arXiv subjects

Toshiyuki Shimono

Publications and source records attributed to Toshiyuki Shimono.

5 recordsLinked to original sources

arXiv2006

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.

quant-ph↗

arXiv2004

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.

quant-ph↗

arXiv2003

Remarks on additivity of the Holevo channel capacity and of the entanglement of formation

The purpose of these notes is to discuss the relation between the additivity questions regarding the quantities (Holevo) capacity of a quantum channel T and entanglement of formation of a given bipartite state. In particular, using the Stinespring dilation theorem, we give a formula for the channel capacity involving entanglement of formation. This can be used to show that additivity of the latter for some states can be inferred from the additivity of capacity for certain channels. We demonstrate this connection for a family of group--covariant channels, allowing us to calculate the entanglement cost for many states, including some where a strictly smaller upper bound on the distillable entanglement is known. Group symmetry is used for more sophisticated analysis, giving formulas valid for a class of channels. This is presented in a general framework, extending recent findings of Vidal, Dur and Cirac (e-print quant-ph/0112131). We speculate on a general relation of superadditivity of the entanglement of formation, which would imply both the general additivity of this function under tensor products and of the Holevo capacity (with or without linear cost constraints).

quant-ph↗

arXiv2003

Additivity of Entanglement of Formation of Two Three-level-antisymmetric States

Quantum entanglement is the quantum information processing resource. Thus it is of importance to understand how much of entanglement particular quantum states have, and what kinds of laws entanglement and also transformation between entanglement states subject to. Therefore, it is essentialy important to use proper measures of entanglement which have nice properties. One of the major candidates of such measures is "entanglement of formation", and whether this measurement is additive or not is an important open problem. We aim at certain states so-called "antisymmetric states" for which the additivity are not solved as far as we know, and show the additivity for two of them. Keywords: quantum entanglement, entanglement of formation, additivity of entanglement measures, antisymmetric states.

quant-ph↗

arXiv2002

Lower Bound for entanglement cost of antisymmetric states

This report gives a lower bound of entanglement cost for antisymmetric states of bipartite d-level systems to be log_2 (d/(d-1)) ebit (for d=3, E_c >= 0.585...). The paper quant-ph/0112131 claims that the value is equal to one ebit for d=3, since all of the eigenvalues of reduced matrix of any pure states living in N times tensor product of antisymmetric space is not greater than 2^(-N) thus the von Neumann entropy is not less than N, but the proof is not true. Hence whether the value is equal to or less than one ebit is not clear at this moment.

quant-ph↗