2,544 research outputs found
Quantum Algorithms for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems
Decision of whether a Boolean equation system has a solution is an NPC
problem and finding a solution is NP hard. In this paper, we present a quantum
algorithm to decide whether a Boolean equation system FS has a solution and
compute one if FS does have solutions with any given success probability. The
runtime complexity of the algorithm is polynomial in the size of FS and the
condition number of FS. As a consequence, we give a polynomial-time quantum
algorithm for solving Boolean equation systems if their condition numbers are
small, say polynomial in the size of FS. We apply our quantum algorithm for
solving Boolean equations to the cryptanalysis of several important
cryptosystems: the stream cipher Trivum, the block cipher AES, the hash
function SHA-3/Keccak, and the multivariate public key cryptosystems, and show
that they are secure under quantum algebraic attack only if the condition
numbers of the corresponding equation systems are large. This leads to a new
criterion for designing cryptosystems that can against the attack of quantum
computers: their corresponding equation systems must have large condition
numbers
Robust creation of entanglement between remote memory qubits
In this Letter we propose a robust quantum repeater architecture building on
the original DLCZ protocol [L.M. Duan \textit{et al.}, Nature \textbf{414}, 413
(2001)]. The architecture is based on two-photon Hong-Ou-Mandel-type
interference which relaxes the long distance stability requirements by about 7
orders of magnitude, from sub wavelength for the single photon interference
required by DLCZ to the coherence length of the photons. Our proposal provides
an exciting possibility for robust and realistic long distance quantum
communication.Comment: Comments are welcome, to appear in Phys. Rev. Lett., accepted versio
Controlling and Detecting Spin Correlations of Ultracold Atoms in Optical lattices
We report on the controlled creation of a valence bond state of delocalized
effective-spin singlet and triplet dimers by means of a bichromatic optical
superlattice. We demonstrate a coherent coupling between the singlet and
triplet states and show how the superlattice can be employed to measure the
singlet-fraction employing a spin blockade effect. Our method provides a
reliable way to detect and control nearest-neighbor spin correlations in
many-body systems of ultracold atoms. Being able to measure these correlations
is an important ingredient to study quantum magnetism in optical lattices. We
furthermore employ a SWAP operation between atoms being part of different
triplets, thus effectively increasing their bond-length. Such SWAP operation
provides an important step towards the massively parallel creation of a
multi-particle entangled state in the lattice.Comment: 6 pages, 4 figure
Deterministic spin-wave interferometer based on Rydberg blockade
The spin-wave (SW) NOON state is an -particle Fock state with two atomic
spin-wave modes maximally entangled. Attributed to the property that the phase
is sensitive to collective atomic motion, the SW NOON state can be utilized as
a novel atomic interferometer and has promising application in quantum enhanced
measurement. In this paper we propose an efficient protocol to
deterministically produce the atomic SW NOON state by employing Rydberg
blockade. Possible errors in practical manipulations are analyzed. A feasible
experimental scheme is suggested. Our scheme is far more efficient than the
recent experimentally demonstrated one, which only creates a heralded
second-order SW NOON state.Comment: 5 pages, 2 figure
Fault-tolerant quantum repeater with atomic ensembles and linear optics
We present a detailed analysis of a new robust quantum repeater architecture
building on the original DLCZ protocol [L.M. Duan \textit{et al.}, Nature
(London) \textbf{414}, 413 (2001)]. The new architecture is based on two-photon
Hong-Ou-Mandel-type interference which relaxes the long-distance
interferometric stability requirements by about 7 orders of magnitude, from
sub-wavelength for the single photon interference required by DLCZ to the
coherence length of the photons, thereby removing the weakest point in the DLCZ
schema. Our proposal provides an exciting possibility for robust and realistic
long-distance quantum communication.Comment: Comments are welcome, to appear in Phys. Rev. A, accepted versio
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