arXiv subjects

Hiroo Azuma

Publications and source records attributed to Hiroo Azuma.

40 records · Page 3Linked to original sources

arXiv2000

A method of enciphering quantum states

In this paper, we propose a method of enciphering quantum states of two-state systems (qubits) for sending them in secrecy without entangled qubits shared by two legitimate users (Alice and Bob). This method has the following two properties. First, even if an eavesdropper (Eve) steals qubits, she can extract information from them with certain probability at most. Second, Alice and Bob can confirm that the qubits are transmitted between them correctly by measuring a signature. If Eve measures m qubits one by one from n enciphered qubits and sends alternative ones (the Intercept/Resend attack), a probability that Alice and Bob do not notice Eve's action is equal to (3/4)^m or less. Passwords for decryption and the signature are given by classical binary strings and they are disclosed through a public channel. Enciphering classical information by this method is equivalent to the one-time pad method with distributing a classical key (random binary string) by the BB84 protocol. If Eve takes away qubits, Alice and Bob lose the original quantum information. If we apply our method to a state in iteration, Eve's success probability decreases exponentially. We cannot examine security against the case that Eve makes an attack with using entanglement. This remains to be solved in the future.

quant-ph↗

arXiv2000

Building partially entangled states with Grover's amplitude amplification process

We discuss how to build some partially entangled states of $n$ two-state quantum systems (qubits). The optimal partially entangled state with a high degree of symmetry is considered to be useful for overcoming a shot noise limit of Ramsey spectroscopy under some decoherence. This state is invariant under permutation of any two qubits and inversion between the ground state $|0\ket$ and an excited state $|1\ket$ for each qubit. We show that using selective phase shifts in certain basis vectors and Grover's inversion about average operations, we can construct this high symmetric entangled state by $({polynomial in $n$})\times 2^{n/2}$ successive unitary transformations that are applied on two or three qubits. We can apply our method to build more general entangled states.

quant-ph↗

arXiv1994

$W_{\infty}$ algebra in the integer quantum Hall effects

We investigate the $W_{\infty}$ algebra in the integer quantum Hall effects. Defining the simplest vacuum, the Dirac sea, we evaluate the central extension for this algebra. A new algebra which contains the central extension is called the $W_{1+\infty}$ algebra. We show that this $W_{1+\infty}$ algebra is an origin of the Kac-Moody algebra which determines the behavior of edge states of the system. We discuss the relation between the $W_{1+\infty}$ algebra and the incompressibility of the integer quantum Hall system.

hep-th↗

arXiv1993

Explicit Relation of Quantum Hall Effect and Calogero-Sutherland Model

Explicit relation between Laughlin state of the quantum Hall effect and one-dimensional(1D) model with long-ranged interaction ($1/r^2$) is discussed. By rewriting lowest Landau level wave functions in terms of 1D representation, Laughlin state can be written as a deformation of the ground state of Calogero-Sutherland model. Corresponding to Laughlin state on different geometries, different types of 1D $1/r^2$ interaction models are derived.

hep-th↗