Quantum Communication Systems with Symmetric and Asymmetric Gaussian Channels

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Quantum Communication Systems with Symmetric and
AsymmetricGaussian Channels

• Masashi Ban

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Quantum Communication System
Quantum Teleportation
Dense Coding
Noisy Quantum Channel Environment
Noisy Quantum Channel Environment
Entangled State
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Gaussian Quantum Channel
Gaussian State
Gaussian State
Gaussian State Characteristic Function is
Gaussian.
Displacement Operator
Gaussian State Wigner Function is Gaussian.
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Gaussian Quantum Channel 1
System-environment Interaction

• von Hove limit
• Thermal Equilibrium of the Environment

Linear Dissipative Channel (Quantum Master
Equation)
Quantum State of the System
Damping Constant
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Fokker-Planck Equation for the Wigner Function
General Solution of the Fokker-Planck Equation
Characteristic Function of the Quantum State
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Quantum State of Two-Mode System
Wigner Function
Characteristic Function
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Gaussian Quantum Channel 2
Random Displacement
Quantum Thermalizing Channel
Equivalent to Quantum Teleportation Channel
Classical Communication
Entangled State
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Quantum State of Two-Mode System
Wigner Function
Characteristic Function
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Two-mode Gaussian State
Characteristic Function
Uncertainty Relation
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Inseparability of Two-mode Gaussian State
Necessary and Sufficient Condition for
Inseparable Gaussian State
Mixed EPR State (noisy two-mode squeezed-vacuum
state and so on)
Uncertainty Relation
Inseparability Condition
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Output Gaussian State of Linear Dissipative
Channel
Output Gaussian State of Quantum Thermalizing
Channel

• Inseparability of Output Gaussian State
• Quantum Communication with Output Gaussian State

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Inseparability of Output Gaussian State 1 (Linear
Dissipative Channel)
Necessary and Sufficient Condition of
Inseparability
Minimization of under the
condition
?
Entangled State
Entangled State
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Symmetric Gaussian State
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Inseparability of Output Gaussian State
2 (Quantum Thermalizing Channel)
Necessary and Sufficient Condition of
Inseparability
Minimization of under the
condition
?
Entangled State
Entangled State
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Symmetric Gaussian State
For Pure Two-mode Gaussian States
Inseparable
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Continuous Variable Quantum Teleportation
Bell Measurement (Homodyne Detection)
Displacement
Classical Communication
Noisy Quantum Channel
Noisy Quantum Channel
Two-mode Squeezed-vacuum State
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Input-Output Relation of the Teleportation
Wigner Function of the Shared Quantum State
Wigner Function of Two-mode Squeezed-vacuum State
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Linear Dissipative Channel
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Teleportation of Coherent State
Coherent State
Thermal Coherent State
Fidelity
Optimum Value of the Squeezing Parameter
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Quantum Thermalizing Channel
Fidelity
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Continuous Variable Dense Coding
Bell Measurement (Homodyne Detection)
Displacement
Noisy Quantum Channel
Noisy Quantum Channel
Two-mode Squeezed-vacuum State
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Conditional Probability (Channel Matrix)
Received Quantum State
Probability Operator Measure of the Bell
Measurement
Input Probability
Output Probability
Shannons Mutual Information
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Linear Dissipative Channel
Quantum Thermalizing Channel
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Entanglement of Symmetric Gaussian State
Covariance Matrix of Symmetric Gaussian State
Standard Form
Entanglement of Formation
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Linear Dissipative Channel Two-mode
Squeezed-vacuum State
Covariance Matrix
Entanglement of Formation
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Necessary and Sufficient Condition of
Inseparability
Negativity of Partial Transposition
Entanglement of Formation
The output state is always entangled for the
environment with zero temperature
Separability and Inseparability
n
kt
n0.1
r0.5
separable
separable
kt
kt
Entangled
Entangled
r
n
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Quantum Thermalizing Channel Two-mode Squeezed
State
Covariance Matrix
Entanglement of Formation
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Necessary and Sufficient Condition of
Inseparability
Negativity of Partial Transposition
Separability and Inseparability
separable
n
entangled
r
n
r