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Quantum Information Capsule and Its Applications to Communication Through Quantum Fields

Yamaguchi Koji 東北大学

2021.03.25

概要

Where is information stored in quantum systems? This fundamental question plays a crucial role in black hole physics. Ever since Hawking discovered a potential problem to incorporate quantum field theory with gravity in 1976 [1], it still remains elusive whether Nature is or is not able to destroy information in black holes emitting Hawking radiation [2]. If information is preserved in black hole evaporation processes, which is supported by the AdS/CFT correspondence [3], it is quite important to explore the structure of information storage. Several candidates for the information-carrying degrees of freedom have been proposed such as the Hawking radiation itself [4, 5], hidden messengers in it [6], black hole quasi-normal modes [7], soft hairs [8–10], and the zero-point fluctuation [11] as the purification partner of the Hawking radiation [12]. On the other hand, investigation on information storage is also of practical importance in developments of quantum tech- nologies such as quantum computation [13], quantum repeaters [14] in quantum network [15], quantum cryptography [16] and quantum authentication [17].

In this thesis, based on the author’s published works [18–21], he will address the question of where information is stored and provide a new tool to identify and help isolate the exact degrees of freedom carrying information in quantum systems, called quantum information capsule (QIC). In particular, a formula to identify QIC in quantum fields [19, 21] is of fundamental importance since a formula to identify the partner mode in Ref. [22] can be derived from it, which has been used in studies of information storage in quantum fields in curved spacetimes [12, 22, 23] and of protocols to extract entanglement from a field [24, 25]. In addition, the results in these works are also expected to be useful to control and help optimize the flow of information in quantum communications, e.g., in and between quantum computers. As an explicit application of the QIC technique, the author investigated communication through quantum fields in Ref. [21]. A new communication protocol using the vacuum fluctuations of the quantum field is proposed, with which the efficiency of information transmission can be enhanced.

Let us start with analyzing information stored in classical systems such as hard disks in conventional classical computers. As a simple model, consider a storage system composed of N units, each of which is capable of storing one bit information, i.e., it can be either 0 or 1. The state of this system can be described by an N -length binary number b = b1b2 · · · bN , where bi = 0 or 1. Suppose that the system is initialized to a fixed binary number b and one bit information c = 0 or 1 is encoded into the first unit by the exclusive disjunction ⊕.

As a consequence, the state of the storage turns into b′1b2 bN , where b′1 := b1 c. In this case, the encoded information can trivially be retrieved by reading out the first unit since the encoded information c is uniquely determined as c = b1 b′1. Therefore, information is locally stored in the storage system. A schematic picture of this situation is depicted in Fig. 1.1.

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