2 research outputs found
Qubit Channels Which Require Four Inputs to Achieve Capacity: Implications for Additivity Conjectures
An example is given of a qubit quantum channel which requires four inputs to
maximize the Holevo capacity. The example is one of a family of channels which
are related to 3-state channels. The capacity of the product channel is studied
and numerical evidence presented which strongly suggests additivity. The
numerical evidence also supports a conjecture about the concavity of output
entropy as a function of entanglement parameters. However, an example is
presented which shows that for some channels this conjecture does not hold for
all input states. A numerical algorithm for finding the capacity and optimal
inputs is presented and its relation to a relative entropy optimization
discussed.Comment: 19 pages, 15 figures. several typos corrected in v
Analysis of the Entanglement Cost and Calculation of the Holevo Capacity
``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.Comment: A doctoral dissertation, the University of Tokyo, 112 pages, 65
figure file