Analysis of the Entanglement Cost and Calculation of the Holevo Capacity

Abstract

``Beam me over,'' Alice: A cricket's quantum journey This thesis addresses two known quantities in quantum information science: (1) entanglement cost, and (2) Holevo capacity. These quantities will be crucial values when teleportation becomes common in daily life, perhaps centuries from now. Assume that Alice desires to send a singing Japanese cricket to her friend Bob in America, and that Alice and Bob already share a quantum entanglement. First, Alice sends Bob a mass of information bits resulting from the interaction between the cricket she holds in her hand and half of the entanglement. Subsequently, Bob receives the information bits and manipulates the other half of the entanglement, transforming them back into the original cricket. Examining this situation from an instrumental engineering viewpoint, quantifying the amount of the quantum entanglement and the number of information bits is crucial for this transmission. If both values are enough, Alice could even send herself to Bob's place instead of the tiny cricket. The topics of this thesis therefore are: (1) the mathematical properties of the entanglement cost, such as whether it is an additive measure similar to normal length or weight; and (2) how to calculate the Holevo capacity, an ultimately achievable limit of the information conveyance capacity of an information channel, such as of a single photon passing through an optical fiber or space. These two distinct quantities are magically tied together by several ``additive or not'' hypotheses, which await mathematical proof.

arXiv commentA doctoral dissertation, the University of Tokyo, 112 pages, 65 figure files

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