43 research outputs found
Quantum speed limit for noisy dynamics
The laws of quantum physics place a limit on the speed of computation, in
particular the evolution time of a system cannot be arbitrarily fast. Bounds on
the speed of evolution for unitary dynamics have been long studied. A few
bounds on the speed of evolution for noisy dynamics have also been obtained
recently, these bounds, however, are in general not tight. In this article we
present a new framework for quantum speed limit of noisy dynamics. With this
framework we obtain the exact maximal angle that a noisy dynamics can achieve
at any given time, this then provides tight bounds on the evolution time for
noisy dynamics. The obtained bound reveals that noisy dynamics are generically
different from unitary dynamics, in particular we show that the
'orthogonalization' time, which is the minimum time needed to evolve any state
to its orthogonal states, is in general not applicable to noisy dynamics.Comment: 6 pages. Comments are welcom
Disguising quantum channels by mixing and channel distance trade-off
We consider the reverse problem to the distinguishability of two quantum
channels, which we call the disguising problem. Given two quantum channels, the
goal here is to make the two channels identical by mixing with some other
channels with minimal mixing probabilities. This quantifies how much one
channel can disguise as the other. In addition, the possibility to trade off
between the two mixing probabilities allows one channel to be more preserved
(less mixed) at the expense of the other. We derive lower- and upper-bounds of
the trade-off curve and apply them to a few example channels. Optimal trade-off
is obtained in one example. We relate the disguising problem and the
distinguishability problem by showing the the former can lower and upper bound
the diamond norm. We also show that the disguising problem gives an upper bound
on the key generation rate in quantum cryptography.Comment: 27 pages, 8 figures. Added new results for using the disguising
problem to lower and upper bound the diamond norm and to upper bound the key
generation rate in quantum cryptograph
Time-Energy Costs of Quantum Measurements
Time and energy of quantum processes are a tradeoff against each other. We
propose to ascribe to any given quantum process a time-energy cost to quantify
how much computation it performs. Here, we analyze the time-energy costs for
general quantum measurements, along a similar line as our previous work for
quantum channels, and prove exact and lower bound formulae for the costs. We
use these formulae to evaluate the efficiencies of actual measurement
implementations. We find that one implementation for a Bell measurement is
optimal in time-energy. We also analyze the time-energy cost for unambiguous
state discrimination and find evidence that only a finite time-energy cost is
needed to distinguish any number of states.Comment: 10 pages, 6 figure
Time-Energy Measure for Quantum Processes
Quantum mechanics sets limits on how fast quantum processes can run given
some system energy through time-energy uncertainty relations, and they imply
that time and energy are tradeoff against each other. Thus, we propose to
measure the time-energy as a single unit for quantum channels. We consider a
time-energy measure for quantum channels and compute lower and upper bounds of
it using the channel Kraus operators. For a special class of channels (which
includes the depolarizing channel), we can obtain the exact value of the
time-energy measure. One consequence of our result is that erasing quantum
information requires times more time-energy resource than
erasing classical information, where is the system dimension.Comment: 13 pages, 2 figure