Dates: 11th-12th, February, 2008

Place: Lecture Room (Room 207), 2F Graduate School of Information Sciences, Tohoku University

Organizer: Deepening and Expansion of Statistical Mechanical Informatics (DEX-SMI), Grant-in-Aid for Scientific Research on Priority Areas, MEXT & Graduate School of Information Sciences, Tohoku University

Contact: Masahito Hayashi

10:00-10:50 Emilio Bagan (Universitat Autonoma de Barcelona)

11:00-11:50 Motohisa Fukuda (University of California, Davis)

11:50-13:30 Lunch Time

13:30-14:00 Tokishiro Karasawa (NII)14:10-14:40 Gen Kimura (Tohoku University)

14:50-15:30 Kae Nemoto (NII)

15:30-15:50 Tea Break

15:50-16:30 Satoshi Ishizaka (NEC)16:40-17:30 Giulio Chiribella (University of Pavia)

17:40-18:10 Tsuyoshi Ito (NII)

18:30 - Banquet

9:50-10:30 Ryo Namiki (Osaka University)

10:40-11:10 Akihisa Hayashi (Fukui University)

11:20-12:10 Ramon Munoz Tapia (Universitat Autonoma de Barcelona)

12:10-13:50 Lunch Time

13:50-14:40 John Calsamiglia (Universitat Autonoma de Barcelona)14:50-15:40 Masahito Hayashi (Tohoku University)

15:40-16:00 Tea Break

16:00-16:30 Hiroshi Imai (Osaka Univeristy)16:40-17:30 Milan Mosonyi (Tohoku University)

Title: New results in quantum-limited metrology

Emilio Bagan (Universitat Autonoma de Barcelona)

Abstract: We consider the estimation of an unknown coupling constant in a nonlinear k-body Hamiltonian using n-body system states (k << n). The lowest bound on the uncertainty in these protocols scales as 1/ n^k, for which one is required to prepare the n-body system in a highly entangled state. We show that for initial product states the scaling goes as 1/n^(k-1/2) and can be attained with simple separable measurements. Using a simple model based on the evolution of angular-momentum coherent states, we illustrate these results in the particularly important case of k=2, which can be implemented with Bose-Einstein condensates. We also show that phase decoherence does not change the scaling 1/n^(3/2).

Title: Additivity conjectures, and counterexamples to multiplicativity conjecture by probabilistic approach

Motohisa Fukuda (University of California, Davis)

Abstract: Additivity conjectures play an important role in quantum information theory in the sense that if it is ture we would be able to write the classical capacity over quantum channels by one-shot formula, called the Holevo capacity. In this talk, first, we discuss how the conjectures can reduce to rather simple problems. Secondly, we consider counterexamples to multiplicativity conjecture, which were based on probabilistic argument.

Title: Minimum errors on gate implementations caused by conservation laws

Tokishiro Karasawa (NII)

Abstract: Physical systems of gate implementations in quantum computing generally consist of registers, or qubits, and their ancilla systems which control the qubits to perform quantum gates. It is physically natural to assume that conservation laws are satisfied in the interaction between the qubits and the ancilla systems without assuming any interaction with their environments. However, it has been shown that the conservation laws cause a dynamical decoherence on the qubits. Lower bounds of the error probability for the quantum NOT gate has been obtained by a new method which analyzes the gate trace distance between the output state from a physical implementation under a conservation law and the one from ideal unitary map [T. Karasawa and M. Ozawa, Phys. Rev. A 75, 032324 (2007)]. In this talk, we will discuss on a generalization of this study to an arbitrary quantum gate on a single qubit and give the precision limit in terms of the size of the ancilla system and the amount of rotation of the unitary gate.

Title: Detection of Possible Correlations from Information of Subsystem

Gen Kimura (Tohoku University) (with Hiromichi Ohno and Hiroyuki Hayashi)

Abstract: How can we detect possible correlations between the system of interest and its environment, only from the local information of the system?
To answer this general question in quantum mechanical systems, we provide a criterion to detect correlations using a dynamical information.
This clarifies also the role of correlations in the mechanism of decoherence in open quantum mechanics.

Title: Applications on qubus architecture

Kae Nemoto (NII)

Most protocols in quantum information processing require two types of operations: single-qubit manipulation and two-qubit operation. However, it is very difficult to realize these two types of operations, keeping quantum coherence at the same time. We propose a new scheme that computational qubits are connected via continuous-variable bus mode, and show that quantum computation via quantum bus (Qubus computation) is universal in QIP. We discuss advantages and disadvantages of the qubus architecture in its applications.

Title: An efficient distillation protocol for maximally entangled mixed states

Satoshi Ishizaka (NEC)

Abstract: It is a very hard task to determine the optimal amount of distillable entanglement even for mixed state in two qubits. Indeed, it has been determined only for the Bell diagonal states of rank 2. In this talk, we show an efficient entanglement distillation protocol for the second simplest non-trivial mixed state in two qubits: maximally entangled mixed (MEM) states of rank 2. We also discuss the asymptotic relative entropy of entanglement of the MEM states and its information theoretical meaning.

