states of distributed quantum systems that play a significant role in quantum
error correction, multi-party quantum communication, and quantum computation
within the framework of the one-way quantum computer. We characterize and
quantify the genuine multi-particle entanglement of such graph states in terms
of the Schmidt measure, to which we provide upper and lower bounds in graph
theoretical terms. Several examples and classes of graphs will be discussed,
where these bounds coincide. These examples include trees, cluster states of
different dimension, graphs that occur in quantum error correction, such as the
concatenated [7,1,3]-CSS code, and a graph associated with the quantum Fourier
transform in the one-way computer. We also present general transformation rules
for graphs when local Pauli measurements are applied, and give criteria for the
equivalence of two graphs up to local unitary transformations, employing the
stabilizer formalism. For graphs of up to seven vertices we provide complete
characterization modulo local unitary transformations and graph isomorphies.Comment: 22 pages, 15 figures, 2 tables, typos corrected (e.g. in measurement
rules), references added/update
Entanglement measures and approximate quantum error correction
It is shown that, if the loss of entanglement along a quantum channel is
sufficiently small, then approximate quantum error correction is possible,
thereby generalizing what happens for coherent information. Explicit bounds are
obtained for the entanglement of formation and the distillable entanglement,
and their validity naturally extends to other bipartite entanglement measures
in between. Robustness of derived criteria is analyzed and their tightness
compared. Finally, as a byproduct, we prove a bound quantifying how large the
gap between entanglement of formation and distillable entanglement can be for
any given finite dimensional bipartite system, thus providing a sufficient
condition for distillability in terms of entanglement of formation.Comment: 7 pages, two-columned revtex4, no figures. v1: Deeply revised and
extended version: different entanglement measures are separately considered,
references are added, and some remarks are stressed. v2: Added a sufficient
condition for distillability in terms of entanglement of formation; published
versio
Quantum error correction : an introductory guide
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to gate compilation strategies at the software level. As such, familiarity with quantum coding is an essential prerequisite for the understanding of current and future quantum computing architectures. In this review, we provide an introductory guide to the theory and implementation of quantum error correction codes. Where possible, fundamental concepts are described using the simplest examples of detection and correction codes, the working of which can be verified by hand. We outline the construction and operation of the surface code, the most widely pursued error correction protocol for experiment. Finally, we discuss issues that arise in the practical implementation of the surface code and other quantum error correction codes
Security of two quantum cryptography protocols using the same four qubit states
The first quantum cryptography protocol, proposed by Bennett and Brassard in
1984 (BB84), has been widely studied in the last years. This protocol uses four
states (more precisely, two complementary bases) for the encoding of the
classical bit. Recently, it has been noticed that by using the same four
states, but a different encoding of information, one can define a new protocol
which is more robust in practical implementations, specifically when attenuated
laser pulses are used instead of single-photon sources [V. Scarani et al.,
Phys. Rev. Lett. {\bf 92}, 057901 (2004); referred to as SARG04]. We present a
detailed study of SARG04 in two different regimes. In the first part, we
consider an implementation with a single-photon source: we derive bounds on the
error rate for security against all possible attacks by the eavesdropper.
The lower and the upper bound obtained for SARG04 ( and
respectively) are close to those obtained for BB84 ( and respectively). In the second part, we consider the
realistic source consisting of an attenuated laser and improve on previous
analysis by allowing Alice to optimize the mean number of photons as a function
of the distance. SARG04 is found to perform better than BB84, both in secret
key rate and in maximal achievable distance, for a wide class of Eve's attacks.Comment: 19 pages, 7 figures, published versio
Quantum Key Distribution using Multilevel Encoding: Security Analysis
We present security proofs for a protocol for Quantum Key Distribution (QKD)
based on encoding in finite high-dimensional Hilbert spaces. This protocol is
an extension of Bennett's and Brassard's basic protocol from two bases, two
state encoding to a multi bases, multi state encoding. We analyze the mutual
information between the legitimate parties and the eavesdropper, and the error
rate, as function of the dimension of the Hilbert space, while considering
optimal incoherent and coherent eavesdropping attacks. We obtain the upper
limit for the legitimate party error rate to ensure unconditional security when
the eavesdropper uses incoherent and coherent eavesdropping strategies. We have
also consider realistic noise caused by detector's noise.Comment: 8 pages, 3 figures, REVTe
New Probable Dwarf Galaxies in Northern Groups of the Local Supercluster
We have searched for nearby dwarf galaxies in 27 northern groups with
characteristic distances 8-15 Mpc based on the Second Palomar Sky Survey
prints. In a total area of about 2000 square degrees, we have found 90
low-surface-brightness objects, more than 60% of which are absent from known
catalogs and lists. We have classified most of these objects (~80%) as
irregular dwarf systems. The first 21-cm line observations of the new objects
with the 100-m Effelsberg radio telescope showed that the typical linear
diameters (1-2 kpc), internal motions (30 km/s), and hydrogen masses
(~2*10^7M_sun) galaxies correspond to those expected for the dwarf population
of nearby groups.Comment: 8 pages, 1 fugur
Randomized Benchmarking of Multi-Qubit Gates
As experimental platforms for quantum information processing continue to
mature, characterization of the quality of unitary gates that can be applied to
their quantum bits (qubits) becomes essential. Eventually, the quality must be
sufficiently high to support arbitrarily long quantum computations. Randomized
benchmarking already provides a platform-independent method for assessing the
quality of one-qubit rotations. Here we describe an extension of this method to
multi-qubit gates. We provide a platform-independent protocol for evaluating
the performance of experimental Clifford unitaries, which form the basis of
fault-tolerant quantum computing. We implemented the benchmarking protocol with
trapped-ion two-qubit phase gates and one-qubit gates and found an error per
random two-qubit Clifford unitary of , thus setting the first
benchmark for such unitaries. By implementing a second set of sequences with an
extra two-qubit phase gate at each step, we extracted an error per phase gate
of . We conducted these experiments with movable,
sympathetically cooled ions in a multi-zone Paul trap - a system that can in
principle be scaled to larger numbers of ions.Comment: Corrected description of parallel single-qubit benchmark experiment.
Results unchange
Measurement-based quantum computation beyond the one-way model
We introduce novel schemes for quantum computing based on local measurements
on entangled resource states. This work elaborates on the framework established
in [Phys. Rev. Lett. 98, 220503 (2007), quant-ph/0609149]. Our method makes use
of tools from many-body physics - matrix product states, finitely correlated
states or projected entangled pairs states - to show how measurements on
entangled states can be viewed as processing quantum information. This work
hence constitutes an instance where a quantum information problem - how to
realize quantum computation - was approached using tools from many-body theory
and not vice versa. We give a more detailed description of the setting, and
present a large number of new examples. We find novel computational schemes,
which differ from the original one-way computer for example in the way the
randomness of measurement outcomes is handled. Also, schemes are presented
where the logical qubits are no longer strictly localized on the resource
state. Notably, we find a great flexibility in the properties of the universal
resource states: They may for example exhibit non-vanishing long-range
correlation functions or be locally arbitrarily close to a pure state. We
discuss variants of Kitaev's toric code states as universal resources, and
contrast this with situations where they can be efficiently classically
simulated. This framework opens up a way of thinking of tailoring resource
states to specific physical systems, such as cold atoms in optical lattices or
linear optical systems.Comment: 21 pages, 7 figure
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