303 research outputs found
Comparison of mixed quantum states
In this article, we study the problem of comparing mixed quantum states:
given unknown mixed quantum states, can one determine whether they are
identical or not with an unambiguous quantum measurement? We first study
universal comparison of mixed quantum states, and prove that this task is
generally impossible to accomplish. Then, we focus on unambiguous comparison of
mixed quantum states arbitrarily chosen from a set of mixed quantum
states. The condition for the existence of an unambiguous measurement operator
which can produce a conclusive result when the unknown states are actually the
same and the condition for the existence of an unambiguous measurement operator
when the unknown states are actually different are studied independently. We
derive a necessary and sufficient condition for the existence of the first
measurement operator, and a necessary condition and two sufficient conditions
for the second. Furthermore, we find that the sufficiency of the necessary
condition for the second measurement operator has simple and interesting
dependence on and . At the end, a unified condition is obtained for the
simultaneous existence of these two unambiguous measurement operators.Comment: 9 page
Random unitary dynamics of quantum networks
We investigate the asymptotic dynamics of quantum networks under repeated
applications of random unitary operations. It is shown that in the asymptotic
limit of large numbers of iterations this dynamics is generally governed by a
typically low dimensional attractor space. This space is determined completely
by the unitary operations involved and it is independent of the probabilities
with which these unitary operations are applied. Based on this general feature
analytical results are presented for the asymptotic dynamics of arbitrarily
large cyclic qubit networks whose nodes are coupled by randomly applied
controlled-NOT operations.Comment: 4 pages, 2 figure
Perfect transfer of multiple excitations in quantum networks
We present a general formalism to the problem of perfect state-transfer
(PST), where the state involves multiple excitations of the quantum network. A
key feature of our formalism is that it allows for inclusion of nontrivial
interactions between the excitations. Hence, it is perfectly suited to
addressing the problem of PST in the context of various types of physical
realizations. The general formalism is also flexible enough to account for
situations where multiple excitations are "focused" onto the same site.Comment: close to the version published in Phys. Rev. A. In version 2, a typo
has been corrected in Sec. III
Complex chaos in conditional qubit dynamics and purification protocols
Selection of an ensemble of equally prepared quantum systems, based on
measurements on it, is a basic step in quantum state purification. For an
ensemble of single qubits, iterative application of selective dynamics has been
shown to lead to complex chaos, which is a novel form of quantum chaos with
true sensitivity to the initial conditions. The Julia set of initial valuse
with no convergence shows a complicated structre on the complex plane. The
shape of the Julia set varies with the parameter of the dynamics. We present
here results for the two qubit case demonstrating how a purification process
can be destroyed with chaotic oscillations
Complex chaos in the conditional dynamics of qubits
We analyze the consequences of iterative measurement-induced nonlinearity on
the dynamical behavior of qubits. We present a one-qubit scheme where the
equation governing the time evolution is a complex-valued nonlinear map with
one complex parameter. In contrast to the usual notion of quantum chaos,
exponential sensitivity to the initial state occurs here. We calculate
analytically the Lyapunov exponent based on the overlap of quantum states, and
find that it is positive. We present a few illustrative examples of the
emerging dynamics.Comment: 4 pages, 3 figure
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