1 December 2017 - Vienna - Abstracts
Speaker: Daniel Reitzner (RCQI, Bratislava)
Title: Navigating a maze using quantum-walk searches
Abstract: We show that it is possible to use a quantum walk to find a path from one marked vertex to another. In the specific case of M stars connected in a chain, one can find the path from the first star to the last one in O(M√N) steps, where N is the number of spokes of each star. First we provide analytical result showing this speedup by starting in a phase-modulated highly superposed initial state. Next, we show, that the search can also be performed by a series of successive searches when we start at the last known position and search for the next connection in O(√N) steps. For this result we use the analytical solution that can be obtained for a ring of stars of double the length of the chain.
Title: Navigating a maze using quantum-walk searches
Abstract: We show that it is possible to use a quantum walk to find a path from one marked vertex to another. In the specific case of M stars connected in a chain, one can find the path from the first star to the last one in O(M√N) steps, where N is the number of spokes of each star. First we provide analytical result showing this speedup by starting in a phase-modulated highly superposed initial state. Next, we show, that the search can also be performed by a series of successive searches when we start at the last known position and search for the next connection in O(√N) steps. For this result we use the analytical solution that can be obtained for a ring of stars of double the length of the chain.
Speaker: Martin Plesch (Brno)
Title: Loss of Information in Quantum Guessing Game
Abstract: Incompatibility of certain measurements - impossibility of obtaining deterministic outcomes simultaneously - is a well-known property of quantum mechanics. This feature can be utilized in many contexts, ranging from Bell inequalities to device dependent QKD protocols. Typically, in these applications the measurements are chosen from a predetermined set based on a classical random variable. One can naturally ask, whether the non-determinism of the outcomes is due to intrinsic hiding property of quantum mechanics, or rather by the fact that classical, incoherent information entered the system via the choice of the measurement. Authors of [1] examined this question for a specific case of two mutually unbiased measurements on systems of different dimensions. They have somewhat surprisingly shown that in case of qubits, if the measurements are chosen coherently with the use of a controlled unitary, outcomes of both measurements can be guessed deterministically. Here we extend their analysis and show that specifically for qubits, measurement result for any set of measurements with any a-priori probability distribution can be faithfully guessed by a suitable state preparation and measurement. We also show that up to a small set of specific cases, this is not possible for higher dimensions. This result manifests a deep difference in properties of qubits and higher dimensional systems and suggests that these systems might offer higher security in specific cryptographic protocols. More fundamentally, the results show that the impossibility of predicting a result of a measurement is not caused solely by a loss of coherence between the choice of the measurement and the guessing procedure.
[1] F. Rozpędek, J. Kaniewski, P. J. Coles, and S. Wehner, New J. Phys. 19, 023038 (2017).
Title: Loss of Information in Quantum Guessing Game
Abstract: Incompatibility of certain measurements - impossibility of obtaining deterministic outcomes simultaneously - is a well-known property of quantum mechanics. This feature can be utilized in many contexts, ranging from Bell inequalities to device dependent QKD protocols. Typically, in these applications the measurements are chosen from a predetermined set based on a classical random variable. One can naturally ask, whether the non-determinism of the outcomes is due to intrinsic hiding property of quantum mechanics, or rather by the fact that classical, incoherent information entered the system via the choice of the measurement. Authors of [1] examined this question for a specific case of two mutually unbiased measurements on systems of different dimensions. They have somewhat surprisingly shown that in case of qubits, if the measurements are chosen coherently with the use of a controlled unitary, outcomes of both measurements can be guessed deterministically. Here we extend their analysis and show that specifically for qubits, measurement result for any set of measurements with any a-priori probability distribution can be faithfully guessed by a suitable state preparation and measurement. We also show that up to a small set of specific cases, this is not possible for higher dimensions. This result manifests a deep difference in properties of qubits and higher dimensional systems and suggests that these systems might offer higher security in specific cryptographic protocols. More fundamentally, the results show that the impossibility of predicting a result of a measurement is not caused solely by a loss of coherence between the choice of the measurement and the guessing procedure.
[1] F. Rozpędek, J. Kaniewski, P. J. Coles, and S. Wehner, New J. Phys. 19, 023038 (2017).
Speaker: Péter Vrana (Budapest)
Title: Strong converse exponents for pure state entanglement transformations
Title: Strong converse exponents for pure state entanglement transformations
Speaker: Claude Klöckl (IQOQI Vienna)
Title: On the classification and derivation of entropic inequalites for the linear entropy. (Or: Why the ugly little brother of the Reyni family is relevant after all..... )
Abstract: Information theory has suceeded in obtaining a complete classification of all possible entropic inequalites for the Shannon entropy. Quantum Information has aimed to parallel this remarkable result with sucess for the von-Neumann and Reyni case. We will briefly review the state-of-the art regarding known properties, entropic inequalites & their classification for the most important families of entropies. Namely, Shannon / von-Neuman, (Quantum-)Reyni and (Quantum-)Tsallis. Among these the Tsallis familiy is probably the most exotic and least studied. Even though the Tsallis entropies have received very thorough studies from a pure maths perspective and by some authors from the field of complex systems, their physical relevance is still debated. However, it should not be overlooked that one particular member of the Tsallis family is of utmost importance in quantum information theory: the linear entropy. We contribute a novel perspective on the derivation of non-linear linear (sic!) entropy inequalities. This is achieved by means of the famous Bloch decomposition.
Title: On the classification and derivation of entropic inequalites for the linear entropy. (Or: Why the ugly little brother of the Reyni family is relevant after all..... )
Abstract: Information theory has suceeded in obtaining a complete classification of all possible entropic inequalites for the Shannon entropy. Quantum Information has aimed to parallel this remarkable result with sucess for the von-Neumann and Reyni case. We will briefly review the state-of-the art regarding known properties, entropic inequalites & their classification for the most important families of entropies. Namely, Shannon / von-Neuman, (Quantum-)Reyni and (Quantum-)Tsallis. Among these the Tsallis familiy is probably the most exotic and least studied. Even though the Tsallis entropies have received very thorough studies from a pure maths perspective and by some authors from the field of complex systems, their physical relevance is still debated. However, it should not be overlooked that one particular member of the Tsallis family is of utmost importance in quantum information theory: the linear entropy. We contribute a novel perspective on the derivation of non-linear linear (sic!) entropy inequalities. This is achieved by means of the famous Bloch decomposition.