Title: Optimal cloning of quantum channels

Giulio Chiribella (University of Pavia)

Abstract: Optimal cloning of quantum states has been extensively studied since the very beginning of Quantum Information, and most of its features are now well understood, especially in relation with quantum cryptography and quantum state estimation. On the contrary, almost nothing is known at the present moment about the cloning of quantum channels. Cloning an unknkown channel means to insert it in a larger network which is designed to optimally emulate several independent uses of the channel on independent input states. Remarkably, cloning quantum states is not a primitive for cloning quantum channels. In this talk I will first address the general problem of cloning quantum channels, and then present the optimal universal cloning of unitary channels, comparing the performances of the optimal quantum cloning network with those of the optimal quantum channel estimation.

TiTle: Generalized Tsirelson inequalities, commuting-operator provers, and multi-prover interactive proof systems

Tsuyoshi Ito (NII)

Abstract: Quantum nonlocality arises in the quantum information theory as the difFeence between the unentangled value and the entangled value of nonlocal games. In this talk, we introduce a class of "commuting-operator strategies," which include usual entangled strategies and which are useful to prove an upper bound of the entangled value of nonlocal games. We apply the technique to a variant of the Magic Square game (Aravind 2002; Cleve, Hoyer, Toner, Watrous 2004), and obtain an n-party generalization of the generalized Tsirelson inequalities by Wehner (2006). This is a joint work with Hirotada Kobayashi, Daniel Preda, Xiaoming Sun and Andrew C.-C. Yao. (http://arxiv.org/abs/0712.2163)

Title: Inseparability of quantum channel

Ryo Namiki (Osaka University)

If a quantum channel or process cannot be described by any measure-and-prepare scheme, we may say the channel is in quantum domain (QD) since it can transmit quantum correlations. The concept of QD clarifies the role of quantum channel in quantum information theory based on the local-operation-and-classical-communication (LOCC) paradigm: The quantum channel is only useful if it cannot be simulated by LOCC.
We present a verification scheme of QD channel for continuous variable quantum channels based on measured fidelities assuming the input of coherent states with a Gaussian prior probability distribution.

Title: Locality and nonlocality in pure-state identification problems

Akihisa Hayashi (Fukui University)

Abstract: We consider identification problems of two bipartite pure states, in which no prior classical knowledge on the states is assumed. We calculate the optimal success probability by LOCC in the cases of inconclusive and conclusive identification. We show that the inconclusive identification can be optimally performed locally, whereas it is impossible in the conclusive identication.

http://arxiv.org/abs/0801.0128

http://arxiv.org/abs/0712.2906

Title: Recycling of information

Ramon Munoz Tapia (Universitat Autonoma de Barcelona)

Abstract: Given a finite number of copies of an unknown qubit state that have already been measured optimally, we quantify the information that can be extracted about the original unknown state and show how the state degrades by the sequence of measurements. We also present some interesting variations, where we device a procedure where the information about a state is equally distributed among a number of observers that squentially measure the state.

This talk is partly
based on http://arxiv.org/abs/0708.1086

Title: An operational distinguishability measure for states: The Quantum Chernoff bound

John Calsamiglia (Universitat Autonoma de Barcelona)

Abstract: The Chernoff bound gives the minimal probability of error when discriminating two hypothesis given a large number of observations. Here, we present the quantum counterpart of this problem, i.e, when the hypothesis correspond to two quantum states, thereby solving a longstanding open problem. From this bound we obtain a physically meaningful distinguishability measure and show that the corresponding metric coincides with the Wigner-Yanase metric. We give a second distinguishability measure based on fixed local measurements on every copy and show that it is smaller than the quantum Chernoff bound, for which more general measurements (possibly collective) are required. We give closed expressions of these quantities for the cases of qubit and Gaussian states.

Title: Chernoff and Hoeffding bounds in one-way LOCC

Masahito Hayashi (Tohoku University)

Abstract: In this talk, we compare the error exponent for two state discrimination between the two cases; the one-way adaptive improvement is allowed or is not allowed. We proved that there is no difFeence between two cases. That is, adaptive improvement cannot improve error exponent in the two state discrimination.

Title: Fiber bundle over manifolds of quantum channels and its application to quantum statistics

Hiroshi Imai (Osaka Univeristy)

Abstract: See this file

Title: Error exponents in hypothesis testing for correlated states

Milan Mosonyi (Tohoku University)

Abstract: We study various error exponents in a simple hypothesis testing problem, and prove the theorems for the quantum Chernoff and Hoeffding bounds and Stein's lemma in a setting where both hypotheses can be correlated quantum states. Our main focus is on states of an infinite spin chain that satisfy a certain factorization property. Our results apply to the discrimantion problem of global Gibbs states and certain finitely correlated states.

http://arxiv.org/abs/0706.2141

http://arxiv.org/abs/0707.2020