Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Modern Optics

Quadrature operators with arbitrary phase and applications to phase-space distribution and quantum communication

Masashi Ban, Sachiko Kitajima, Fumiaki Shibata

Published Mar 24, 2014• 1 citation
Publisher

Abstract

Quadrature operators with arbitrary phase are studied from a point of view of the phase-space representation of quantum states, and the results are applied to simultaneous measurement and quantum communication. The Wigner function of arbitrary phase quadrature variables is introduced, which is a generalization of the usual Wigner function of position and momentum. The Kirkwood distribution is also extended for arbitrary phase quadrature variables. The simultaneous measurement of two quadrature operators is investigated using a beam splitter model and a generalized version of the Arthurs-Kelley model. The quantum teleportation of continuous variables is considered in terms of arbitrary phase quadrature variables. A general formula is derived that provides the quantum teleportation channel. The fidelity of the quantum teleportation with an uncontrollable phase is calculated for a coherent state. Furthermore, the mutual information of the quantum dense coding of continuous variables is obtained when classical information is encoded on arbitrary phase quadrature variables. The result is compared with that of the communication system, where information is transmitted using coherent and squeezed states.

DOI
10.1080/09500340.2014.900826

Related papers

Quantum communication with continuous variables

Pieter Kok, Brendon W. Lovett

Qubits are not the only information carriers that can be used for quantum information processing. In this chapter, we will focus on quantum communication with ‘continuous quantum variables’, or continuous variables for short. In the context of quantum information processing we will also call continuous variables ‘qunats’. We have seen in Chapter 2 that a natural representation of a continuous variable is given by the position of a particle. The conjugate continuous variable is then the momentum of the particle. Unfortunately, the eigenstates of the position and momentum operators are not physical, and we have to construct suitable approximations to these states that can be created in the laboratory. Any practical information processing device must then take into account the deviation of the actual states from the ideal position and momentum eigenstates. Rather than the position and momentum of a particle, we will consider here the two position and momentum quadratures of an electromagnetic field mode. These operators obey the same commutation relations as the canonical position and momentum operators, but they are not the physical position and momentum of field excitations. Approximate eigenstates of the quadrature operators can be constructed in the form of squeezed coherent states. We define a quantum mechanical phase space for quadrature operators, similar to a classical phase space for position and momentum. Probability distributions in the classical phase space then become quasi-probability distributions over the quadrature phase space.We will develop one of these distributions, namely the Wigner function, and identify certain phase-space transformations of the Wigner function with linearoptical and squeezing operations.

Cambridge University Press eBooks•Apr 22, 2010•32 citations

QUANTUM GATES AND PROTOCOLS WITH SPHERICAL WIGNER FUNCTIONS

Orsolya Kálmán, M. G. Benedict

The fundamental concepts and operations of quantum information theory are considered in the framework of a phase space formulation of quantum mechanics, where the states of one or several qubits are represented by a specific continuous quasiprobability distribution function on the Bloch sphere or on its generalizations. The function we use is the spherical Wigner function. It is shown that the usual transformations of quantum information theory are certain rotations or more general transformations of this Wigner function. We show that the standard teleportation and dense coding protocols can be appropriately formulated in terms of the Wigner function.

International Journal of Quantum Information•Sep 1, 2005•1 citation

Quantum teleportation via mixed two-mode squeezed states in the coherent-state representation

Jinhyoung Lee, M. S. Kim, S. Lee

Quantum teleportation for continuous variables is generally described in phase space by using the Wigner functions. We study quantum teleportation via a mixed two-mode squeezed state in Hilbert-Schmidt space by using the coherent-state representation and operators. This shows directly how the teleported state is related to the original state. PACS numbers: 03.67.-a, 89.70.+c

Journal of the Korean Physical Society•Apr 1, 2003•1 citation

Coherent communication with continuous quantum variables

Mark M. Wilde, Hari Krovi, Todd A. Brun

The coherent bit (cobit) channel is a resource intermediate between classical and quantum communication. It produces coherent versions of teleportation and superdense coding. We extend the cobit channel to continuous variables by providing a definition of the coherent nat (conat) channel. We construct several coherent protocols that use both a position-quadrature and a momentum-quadrature conat channel with finite squeezing. Finally, we show that the quality of squeezing diminishes through successive compositions of coherent teleportation and superdense coding.

arXiv:quant-ph/0612170•Physical Review A•Jun 14, 2007•23 citations

Phase-space approach to continuous variable quantum teleportation

Masashi Ban

The phase-space method is applied for considering continuous variable quantum teleportation. It is found that the continuous variable quantum teleportation transforms the $s$-parametrized phase-space function of an input state into the $(s+\ensuremath{\delta})$-parametrized phase-space function, where the parameter $\ensuremath{\delta}$ is determined by the shared quantum entanglement. It is shown from this result that the Wigner function of the teleported state is always non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}2∕3$ and the Glauber-Sudarshan $P$ function non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}1∕2$, where ${\mathcal{F}}_{c}$ is the fidelity of the coherent-state teleportation. Furthermore the fidelity between input and output states is calculated when Gaussian states are teleported.

