309 research outputs found
New measure of electron correlation
We propose to quantify the "correlation" inherent in a many-electron (or
many-fermion) wavefunction by comparing it to the unique uncorrelated state
that has the same single-particle density operator as it does.Comment: Final version to appear in PR
Non-additivity of quantum capacity for multiparty communication channels
We investigate multiparty communication scenarios where information is sent
from several sender to several receivers. We establish a relation between the
quantum capacity of multiparty communication channels and their distillability
properties which enables us to show that the quantum capacity of such channels
is not additive.Comment: 4 pages, 1 figur
On the role of entanglement in quantum computational speed-up
For any quantum algorithm operating on pure states we prove that the presence
of multi-partite entanglement, with a number of parties that increases
unboundedly with input size, is necessary if the quantum algorithm is to offer
an exponential speed-up over classical computation. Furthermore we prove that
the algorithm can be classically efficiently simulated to within a prescribed
tolerance \eta even if a suitably small amount of global entanglement
(depending on \eta) is present. We explicitly identify the occurrence of
increasing multi-partite entanglement in Shor's algorithm. Our results do not
apply to quantum algorithms operating on mixed states in general and we discuss
the suggestion that an exponential computational speed-up might be possible
with mixed states in the total absence of entanglement. Finally, despite the
essential role of entanglement for pure state algorithms, we argue that it is
nevertheless misleading to view entanglement as a key resource for quantum
computational power.Comment: Main proofs simplified. A few further explanatory remarks added. 22
pages, plain late
Off-diagonal geometric phase for mixed states
We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067
(2000)] to mixed quantal states. The nodal structure of this phase in the qubit
(two-level) case is compared with that of the diagonal mixed state geometric
phase [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]. Extension to higher dimensional
Hilbert spaces is delineated. A physical scenario for the off-diagonal mixed
state geometric phase in polarization-entangled two-photon interferometry is
proposed.Comment: small corrections; journal reference adde
On quantum coding for ensembles of mixed states
We consider the problem of optimal asymptotically faithful compression for
ensembles of mixed quantum states. Although the optimal rate is unknown, we
prove upper and lower bounds and describe a series of illustrative examples of
compression of mixed states. We also discuss a classical analogue of the
problem.Comment: 23 pages, LaTe
Quantum complexities of ordered searching, sorting, and element distinctness
We consider the quantum complexities of the following three problems:
searching an ordered list, sorting an un-ordered list, and deciding whether the
numbers in a list are all distinct. Letting N be the number of elements in the
input list, we prove a lower bound of \frac{1}{\pi}(\ln(N)-1) accesses to the
list elements for ordered searching, a lower bound of \Omega(N\log{N}) binary
comparisons for sorting, and a lower bound of \Omega(\sqrt{N}\log{N}) binary
comparisons for element distinctness. The previously best known lower bounds
are {1/12}\log_2(N) - O(1) due to Ambainis, \Omega(N), and \Omega(\sqrt{N}),
respectively. Our proofs are based on a weighted all-pairs inner product
argument.
In addition to our lower bound results, we give a quantum algorithm for
ordered searching using roughly 0.631 \log_2(N) oracle accesses. Our algorithm
uses a quantum routine for traversing through a binary search tree faster than
classically, and it is of a nature very different from a faster algorithm due
to Farhi, Goldstone, Gutmann, and Sipser.Comment: This new version contains new results. To appear at ICALP '01. Some
of the results have previously been presented at QIP '01. This paper subsumes
the papers quant-ph/0009091 and quant-ph/000903
Simple Realization Of The Fredkin Gate Using A Series Of Two-body Operators
The Fredkin three-bit gate is universal for computational logic, and is
reversible. Classically, it is impossible to do universal computation using
reversible two-bit gates only. Here we construct the Fredkin gate using a
combination of six two-body reversible (quantum) operators.Comment: Revtex 3.0, 7 pages, 3 figures appended at the end, please refer to
the comment lines at the beginning of the manuscript for reasons of
replacemen
Quantum data processing and error correction
This paper investigates properties of noisy quantum information channels. We
define a new quantity called {\em coherent information} which measures the
amount of quantum information conveyed in the noisy channel. This quantity can
never be increased by quantum information processing, and it yields a simple
necessary and sufficient condition for the existence of perfect quantum error
correction.Comment: LaTeX, 20 page
On classical models of spin
The reason for recalling this old paper is the ongoing discussion on the
attempts of circumventing certain assumptions leading to the Bell theorem
(Hess-Philipp, Accardi). If I correctly understand the intentions of these
Authors, the idea is to make use of the following logical loophole inherent in
the proof of the Bell theorem: Probabilities of counterfactual events A and A'
do not have to coincide with actually measured probabilities if measurements of
A and A' disturb each other, or for any other fundamental reason cannot be
performed simulaneously. It is generally believed that in the context of
classical probability theory (i.e. realistic hidden variables) probabilities of
counterfactual events can be identified with those of actually measured events.
In the paper I give an explicit counterexample to this belief. The "first
variation" on the Aerts model shows that counterfactual and actual problems
formulated for the same classical system may be unrelated. In the model the
first probability does not violate any classical inequality whereas the second
does. Pecularity of the Bell inequality is that on the basis of an in principle
unobservable probability one derives probabilities of jointly measurable random
variables, the fact additionally obscuring the logical meaning of the
construction. The existence of the loophole does not change the fact that I was
not able to construct a local model violating the inequality with all the other
loopholes eliminated.Comment: published as Found. Phys. Lett. 3 (1992) 24
Effects of motion in cavity QED
We consider effects of motion in cavity quantum electrodynamics experiments
where single cold atoms can now be observed inside the cavity for many Rabi
cycles. We discuss the timescales involved in the problem and the need for good
control of the atomic motion, particularly the heating due to exchange of
excitation between the atom and the cavity, in order to realize nearly unitary
dynamics of the internal atomic states and the cavity mode which is required
for several schemes of current interest such as quantum computing. Using a
simple model we establish ultimate effects of the external atomic degrees of
freedom on the action of quantum gates. The perfomance of the gate is
characterized by a measure based on the entanglement fidelity and the motional
excitation caused by the action of the gate is calculated. We find that schemes
which rely on adiabatic passage, and are not therefore critically dependent on
laser pulse areas, are very much more robust against interaction with the
external degrees of freedom of atoms in the quantum gate.Comment: 10 pages, 5 figures, REVTeX, to be published in Walls Symposium
Special Issue of Journal of Optics
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