Dates: 2-4 March, 2009

Place: 12F, National Institute of Informatics (NII), Tokyo, Japan

Organizer: Deepening and Expansion of Statistical Mechanical Informatics (DEX-SMI), Grant-in-Aid for Scientific Research on Priority Areas, MEXT.

- Masahito Hayashi (Chair),
*Tohoku University* - Kae Nemoto,
*NII* - Hiroshi Imai,
*NII* - Keiji Matsumoto,
*NII*

Contact: Masahito Hayashi

**2th, March, 2009**

13:20-13:30 Opening: Masahito Hayashi

13:30-14:15 Masahito Hayashi (Tohoku Univ.)14:25-15:10 Masato Koashi (Osaka Univ.) Fumitaka Takenaga, Takashi Yamamoto, and Nobuyuki Imoto

15:10-15:30 Tea break

15:30-16:15 Miguel Navascues (Imperial College London), Masaki Owari, Martin B. Plenio16:25-16:55 Yutaka Shikano (Tokyo Institute of Technology), Seth Lloyd (MIT), Akio Hosoya (Tokyo Institute of Technology)

16:55-16:15 Tea break

17:15-18:00 Giacomo Mauro D'Ariano (Pavia Univ.)**3rd, March, 2009**

10:45-11:05 Tea break

11:05- 11:50 John Calsamiglia (Universitat Autonoma Barcelona)11:50-13:30 Lunch Time

13:30- 14:15 Masahiro Takeoka (NICT) K. Tsujino, M. Sasaki, C. Wittmann, K. N. Cassemiro, G. Leuchs, and U. L. Andersen14:25-15:10 Emilio Bagan (Universitat Autonoma Barcelona)

15:10-15:30 Tea break

15:30-16:15 Dominic Berry (Macquarie University), B. L. Higgins, H. M. Wiseman, S. D. Bartlett, M. W. Mitchell, and G. J. Pryde16:15-16:35 Tea break

16:35-17:15 Hiroshi Imai (NII), Masahito Hayashi (Tohoku Univ.)17:25-17:50 Yu Matsumoto (Tohoku Univ.), Masahito Hayashi (Tohoku Univ.)

**4th, March, 2009**

10:45-11:05 Tea break

11:05-11:50 Keiji Matsumoto (NII)11:50-13:30 Lunch Time

13:30-14:00 Yu Watanabe (Tokyo Institute of Technology), Takahiro Sagawa (Univ. of Tokyo) and Masahito Ueda (Univ. of Tokyo)14:10-14:55 Akihisa Hayashi (Fukui Univ.)

14:55-15:15 Tea break

15:15-16:00 Paolo Perinotti (Pavia Univ.)16:00-16:45 Giulio Chiribella (Pavia Univ.)

16:45-16:50 Closing remarks

Masahito Hayashi (Tohoku Univ.)

Title: Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
Presentation file

Abstract:
In the asymptotic setting, the optimal test for hypotheses testing of the maximally entangled state is derived under several locality conditions for measurements. The optimal test is obtained in several cases with the asymptotic framework as well as the finite-sample framework. In addition, the experimental scheme for the optimal test is presented.
Related manuscript:
http://arxiv.org/abs/0810.3380

Masato Koashi (Osaka Univ.)
Fumitaka Takenaga, Takashi Yamamoto, and Nobuyuki Imoto

Title: Quantum nonlocality without entanglement in a pair of qubits

Abstract:
We consider unambiguous discrimination of two separable bipartite
states, one being pure and the other being a rank-2 mixed state.
There is a gap between the optimal success probability under global
measurements and the one achieved by generalized measurements with
separable measurement operators. We show that even the latter success
probability cannot be achieved via local operations and classical
communication, leaving a nonzero gap in between.

Related manuscript:
http://arxiv.org/abs/0709.3196

Miguel Navascues (Imperial College London) Masaki Owari, Martin B. Plenio

Title: Merging state estimation and entanglement theory

Abstract: In this talk, I will try to convince the audience that there exists a
connection between state estimation and entanglement theory from which
both fields can mutually benefit. On one hand, I will use recent results
on probabilistic state estimation in order to analyze the speed of
convergence of the Doherty-Parrilo-Spedalieri (DPS) criterion for
entanglement detection. More concretely, I will show how to derive non
trivial upper bounds for the distance between the states returned by the
computer and the set of separable states, in terms of trace distance,
operator norm distance and entanglement robustness. On the other hand, I
will show how the DPS criterion can be applied to provide two converging
numerical sequences of upper and lower bounds for the optimal fidelity
in any pure state estimation problem.

