22,190 research outputs found
A model of adaptive decision making from representation of information environment by quantum fields
We present the mathematical model of decision making (DM) of agents acting in
a complex and uncertain environment (combining huge variety of economical,
financial, behavioral, and geo-political factors). To describe interaction of
agents with it, we apply the formalism of quantum field theory (QTF). Quantum
fields are of the purely informational nature. The QFT-model can be treated as
a far relative of the expected utility theory, where the role of utility is
played by adaptivity to an environment (bath). However, this sort of
utility-adaptivity cannot be represented simply as a numerical function. The
operator representation in Hilbert space is used and adaptivity is described as
in quantum dynamics. We are especially interested in stabilization of solutions
for sufficiently large time. The outputs of this stabilization process,
probabilities for possible choices, are treated in the framework of classical
DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism
(QBism). We demonstrate the quantum-like interference effect in DM which is
exhibited as a violation of the formula of total probability and hence the
classical Bayesian inference scheme.Comment: in press in Philosophical Transactions
Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication
This paper studies the difficulty of discriminating between an arbitrary
quantum channel and a "replacer" channel that discards its input and replaces
it with a fixed state. We show that, in this particular setting, the most
general adaptive discrimination strategies provide no asymptotic advantage over
non-adaptive tensor-power strategies. This conclusion follows by proving a
quantum Stein's lemma for this channel discrimination setting, showing that a
constant bound on the Type I error leads to the Type II error decreasing to
zero exponentially quickly at a rate determined by the maximum relative entropy
registered between the channels. The strong converse part of the lemma states
that any attempt to make the Type II error decay to zero at a rate faster than
the channel relative entropy implies that the Type I error necessarily
converges to one. We then refine this latter result by identifying the optimal
strong converse exponent for this task. As a consequence of these results, we
can establish a strong converse theorem for the quantum-feedback-assisted
capacity of a channel, sharpening a result due to Bowen. Furthermore, our
channel discrimination result demonstrates the asymptotic optimality of a
non-adaptive tensor-power strategy in the setting of quantum illumination, as
was used in prior work on the topic. The sandwiched Renyi relative entropy is a
key tool in our analysis. Finally, by combining our results with recent results
of Hayashi and Tomamichel, we find a novel operational interpretation of the
mutual information of a quantum channel N as the optimal type II error exponent
when discriminating between a large number of independent instances of N and an
arbitrary "worst-case" replacer channel chosen from the set of all replacer
channels.Comment: v3: 35 pages, 4 figures, accepted for publication in Communications
in Mathematical Physic
Quantum system characterization with limited resources
The construction and operation of large scale quantum information devices
presents a grand challenge. A major issue is the effective control of coherent
evolution, which requires accurate knowledge of the system dynamics that may
vary from device to device. We review strategies for obtaining such knowledge
from minimal initial resources and in an efficient manner, and apply these to
the problem of characterization of a qubit embedded into a larger state
manifold, made tractable by exploiting prior structural knowledge. We also
investigate adaptive sampling for estimation of multiple parameters
Multiple copy 2-state discrimination with individual measurements
We address the problem of non-orthogonal two-state discrimination when
multiple copies of the unknown state are available. We give the optimal
strategy when only fixed individual measurements are allowed and show that its
error probability saturates the collective (lower) bound asymptotically. We
also give the optimal strategy when adaptivity of individual von Neumann
measurements is allowed (which requires classical communication), and show that
the corresponding error probability is exactly equal to the collective one for
any number of copies. We show that this strategy can be regarded as Bayesian
updating.Comment: 5 pages, RevTe
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