Charles Bennett
IBM Research, Physical Sciences, Department Member
The first essay discusses, in nontechnical terms, the paradox implicit in defining a random integer as one without remarkable properties, and the resolution of that paradox at the cost of making randomness a property which most integers... more
The first essay discusses, in nontechnical terms, the paradox implicit in defining a random integer as one without remarkable properties, and the resolution of that paradox at the cost of making randomness a property which most integers have but can’t be proved to have. The second essay briefly reviews the search for randomness in the digit sequences of natural irrational numbers like π and artificial ones like Champernowne’s C = 0.12345678910111213 . . ., and discusses at length Chaitin’s definable-but-uncomputable number Ω, whose digit sequence is so random that no betting strategy could succeed against it. Other, Cabalistic properties of Ω are pointed out for the first time.
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Research Interests: Mathematics, Computer Science, Physics, Quantum Physics, Quantum Information, and 13 moreQuantum Information Processing, Quantum entanglement, Community Capacity, Quantum Information Theory, Unitary State, Quantum Computer, Bipartite Graph, Quantum Gate, Electrical And Electronic Engineering, Generalization Bounds, Discrete time, nonlocal interaction, and Quantum Channel
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We consider interactions as bidirectional channels. We investigate the capacities for interaction Hamiltonians and non- local unitary gates to generate entanglement and transmit clas- sical information. We give analytic expressions for... more
We consider interactions as bidirectional channels. We investigate the capacities for interaction Hamiltonians and non- local unitary gates to generate entanglement and transmit clas- sical information. We give analytic expressions for the entangle- ment generating capacity and entanglement-assisted one-way clas- sical communication capacity of interactions, and show that these quantities are additive, so that the asymptotic capacities equal the corresponding -shot capacities. We give general bounds on other capacities, discuss some examples, and conclude with some open questions.
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Research Interests: Art History and Art
The entanglement-assisted classical capacity of a noisy quantum channel (CE) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver... more
The entanglement-assisted classical capacity of a noisy quantum channel (CE) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have access to the resource of shared quantum entanglement, which may be used up by the communication protocol. We show that the capacity CE is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs ρ, of the entropy of the channel input plus the entropy of the channel output minus their joint entropy, the latter being defined as the entropy of an entangled purification of ρ after half of it has passed through the channel. We calculate entanglement-assisted capacities for two interesting quantum channels, the qubit amplitude damping channel and the bosonic channel with amplification/attenuation and Gaussian noise. We discuss how many independent parameters are required to complete...
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Research Interests: Mathematics, Computer Science, Pure Mathematics, Space, TIME, and 3 moreComputation, Turing machine, and Time
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Research Interests: Physics, Theoretical Physics, Thermodynamics, Quantum Information, Quantum Theory, and 12 moreChemical Kinetics, Quantum entanglement, Non-equilibrium thermodynamics, Second Law, Quantum Computer, Quantum and classical statistical mechanics, Biological systems, Molecular Dynamic Simulation, Equation of State, Maximum entropy, Spin Echo, and Molecular dynamic
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When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media,... more
When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a communications channel on which it is impossible in principle to eavesdrop without a high probability of being detected. With such a channel, a one-time pad can safely be reused many times as long as no eavesdrop is detected, and, planning ahead, part of the capacity of these uncompromised transmissions can be used to send fresh random bits with which to replace the one-time pad when an eavesdrop finally is detected. Unlike other schemes for stretching a one-time pad, this scheme does not depend on complexity-theoretic assumptions such as the difficulty of factoring.