Yutaka Shikano (Tokyo Institute of Technology), Seth Lloyd (MIT), Akio Hosoya (Tokyo Institute of Technology)

Title: Optimal Quantum Covariant Clock

Abstract:
We cannot measure time directly but we can measure a clock and then
infer the time from the position of the hand we read. This feature of
measuring time is more acute in quantum mechanics because there is no
self-adjoint time operator if the Hamiltonian is bounded below. The time
in the Schroedinger equation is only a parameter but not a physical
observable. Any physical object can be a clock but its quality may vary.
It is reasonable to consider a clock is good if it has a high precision
and its accuracy is maintained for a long time. We are going to explore
the best quantum clock of the highest possible precision given a finite
energy range, which keeps accuracy in an arbitrarily long time passage.

Giacomo Mauro D'Ariano (Pavia Univ.)

Title: Probabilistic theories: what is special about Quantum Mechanics?
Presentation file

Abstract:
Quantum Mechanics (QM) is a very special probabilistic theory, yet we don't know which operational principles make it so. Here I will analyze the possibility of deriving QM as the mathematical representation of a "fair operational framework", i.e. a set of rules which allows the experimenter to make predictions on future "events" on the basis of suitable "tests", e.g. without interferences from uncontrollable sources. Two postulates need to be satisfied by any fair operational framework: NSF: "no-signaling from the future" (for the possibility of making predictions on the basis of past tests) FAITH: "existence of faithful states" (for the possibility of calibrating all tests and of preparing any state). I will show that all theories satisfying NSF admit a C*-algebra representation of events as linear transformations of effects. Based on a very general notion of dynamical independence, it is easy to see that all such probabilistic theories are "no-signaling without interaction" (shortly "no-signaling")--another requirement for a fair operational framework. Postulate FAITH then implies the "local observability principle", along with the tensor-product structure for the linear spaces of states and effects.
What is special about QM is that also "effects make a C*-algebra. However, whereas the sum of effects can be operationally defined, the notion of effect abhors any kind of composition. Based on another very natural postulate--AE: atomicity of evolution--along with a purely mathematical postulate--CJ: Choi-Jamiolkowski isomorphism--it is possible to identify effects with atomic events, through which we can then define composition.

Related manuscript:
http://arxiv.org/abs/0807.4383([v3] Tue, 31 Mar 2009)
appear in "Philosophy of Quantum Information and Entanglement" Eds A. Bokulich and G. Jaeger (Cambridge University Press, Cambridge UK)

Masaki Owari (Imperial College London), M. B. Plenio, E. S. Polzik, A. Serafini, M. M. Wolf

Title: Squeezing the limit: Quantum benchmarks for the teleportation and storage of squeezed states
Presentation file

Abstract:
We derive fidelity benchmarks for the quantum storage and
teleportation of squeezed states of continuous variable systems, for input
ensembles where the degree of squeezing $s$ is fixed, no information about
its orientation in phase space is given, and the distribution of phase space
displacements is a Gaussian. In the limit where the latter becomes flat, we
prove analytically that the maximal classical achievable fidelity (which is
1/2 without squeezing, for $s=1$) is given by $\sqrt{s}/(1+s)$, vanishing
when the degree of squeezing diverges. For mixed states, as well as for
general distributions of displacements, we reduce the determination of the
benchmarks to the solution of a finite-dimensional semidefinite program,
which yields accurate, certifiable bounds thanks to a rigorous analysis of
the truncation error. This approach may be easily adapted to more general
ensembles of input states.

Related manuscript: New Journal of Physics, vol. 10, 113014, (2008)
http://arxiv.org/abs/0808.2260

John Calsamiglia (Universitat Autonoma Barcelona)

Title: Phase-Covariant Quantum Benchmarks for Quantum Storage and Teleportation
Presentation file

Abstract: We give a quantum benchmark for teleportation and quantum
storage experiments suited for pure and mixed test states. The
benchmark is based on the average fidelity over a family of phase-
covariant states and certifies that an experiment can not be emulated
by a classical setup, i.e., by a measure-and-prepare scheme. We give
an analytical solution for qubits, which shows important differences
with standard state estimation approach, and compute the value of the
benchmark for coherent and squeezed states, both pure and mixed.

Related manuscript:
http://arxiv.org/abs/0807.5126

Title: Experimental implementation of near-optimal quantum measurements of optical coherent state Presentation file

Abstract: The optimal discrimination of optical coherent states is a fundamental task in quantum information theory as well as an important primitive in optical communication. We propose and experimentally demonstrate a new and simple near-optimal quantum measruement strategy capable of discriminating two coherent states with smaller average error probability than the homodyne detection. Our proof-of-principle experiment clearly shows the lower error probability than that of the homodyne limit after compensating quantum efficiency (QE) of the photon detector. We discuss the necessary QE to truly outperform the homodyne limit without compensating experimental imperfections and show that it is feasible with the current technology.