Physical Review A•May 17, 2004•37 citations

Quantum dense coding of continuous variables in a noisy quantum channel

Masashi Ban

Quantum dense coding of continuous variables via a two-mode squeezed vacuum state is considered for a noisy quantum channel. Classical information is encoded in the two quadrature components of one mode of a two-mode squeezed vacuum state and the encoded mode is sent through a noisy quantum channel which is assumed to be linearly dissipative. Decoding at the receiver side is performed by simultaneous measurement of two quadrature components of the two-mode state. By calculating the error probability of a binary communication system, we examine whether the dense coding is effective or not when a quantum channel is noisy.

Journal of Optics B Quantum and Semiclassical Optics•Nov 30, 2000•41 citations
Quadrature operators with arbitrary phase are studied from a point of view of the phase-space representation of quantum states, and the results are applied to simultaneous measurement and quantum communication. The Wigner function of arbitrary phase quadrature variables is introduced, which is a generalization of the usual Wigner function of position and momentum. The Kirkwood distribution is also extended for arbitrary phase quadrature variables. The simultaneous measurement of two quadrature operators is investigated using a beam splitter model and a generalized version of the Arthurs-Kelley model. The quantum teleportation of continuous variables is considered in terms of arbitrary phase quadrature variables. A general formula is derived that provides the quantum teleportation channel. The fidelity of the quantum teleportation with an uncontrollable phase is calculated for a coherent state. Furthermore, the mutual information of the quantum dense coding of continuous variables is obtained when classical information is encoded on arbitrary phase quadrature variables. The result is compared with that of the communication system, where information is transmitted using coherent and squeezed states.
Qubits are not the only information carriers that can be used for quantum information processing. In this chapter, we will focus on quantum communication with ‘continuous quantum variables’, or continuous variables for short. In the context of quantum information processing we will also call continuous variables ‘qunats’. We have seen in Chapter 2 that a natural representation of a continuous variable is given by the position of a particle. The conjugate continuous variable is then the momentum of the particle. Unfortunately, the eigenstates of the position and momentum operators are not physical, and we have to construct suitable approximations to these states that can be created in the laboratory. Any practical information processing device must then take into account the deviation of the actual states from the ideal position and momentum eigenstates. Rather than the position and momentum of a particle, we will consider here the two position and momentum quadratures of an electromagnetic field mode. These operators obey the same commutation relations as the canonical position and momentum operators, but they are not the physical position and momentum of field excitations. Approximate eigenstates of the quadrature operators can be constructed in the form of squeezed coherent states. We define a quantum mechanical phase space for quadrature operators, similar to a classical phase space for position and momentum. Probability distributions in the classical phase space then become quasi-probability distributions over the quadrature phase space.We will develop one of these distributions, namely the Wigner function, and identify certain phase-space transformations of the Wigner function with linearoptical and squeezing operations.
The fundamental concepts and operations of quantum information theory are considered in the framework of a phase space formulation of quantum mechanics, where the states of one or several qubits are represented by a specific continuous quasiprobability distribution function on the Bloch sphere or on its generalizations. The function we use is the spherical Wigner function. It is shown that the usual transformations of quantum information theory are certain rotations or more general transformations of this Wigner function. We show that the standard teleportation and dense coding protocols can be appropriately formulated in terms of the Wigner function.
The coherent bit (cobit) channel is a resource intermediate between classical and quantum communication. It produces coherent versions of teleportation and superdense coding. We extend the cobit channel to continuous variables by providing a definition of the coherent nat (conat) channel. We construct several coherent protocols that use both a position-quadrature and a momentum-quadrature conat channel with finite squeezing. Finally, we show that the quality of squeezing diminishes through successive compositions of coherent teleportation and superdense coding.
The phase-space method is applied for considering continuous variable quantum teleportation. It is found that the continuous variable quantum teleportation transforms the sss-parametrized phase-space function of an input state into the $(s+\ensuremath{\delta})$-parametrized phase-space function, where the parameter $\ensuremath{\delta}$ is determined by the shared quantum entanglement. It is shown from this result that the Wigner function of the teleported state is always non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}2∕3$ and the Glauber-Sudarshan PPP function non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}1∕2$, where Fc{\mathcal{F}}_{c}Fc​ is the fidelity of the coherent-state teleportation. Furthermore the fidelity between input and output states is calculated when Gaussian states are teleported.
Quantum dense coding of continuous variables via a two-mode squeezed vacuum state is considered for a noisy quantum channel. Classical information is encoded in the two quadrature components of one mode of a two-mode squeezed vacuum state and the encoded mode is sent through a noisy quantum channel which is assumed to be linearly dissipative. Decoding at the receiver side is performed by simultaneous measurement of two quadrature components of the two-mode state. By calculating the error probability of a binary communication system, we examine whether the dense coding is effective or not when a quantum channel is noisy.