**Programe**

**Time: ****11:30-12:30 **

**Speaker**: Masahito Hayashi

**Title**: Unattainable & attainable bounds for quantum sensors**Abstract**: In quantum metrology, it is widely believed that the quantum Cramer-Rao bound is attainable bound while it is not true. In order to clarify this point, we explain why the quantum Cramer-Rao bound cannot be attained geometrically. In this manuscript, we investigate noiseless channel estimation under energy constraint for states, using a physically reasonable error function, and present the optimal state and the attainable bound. We propose the experimental generation of the optimal states for enhanced metrology using squeezing transformations. This makes the estimation of unitary channels physically implementable, while existing unitary estimation protocols do not work.

The full paper is avialable from arXiv:1602.07131.

This is a joint work with Sai Vinjanampathy and L. C. Kwek.

**Time: ****12:30-14:30 Lunch**

**Time: 14:30-15:30**

**Speaker**: Ning Cai

**Title**: Classical quantum arbitrarily varying channel when the jammer knows input codeword (a joint work with Holger Boche).**Abstract**: In this work we determine the capacity of random correlated codes for classical quatum channel in the scenario that the jammer knows the input codeword, and extend it to scenarion that the jammer knows both the input codword and message to be sent.

**Time: 15:30-16:00 Coffee Break**

**Time: 16:00-17:00 **

** Speaker: **Janos A. Bergou

**Title**: Optimized measurements for quantum information processing: A geometric approach**Abstract: **In [1] we introduced a geometric approach to solve the longstanding problem of optimum unambiguous discrimination of more than two states. It is an example of a broader class of convex optimization problems. In such problems the constraints imposed by quantum mechanics dene a convex hypersurface while the cost function to be optimized is another hypersurface in the parameter space of the problem. The parameter values for which these two surfaces become tangents determine the optimal solution. The method proved to be quite powerful in delivering solutions to other outstanding problems in measurement optimization, as well. It allowed us to develop a theory of sequential measurements performed by subsequent observers on the same quantum system, bypassing the collapse postulate [2]. In this talk, using probabilistic [3] and deterministic quantum cloning [4], and quantum state separation [5] as illustrative examples we develop a complete geometric solution for nding their optimal success probabilities. In some cases the method delivers analytical results, in others it leads to intuitive and straightforward numerical solutions. We close with the discussion of two works in progress: geometric view of the measurement that maximizes the mutual information and the sequential measurement for the minimum error discrimination of qubit states. This later is the quintessential projective measurement, so a non-destructive implementation and its optimizationare of interest for many applications.Acknowledgments. This publication was made possible through the support of a Grant from the John TempletonFoundation. The opinions expressed in this publication are those of the authors and do not necessarily reect theviews of the John Templeton Foundation. Partial nancial support by a Grant from PSC-CUNY is also gratefullyacknowledged.[1] J. A. Bergou, U. Futschik, and E. Feldman, Optimal unambiguous discrimination of pure quantum states, Phys. Rev. Lett.108, 250502 (2012).[2] J. A. Bergou, E. Feldman, and M. Hillery, Extracting information from a qubit by multiple observers: Toward a theory ofsequential state discrimination, Phys. Rev. Lett. 111, 100501 (2013).[3] V. Yerokhin, A. Shehu, E. Feldman, E. Bagan, and J. A. Bergou, Probabilistically perfect cloning of two pure states:Geometric approach, Phys. Rev. Lett. 116, 200401 (2016).[4] V. Yerokhin, A. Shehu, E. Bagan, E. Feldman, and J. A. Bergou, Approximate cloning of quantum states, in preparation.[5] E. Bagan, V. Yerokhin, A. Shehu, E. Feldman, and J. A. Bergou, A geometric approach to quantum state separation, NewJournal of Physics 17, 123015 (2015).

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