As a related topic, we discuss alternative figures of merit to evaluate the classical communication performance, that is reliability function and its cut-off rate. Interestingly, a variety of quantum measurements can attain the maximum (single-shot) cut-off rate while some of them are not optimal from the viewpoints of average error probability or mutual information.

Related manuscripts:

http://arxiv.org/abs/0809.4953 [Phys. Rev. Lett. 101, 210501 (2008)]

http://arxiv.org/abs/0706.1038 [Phys. Rev. A 78, 022320 (2008)]

Emilio Bagan (Universitat Autonoma Barcelona)

Title: Phase eatimation with thermal Gaussian states
Presentation file

Abstract:
We consider two classes of Gaussian states: displaced thermal states
and squeezed thermal states; to perform phase estimation. We find that
while for displaced thermal states an increase in temperature gives
rise to a reduction in the precision, for squeezed thermal states it
goes the other way around. In the multiple-copy scenario we analyze
the most paradigmatic measurement strategies (including homodyne and
heterodyne measurements) and discuss their performance as compared to
the optimal schemes. We apply our results to investigate the influence
of losses in an optical metrology experiment.

Related manuscript:
http://arxiv.org/abs/0811.3408

Dominic Berry (Macquarie University), B. L. Higgins, H. M. Wiseman, S. D. Bartlett, M. W. Mitchell, and G. J. Pryde

Title: Phase Measurements at the Theoretical Limit
Presentation file

Abstract:
The interferometric measurement of optical phase is a vital tool for precision measurement. The performance of phase measurements is usually quantified by how the uncertainty scales in terms of the number of resources, N. Standard measurement techniques result in an uncertainty scaling as O(1/sqrt(N)) _ the standard quantum limit (SQL). In contrast, the fundamental limit on phase measurements is the Heisenberg limit of O(1/N). The SQL results from the independent use of resources, so methods of beating the SQL usually involve special nonclassical resource states, such as squeezed states or NOON_ states. Similar results can also be obtained using multiple passes of single photons.

Problems with using nonclassical states or multiple passes are that they may only work over a small range of phases, require initial knowledge of the phase or give ambiguous phase information. We have developed a range of techniques to eliminate these problems, providing unambiguous phase measurements with accuracy close to the theoretical limit. We have experimentally demonstrated a scheme that uses an adaptive technique and multiple passes of single photons to implement the quantum phase estimation algorithm (QPEA), as well as a generalised form of this algorithm.

The QPEA only achieves the SQL due to fat tails in the distribution. Simply combining the QPEA with standard measurements can improve the scaling, although not achieve the theoretical limit. In contrast, our generalised scheme uses multiple measurements to eliminate the fat tails, and achieve the theoretical limit with an overhead factor of only about 1.6. We have now further improved this scheme to achieve the theoretical limit without requiring adaptation, albeit with a slightly increased overhead factor of about 2. Reducing or removing adaptive measurements should make practical implementation of precision phase estimation far easier.

Hiroshi Imai (NII), Masahito Hayashi (Tohoku Univ.)

Title: Fourier Analytic Approach to Phase Estimation
Presentation file

Abstract:
For a unified analysis on the phase estimation, we focus on the limiting distribution. It is shown that the limiting distribution can be given by the absolute square of the Fourier transform of $L^2$ function whose support belongs to $[-1,1]$. Using this relation, we study the relation between the variance of the limiting distribution and its tail probability. As our result, we prove that the protocol minimizing the asymptotic variance does not minimize the tail probability. Depending on the width of interval, we derive the estimation protocol minimizing the tail probability out of a given interval. Such an optimal protocol is given by a prolate spheroidal wave function which often appears in wavelet or time-limited Fourier analysis. Also, the minimum confidence interval is derived with the framework of interval estimation that assures a given confidence coefficient.

http://arxiv.org/abs/0810.5602

Yu Matsumoto (Tohoku Univ.), Masahito Hayashi (Tohoku Univ.)

Title: Identification of rotation axis in Bloch Sphere

Abstract:

Madalin Guta (Nottingham Univ.)

Title: Local asymptotic normality in quantum statistics
Presentation file

Abstract:
Quantum statistics deals with the processing of statistical
information carried by quantum systems. One of the central problems
in quantum statistics is that of estimating an unknown quantum state
by performing general measurements on a (large) number of identically
prepared quantum systems.

We will show how to optimally estimate a completely unknown quantum
state by developing the quantum analogue of the classical statistical
concept of "local asymptotic normality".

