8,639 research outputs found
Optimized maximum-confidence discrimination of N mixed quantum states and application to symmetric states
We study an optimized measurement which discriminates N mixed quantum states
occurring with given prior robabilities. The measurement yields the maximum
achievable confidence for each of the N conclusive outcomes, thereby keeping
the overall probability of inconclusive outcomes as small as possible. It
corresponds to optimum unambiguous discrimination when for each outcome the
confidence is equal to unity. Necessary and sufficient optimality conditions
are derived and general properties of the optimum measurement are obtained. The
results are applied to the optimized maximum-confidence discrimination of N
equiprobable symmetric mixed states. Analytical solutions are presented for a
number of examples, including the discrimination of N symmetric pure states
spanning a d-dimensional Hilbert space (d \leq N) and the discrimination of N
symmetric mixed qubit states.Comment: minor corrections, final versio
Noise-Induced Stabilization of Planar Flows I
We show that the complex-valued ODE
\begin{equation*}
\dot z_t = a_{n+1} z^{n+1} + a_n z^n+\cdots+a_0,
\end{equation*} which necessarily has trajectories along which the dynamics
blows up in finite time, can be stabilized by the addition of an arbitrarily
small elliptic, additive Brownian stochastic term. We also show that the
stochastic perturbation has a unique invariant measure which is heavy-tailed
yet is uniformly, exponentially attracting. The methods turn on the
construction of Lyapunov functions. The techniques used in the construction are
general and can likely be used in other settings where a Lyapunov function is
needed. This is a two-part paper. This paper, Part I, focuses on general
Lyapunov methods as applied to a special, simplified version of the problem.
Part II of this paper extends the main results to the general setting.Comment: Part one of a two part pape
Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination
We consider two different optimized measurement strategies for the
discrimination of nonorthogonal quantum states. The first is conclusive
discrimination with a minimum probability of inferring an erroneous result, and
the second is unambiguous, i. e. error-free, discrimination with a minimum
probability of getting an inconclusive outcome, where the measurement fails to
give a definite answer. For distinguishing between two mixed quantum states, we
investigate the relation between the minimum error probability achievable in
conclusive discrimination, and the minimum failure probability that can be
reached in unambiguous discrimination of the same two states. The latter turns
out to be at least twice as large as the former for any two given states. As an
example, we treat the case that the state of the quantum system is known to be,
with arbitrary prior probability, either a given pure state, or a uniform
statistical mixture of any number of mutually orthogonal states. For this case
we derive an analytical result for the minimum probability of error and perform
a quantitative comparison to the minimum failure probability.Comment: Replaced by final version, accepted for publication in Phys. Rev. A.
Revtex4, 6 pages, 3 figure
Diode pumped Nd:YAG laser development
A low power Nd:YAG laser was constructed which employs GaAs injection lasers as a pump source. Power outputs of 125 mW TEM CW with the rod at 250 K and the pump at 180 K were achieved for 45 W input power to the pump source. Operation of the laser, with array and laser at a common heat sink temperature of 250 K, was inhibited by difficulties in constructing long-life GaAs LOC laser arrays. Tests verified pumping with output power of 20 to 30 mW with rod and pump at 250 K. Although life tests with single LOC GaAs diodes were somewhat encouraging (with single diodes operating as long as 9000 hours without degradation), failures of single diodes in arrays continue to occur, and 50 percent power is lost in a few hundred hours at 1 percent duty factor. Because of the large recent advances in the state of the art of CW room temperature AlGaAs diodes, their demonstrated lifetimes of greater than 5,000 hours, and their inherent advantages for this task, it is recommended that these sources be used for further CW YAG injection laser pumping work
Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results
We study an optimized measurement that discriminates two mixed quantum states
with maximum confidence for each conclusive result, thereby keeping the overall
probability of inconclusive results as small as possible. When the rank of the
detection operators associated with the two different conclusive outcomes does
not exceed unity we obtain a general solution. As an application, we consider
the discrimination of two mixed qubit states. Moreover, for the case of
higher-rank detection operators we give a solution for particular states. The
relation of the optimized measurement to other discrimination schemes is also
discussed.Comment: 7 pages, 1 figure, accepted for publication in Phys. Rev.
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