1,316 research outputs found
A different kind of quantum search
The quantum search algorithm consists of an alternating sequence of selective
inversions and diffusion type operations, as a result of which it can find a
target state in an unsorted database of size N in only sqrt(N) queries. This
paper shows that by replacing the selective inversions by selective phase
shifts of Pi/3, the algorithm gets transformed into something similar to a
classical search algorithm. Just like classical search algorithms this
algorithm has a fixed point in state-space toward which it preferentially
converges. In contrast, the original quantum search algorithm moves uniformly
in a two-dimensional state space. This feature leads to robust search
algorithms and also to conceptually new schemes for error correction.Comment: 13 pages, 4 figure
Quantum computers can search rapidly by using almost any selective transformations
The search problem is to find a state satisfying certain properties out of a
given set. Grover's algorithm drives a quantum computer from a prepared initial
state to the target state and solves the problem quadratically faster than a
classical computer. The algorithm uses selective transformations to distinguish
the initial state and target state from other states. It does not succeed
unless the selective transformations are very close to phase-inversions. Here
we show a way to go beyond this limitation. An important application lies in
quantum error-correction, where the errors can cause the selective
transformations to deviate from phase-inversions. The algorithms presented here
are robust to errors as long as the errors are reproducible and reversible.
This particular class of systematic errors arise often from imperfections in
apparatus setup. Hence our algorithms offer a significant flexibility in the
physical implementation of quantum search.Comment: 8 pages, Accepted for publication in PR
Exponential quantum enhancement for distributed addition with local nonlinearity
We consider classical and entanglement-assisted versions of a distributed
computation scheme that computes nonlinear Boolean functions of a set of input
bits supplied by separated parties. Communication between the parties is
restricted to take place through a specific apparatus which enforces the
constraints that all nonlinear, nonlocal classical logic is performed by a
single receiver, and that all communication occurs through a limited number of
one-bit channels. In the entanglement-assisted version, the number of channels
required to compute a Boolean function of fixed nonlinearity can become
exponentially smaller than in the classical version. We demonstrate this
exponential enhancement for the problem of distributed integer addition.Comment: To appear in Quantum Information Processin
Quantum Bit String Commitment
A bit string commitment protocol securely commits classical bits in such
a way that the recipient can extract only bits of information about the
string. Classical reasoning might suggest that bit string commitment implies
bit commitment and hence, given the Mayers-Lo-Chau theorem, that
non-relativistic quantum bit string commitment is impossible. Not so: there
exist non-relativistic quantum bit string commitment protocols, with security
parameters and , that allow to commit
bits to so that 's probability of successfully cheating when revealing
any bit and 's probability of extracting more than bits of
information about the bit string before revelation are both less than
. With a slightly weakened but still restrictive definition of
security against , can be taken to be for a positive
constant . I briefly discuss possible applications.Comment: Published version. (Refs updated.
Cheat Sensitive Quantum Bit Commitment
We define cheat sensitive cryptographic protocols between mistrustful parties
as protocols which guarantee that, if either cheats, the other has some nonzero
probability of detecting the cheating. We give an example of an unconditionally
secure cheat sensitive non-relativistic bit commitment protocol which uses
quantum information to implement a task which is classically impossible; we
also describe a simple relativistic protocol.Comment: Final version: a slightly shortened version of this will appear in
PRL. Minor corrections from last versio
Multi-Party Pseudo-Telepathy
Quantum entanglement, perhaps the most non-classical manifestation of quantum
information theory, cannot be used to transmit information between remote
parties. Yet, it can be used to reduce the amount of communication required to
process a variety of distributed computational tasks. We speak of
pseudo-telepathy when quantum entanglement serves to eliminate the classical
need to communicate. In earlier examples of pseudo-telepathy, classical
protocols could succeed with high probability unless the inputs were very
large. Here we present a simple multi-party distributed problem for which the
inputs and outputs consist of a single bit per player, and we present a perfect
quantum protocol for it. We prove that no classical protocol can succeed with a
probability that differs from 1/2 by more than a fraction that is exponentially
small in the number of players. This could be used to circumvent the detection
loophole in experimental tests of nonlocality.Comment: 11 pages. To be appear in WADS 2003 proceeding
Bound on distributed entanglement
Using the convex-roof extended negativity and the negativity of assistance as
quantifications of bipartite entanglement, we consider the possible
remotely-distributed entanglement. For two pure states and
on bipartite systems and , we first show that the
possible amount of entanglement remotely distributed on the system by
joint measurement on the system is not less than the product of two
amounts of entanglement for the states and
in two-qubit and two-qutrit systems. We also provide some sufficient
conditions, for which the result can be generalized into higher-dimensional
quantum systems.Comment: 5 page
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