The latter means that the statistical model described by the
collective state of n identically prepared quantum systems converges
in a statistical sense to a model consisting of a classical Gaussian
model and a quantum Gaussian state of d(d-1)/2 harmonic oscillators.
Both Gaussian models have fixed variance and unknown mean which can
be easily estimated by means of standard (heterodyne/homodyne)
measurements. This optimal measurement can be pulled back to an
optimal strategy for estimating the quantum state.

http://arxiv.org/abs/0804.3876

Keiji Matsumoto (NII)

Title: Monotone metrics on quantum channels

Abstract:

Yu Watanabe (Tokyo Institute of Technology), Takahiro Sagawa (Univ. of Tokyo) and Masahito Ueda (Univ. of Tokyo)

Title: Visualization of Quantum Operations
Presentation file

Abstract:
Recently many technologies of controlling quantum states have
developed. In particular, methods
of transferring arbitrary quantum states from one system to another have
been proposed and some of
them have been experimentally implemented. These technologies are important
for making quantum
computers and quantum networks. However there is no general measure of
accuracy of transferring
quantum states which can be applied for any experimental results.

By considering some examples, we relate the accuracy of transferring
quantum states to that of
estimating input states from output states. The accuracy of estimation is
measured by Fisher information.
We think that we can characterize any quantum operations (which is a
mathematical formulation of
quantum state transformations) by using Fisher information. In this talk,
we introduce Fisher
information for estimating input states from output states of any quantum
operations and propose
a method of visualizing quantum operation by quantifying the information.

Akihisa Hayashi (Fukui Univ.)

Title: Unitary process discrimination with error margin
Presentation file

Abstract: Unitary process discrimination with general error margin m is considered.
This interpolates two standard discrimination problems, minium-error
discrimination for m=1 and unambiguous discrimination for m=0.
We will report two solvable cases: discrimination between two unitary
processes
and discrimination among unitary processes generated by a group
projective representation.

Paolo Perinotti (Pavia Univ.)

Title: Estimation and discrimination of quantum networks
Presentation file

Abstract:
We review the theory of quantum combs for description of quantum
networks,
and the theory of testers for measurements of network parameters.
After an overview
of the problems that can be tackled by means of the new theoretical
framework,
we show three important results recently obtained through its
application.

The first problem is optimal discrimination of two transformations
with a finite number of
available uses. The measuring party has a fixed number of identical
black boxes that perform
one unknown transformation and must determine what transformation the
single black box
performs, out of two. In this case the theory simplifies the problem
of taking into account
all possible dispositions of black boxes, (e. g. in parallel or in a
sequence), and provides the
ultimate solution in the case of unitary transformations.

The second problem is optimal covariant estimation of unitary channels
having a finite
number of available uses. This problem is similar to the first one,
but here the possible transformations
are the whole unitary representation of a group. In this case the
theory allows to prove under very general
hypotheses that the parallel disposition is always optimal.

The third problem is optimal tomography of channels and quantum
operations. One wants an experimental
scheme that allows to reconstruct the unknown and completely free
input/output transformation performed
by a black box, using it and measuring it an arbitrary number of
times, independently. Also in this case the
optimal setup can be derived exploiting the general theory, providing
a solution that exhibits some non trivial
aspects that will be discussed.

Related manuscripts:

[1] G. Chiribella, G. M. D'Ariano, and P. Perinotti, Phys. Rev. Lett.
101, 060401 (2008).
http://arxiv.org/abs/0712.1325

[2] G. Chiribella, G. M. D'Ariano, and P. Perinotti, Phys. Rev. Lett.
101, 180501 (2008).

[3] A. Bisio, G. Chiribella, G. M. D’Ariano, S. Facchini, and P.
Perinotti, Phys. Rev. Lett. 102, 010404 (2009).

Giulio Chiribella (Pavia Univ.)

Title: Optimal quantum learning and multiround reference frame alignment
Presentation file

Abstract:
Quantum combs and testers entail a new paradigm of quantum
information processing where the input of transformations and
measurements are quantum channels rather then states. In this talk,
I will present two remarkable applications of this paradigm. The
first application is the optimal automated learning of an unknown
qubit unitary from a finite training set of N examples. The examples
are first exploited in an optimal storing network, whose output state
is then sent to a retrieving machine that optimally reproduces the
unknown unitary M times. The second application is the optimal
alignment of reference frames with multiple rounds of quantum and
classical communication. In this case, quantum combs and testers
provide a simple proof that the precision of reference frame
alignment only depends on the total number of exchanged qubits, and
that a single round of forward quantum communication is sufficient.

Related manuscripts:

[1] G. Chiribella, G. M. D'Ariano, P. Perinotti, Quantum Circuits
Architecture, Phys. Rev. Lett. 101, 060401 (2008),
http://arxiv.org/abs/0712.1325

[2] G. Chiribella, G. M. D'Ariano, P. Perinotti, Optimal covariant
quantum networks,
http://arxiv.org/abs/0812.3922

[3] A. Bisio, G. Chiribella, G. M. D'Ariano, S. Facchini, and P.
Perinotti, Optimal quantum learning of an unknown qubit unitary, in
preparation