arXiv subjects

Howard N. Barnum

Publications and source records attributed to Howard N. Barnum.

3 recordsLinked to original sources

arXiv2010

Quantum Knowledge, Quantum Belief, Quantum Reality: Notes of a QBist Fellow Traveler

I consider the "Quantum Bayesian" view of quantum theory as expounded in a 2006 paper of Caves, Fuchs, and Schack. I argue that one can accept a generally personalist, decision-theoretic view of probability, including probability as manifested in quantum physics, while nevertheless accepting that in some situations, including some in quantum physics, probabilities may in a useful sense be thought of as objectively correct. This includes situations in which the ascription of a quantum state should be thought of as objectively correct. I argue that this does not cause any prima facie objectionable sort of action at a distance, though it may involve adopting the attitude that certain dispositional properties of things are not "localized" at those things. Whether this insouciant view of nonlocality and objectivity can survive more detailed analysis is a matter for further investigation.

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arXiv2007

Semidefinite programming characterization and spectral adversary method for quantum complexity with noncommuting unitary queries

Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model in which the goal is to compute functions of N by N ``black box'' unitary matrices drawn from a set of such matrices, a problem with applications to determining properties of quantum physical systems. We characterize the existence of an algorithm for such a query problem, with given error and number of queries, as equivalent to the feasibility of a certain set of semidefinite programming constraints, or equivalently the infeasibility of a dual of these constraints, which we construct. Relaxing the primal constraints to correspond to mere pairwise near-orthogonality of the final states of a quantum computer, conditional on black-box inputs having distinct function values, rather than bounded-error determinability of the function value via a single measurement on the output states, we obtain a relaxed primal program the feasibility of whose dual still implies the nonexistence of a quantum algorithm. We use this to obtain a generalization, to our not-necessarily-commutative setting, of the ``spectral adversary method'' for quantum query lower bounds.

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arXiv1999

Quantum secure identification using entanglement and catalysis

I consider the use of entanglement between two parties to enable one to authenticate her identity to another over a quantum communication channel. Exploiting the phenomenon of entanglement-catalyzed transformations between pure states gives a potentially reusable entangled identification token. In analyzing this, I consider the independently interesting problem of the best possible approximation to a given pure entangled state realizable using local actions and classical communication by parties sharing a different entangled state.

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