562 research outputs found
Reverse test and quantum analogue of classical fidelity and generalized fidelity
The aim of the present paper is to give axiomatic characterization of quantum
relative entropy utilizing resource conversion scenario. We consider two sets
of axioms: non-asymptotic and asymptotic. In the former setting, we prove that
the upperbound and the lowerbund of D^{Q}({\rho}||{\sigma}) is
D^{R}({\rho}||{\sigma}):=tr{\rho}ln{\sigma}^{1/2}{\rho}^{-1}{\sigma}^{1/2} and
D({\rho}||{\sigma}):= tr{\rho}(ln{\rho}-ln{\sigma}), respectively. In the
latter setting, we prove uniqueness of quantum relative entropy, that is,
D^{Q}({\rho}||{\sigma}) should equal a constant multiple of
D({\rho}||{\sigma}). In the analysis, we define and use reverse test and
asymptotic reverse test, which are natural inverse of hypothesis test.Comment: A new proof of joint convexity of is added. Also, some
technical correction, Title change
Reverse estimation theory, Complementality between RLD and SLD, and monotone distances
Many problems in quantum information theory can be vied as interconversion
between resources. In this talk, we apply this view point to state estimation
theory, motivated by the following observations.
First, a monotone metric takes value between SLD and RLD Fisher metric. This
is quite analogous to the fact that entanglement measures are sandwiched by
distillable entanglement and entanglement cost. Second, SLD add RLD are
mutually complement via purification of density matrices, but its operational
meaning was not clear.
To find a link between these observations, we define reverse estimation
problem, or simulation of quantum state family by probability distribution
family, proving that RLD Fisher metric is a solution to local reverse
estimation problem of quantum state family with 1-dim parameter. This result
gives new proofs of some known facts and proves one new fact about monotone
distances.
We also investigate information geometry of RLD, and reverse estimation
theory of a multi-dimensional parameter family.Comment: Submitted to QIT. Full is in prepareatio
On interaction-free measurement
This manuscript is inspired by the paper [2]. In the paper, they investigate
a method to detect existence of an object with arbitrarily small interaction.
Below, we sketch their protocol to motivate the present manuscript. The object
of their protocol is to detect whether the given blackbox interact with input
states or not, with negligible distortion of the blackbox, and high detection
probability. In this paper, we do two things. First, we prove the above
mentioned protocol is optimal in a certain setting. The main tool here is
adversary method, a classical method in query complexity. Second, we present a
protocol to detect unitary operations with negligible error and no distortion
of the input at all
Convertibility of Observables
Some problems of quantum information, cloning, estimation and testing of
states, universal coding etc., are special example of the following `state
convertibility' problem. In this paper, we consider the dual of this problem,
'observable conversion problem'. Given families of operators
\{L_\theta}\}_{\theta\in\Theta} and \{M_\theta}\}_{\theta\in\Theta} , we
ask whether there is a completely positive (sub) unital map which sends
\{L_\theta}\} to \{M_\theta}\} for each {\theta}. We give necessary and
sufficient conditions for the convertibility in some special cases
On maximization of measured -divergence between a given pair of quantum states
This paper deals with maximization of classical -divergence between the
distributions of a measurement outputs of a given pair of quantum states.
-divergence between the probability density functions and
over a discrete set is defined as . For example,
Kullback-Leibler divergence and Renyi type relative entropy are well-known
examples with good operational meanings. Thus, finding the maximal value
of measured measured -divergence is also an interesting
question. But so far the question is solved only for very restricted example of
. \ The purposes of the present paper is to advance the study further, by
investigating its properties, rewriting the maximization problem to more
tractable form, and giving closed formulas of the quantity in some special
cases
On the First Order Asymptotic Theory of Quantum Estimation
We give a rigorous treatment on the foundation of the first order asymptotic
theory of quantum estimation, with tractable and reasonable regularity
conditions. Different from past works, we do not use Fisher information nor
MLE, and an optimal estimator is constructed based on locally unbiased
estimators. Also, we treat state estimation by local operations and classical
communications (LOCC), and estimation of quantum operations.Comment: dedicated to Prof. Masafumi Akahir
The monodromy representations of local systems associated with Lauricella's
We give the monodromy representations of local systems of twisted homology
groups associated with Lauricella's system of hypergeometric
differential equations under mild conditions on parameters. Our representation
is effective even in some cases when the system is reducible. We
characterize invariant subspaces under our monodromy representations by the
kernel or image of a natural map from a finite twisted homology group to
locally finite one.Comment: 18 pages, 1 figur
Pfaffian of Lauricella's hypergeometric system
We give a Pfaffian system of differential equations annihilating Lauricella's
hypergeometric series of -variables. This system is
integrable of rank . To express the connection form of this system, we
make use of the intersection form of twisted cohomology groups with respect to
integrals representing solutions of this system.Comment: 14 page
Reverse Test and Characterization of Quantum Relative Entropy
The aim of the present paper is to give axiomatic characterization of quantum
relative entropy utilizing resource conversion scenario. We consider two sets
of axioms: non-asymptotic and asymptotic. In the former setting, we prove that
the upperbound and the lowerbund of is
and
, respectively. In the latter setting,
we prove uniqueness of quantum relative entropy, that is,
should equal a constant multiple of
. In the analysis, we define and use reverse test
and asymptotic reverse test, which are natural inverse of hypothesis test
Self-teleportation and its application on LOCC estimation and other tasks
A way to characterize quantum nonlocality is to see difference in the figure
of merit between LOCC optimal protocol and globally optimal protocol in doing
certain task, e.g., state estimation, state discrimination, cloning and
broadcasting. Especially, we focus on the case where tensor of unknown
states.
Our conclusion is that separable pure states are more non-local than
entangled pure states. More specifically, the difference in the figure of the
merit is exponentially small if the state is entangled, and the exponent is log
of the largest Schmidt coefficient. On the other hand, in many cases,
estimation of separable states by LOCC is worse than the global optimal
estimate by .
To show that the gap is exponentially small for entangled states, we propose
self-teleportation protocol as the key component of construct of LOCC
protocols. Objective of the protocol is to transfer Alice's part of quantum
information by LOCC, using intrinsic entanglement of without using any extra resources. This protocol itself is of
interest in its own right
- …