4,636 research outputs found
Entanglement properties of multipartite entangled states under the influence of decoherence
We investigate entanglement properties of multipartite states under the
influence of decoherence. We show that the lifetime of (distillable)
entanglement for GHZ-type superposition states decreases with the size of the
system, while for a class of other states -namely all graph states with
constant degree- the lifetime is independent of the system size. We show that
these results are largely independent of the specific decoherence model and are
in particular valid for all models which deal with individual couplings of
particles to independent environments, described by some quantum optical master
equation of Lindblad form. For GHZ states, we derive analytic expressions for
the lifetime of distillable entanglement and determine when the state becomes
fully separable. For all graph states, we derive lower and upper bounds on the
lifetime of entanglement. To this aim, we establish a method to calculate the
spectrum of the partial transposition for all mixed states which are diagonal
in a graph state basis. We also consider entanglement between different groups
of particles and determine the corresponding lifetimes as well as the change of
the kind of entanglement with time. This enables us to investigate the behavior
of entanglement under re-scaling and in the limit of large (infinite) number of
particles. Finally we investigate the lifetime of encoded quantum superposition
states and show that one can define an effective time in the encoded system
which can be orders of magnitude smaller than the physical time. This provides
an alternative view on quantum error correction and examples of states whose
lifetime of entanglement (between groups of particles) in fact increases with
the size of the system.Comment: 27 pages, 11 figure
A Quantum to Classical Phase Transition in Noisy Quantum Computers
The fundamental problem of the transition from quantum to classical physics
is usually explained by decoherence, and viewed as a gradual process. The study
of entanglement, or quantum correlations, in noisy quantum computers implies
that in some cases the transition from quantum to classical is actually a phase
transition. We define the notion of entanglement length in -dimensional
noisy quantum computers, and show that a phase transition in entanglement
occurs at a critical noise rate, where the entanglement length transforms from
infinite to finite. Above the critical noise rate, macroscopic classical
behavior is expected, whereas below the critical noise rate, subsystems which
are macroscopically distant one from another can be entangled.
The macroscopic classical behavior in the super-critical phase is shown to
hold not only for quantum computers, but for any quantum system composed of
macroscopically many finite state particles, with local interactions and local
decoherence, subjected to some additional conditions.
This phenomenon provides a possible explanation to the emergence of classical
behavior in such systems. A simple formula for an upper bound on the
entanglement length of any such system in the super-critical phase is given,
which can be tested experimentally.Comment: 15 pages. Latex2e plus one figure in eps fil
Stability of macroscopic entanglement under decoherence
We investigate the lifetime of macroscopic entanglement under the influence
of decoherence. For GHZ-type superposition states we find that the lifetime
decreases with the size of the system (i.e. the number of independent degrees
of freedom) and the effective number of subsystems that remain entangled
decreases with time. For a class of other states (e.g. cluster states),
however, we show that the lifetime of entanglement is independent of the size
of the system.Comment: 5 pages, 1 figur
Finite-time quantum-to-classical transition for a Schroedinger-cat state
The transition from quantum to classical, in the case of a quantum harmonic
oscillator, is typically identified with the transition from a quantum
superposition of macroscopically distinguishable states, such as the
Schr\"odinger cat state, into the corresponding statistical mixture. This
transition is commonly characterized by the asymptotic loss of the interference
term in the Wigner representation of the cat state. In this paper we show that
the quantum to classical transition has different dynamical features depending
on the measure for nonclassicality used. Measures based on an operatorial
definition have well defined physical meaning and allow a deeper understanding
of the quantum to classical transition. Our analysis shows that, for most
nonclassicality measures, the Schr\"odinger cat dies after a finite time.
Moreover, our results challenge the prevailing idea that more macroscopic
states are more susceptible to decoherence in the sense that the transition
from quantum to classical occurs faster. Since nonclassicality is prerequisite
for entanglement generation our results also bridge the gap between
decoherence, which appears to be only asymptotic, and entanglement, which may
show a sudden death. In fact, whereas the loss of coherences still remains
asymptotic, we have shown that the transition from quantum to classical can
indeed occur at a finite time.Comment: 9+epsilon pages, 4 figures, published version. Originally submitted
as "Sudden death of the Schroedinger cat", a bit too cool for APS policy :-
Quantum speedup of classical mixing processes
Most approximation algorithms for #P-complete problems (e.g., evaluating the
permanent of a matrix or the volume of a polytope) work by reduction to the
problem of approximate sampling from a distribution over a large set
. This problem is solved using the {\em Markov chain Monte Carlo} method: a
sparse, reversible Markov chain on with stationary distribution
is run to near equilibrium. The running time of this random walk algorithm, the
so-called {\em mixing time} of , is as shown
by Aldous, where is the spectral gap of and is the minimum
value of . A natural question is whether a speedup of this classical
method to , the diameter of the graph
underlying , is possible using {\em quantum walks}.
We provide evidence for this possibility using quantum walks that {\em
decohere} under repeated randomized measurements. We show: (a) decoherent
quantum walks always mix, just like their classical counterparts, (b) the
mixing time is a robust quantity, essentially invariant under any smooth form
of decoherence, and (c) the mixing time of the decoherent quantum walk on a
periodic lattice is , which is indeed
and is asymptotically no worse than the
diameter of (the obvious lower bound) up to at most a logarithmic
factor.Comment: 13 pages; v2 revised several part
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