Fundamental limitations to key distillation from Gaussian states with Gaussian operations

Abstract

We establish fundamental upper bounds on the amount of secret key that can be extracted from quantum Gaussian states by using only local Gaussian operations, local classical processing, and public communication. For one-way public communication, or when two-way public communication is allowed but Alice and Bob first perform destructive local Gaussian measurements, we prove that the key is bounded by the Rényi-$2$ Gaussian entanglement of formation $E_{F,2}^{\mathrm{G}}$. Since the inequality is saturated for pure Gaussian states, this yields an operational interpretation of the Rényi-$2$ entropy of entanglement as the secret key rate of pure Gaussian states that is accessible with Gaussian operations and one-way communication. In the general setting of two-way communication and arbitrary interactive protocols, we argue that $2E_{F,2}^{\mathrm{G}}$ is still an upper bound on the extractable key. We conjecture that the factor of $2$ is spurious, which would imply that $E_{F,2}^{\mathrm{G}}$ coincides with the secret key rate of Gaussian states under Gaussian measurements and two-way public communication. We use these results to prove a gap between the secret key rates obtainable with arbitrary versus Gaussian operations. Such a gap is observed for states produced by sending one half of a two-mode squeezed vacuum through a pure loss channel, in the regime of sufficiently low squeezing or sufficiently high transmissivity. Finally, for a wide class of Gaussian states that includes all two-mode states, we prove a recently proposed conjecture on the equality between $E_{F,2}^{\mathrm{G}}$ and the Gaussian intrinsic entanglement. The unified entanglement quantifier emerging from such an equality is then endowed with a direct operational interpretation as the value of a quantum teleportation game.

arXiv comment25 pages, 4 figures

References in corpus (78)

• Mixed State Entanglement and Quantum Error Correction
• Estimating Mutual Information
• Quantum information with continuous variables
• Gaussian Quantum Information
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Peres-Horodecki separability criterion for continuous variable systems
• Inseparability criterion for continuous variable systems
• Secure quantum key distribution with realistic devices
• Continuous variable quantum cryptography using coherent states
• Quantum key distribution using gaussian-modulated coherent states
• General Benchmarks for Quantum Repeaters
• Fundamental Limits of Repeaterless Quantum Communications
• Free-Space distribution of entanglement and single photons over 144 km
• Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency
• Universal Quantum Computation with Continuous-Variable Cluster States
• Distillation of secret key and entanglement from quantum states
• Satellite-relayed intercontinental quantum network
• Continuous variable quantum information: Gaussian states and beyond
• Continuous variable quantum cryptography
• On the impossibility of distilling Gaussian states with Gaussian operations
• The characterization of Gaussian operations and Distillation of Gaussian States
• Quantum Cryptography without Switching
• Squeezed states of light and their applications in laser interferometers
• Quantum cryptography with squeezed states
• Observation of squeezed light with 10dB quantum noise reduction
• Fundamental rate-loss tradeoff for optical quantum key distribution
• "Squashed Entanglement" - An Additive Entanglement Measure
• Positive Wigner functions render classical simulation of quantum computation efficient
• 30 years of squeezed light generation
• Efficient Classical Simulation of Continuous Variable Quantum Information Processes
• Gaussian transformations and distillation of entangled Gaussian states
• Quantum Distribution of Gaussian Keys with Squeezed States
• Quantum information with Gaussian states
• Continuous-Variable Quantum Key Distribution with Gaussian Modulation -- The Theory of Practical Implementations
• Distributing Secret Keys with Quantum Continuous Variables: Principle, Security and Implementations
• Secure key from bound entanglement
• A No-Go Theorem for Gaussian Quantum Error Correction
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• The entanglement of purification
• Secure quantum key distribution using squeezed states
• Advances in Space Quantum Communications
• Continuity of quantum conditional information
• Locking classical correlation in quantum states
• Gaussian measures of entanglement versus negativities: the ordering of two-mode Gaussian states
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Faithful Squashed Entanglement
• Quantum cryptography with a predetermined key, using continuous variable Einstein-Podolsky-Rosen correlations
• Gaussian Entanglement of Formation
• Continuous-variable quantum key distribution protocols over noisy channels
• Limits and Security of Free-Space Quantum Communications
• Theory of channel simulation and bounds for private communication
• Locking of accessible information and implications for the security of quantum cryptography
• The squashed entanglement of a quantum channel
• Gaussian quantum resource theories
• Limitations of quantum computing with Gaussian cluster states
• Uncertainty, Monogamy, and Locking of Quantum Correlations
• Schur complement inequalities for covariance matrices and monogamy of quantum correlations
• Measurement-induced disturbances and nonclassical correlations of Gaussian states
• No second law of entanglement manipulation after all
• Useful states and entanglement distillation
• Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture
• Simulation of Gaussian channels via teleportation and error correction of Gaussian states
• Composably secure data processing for Gaussian-modulated continuous variable quantum key distribution
• Strong subadditivity for log-determinant of covariance matrices and its applications
• From log-determinant inequalities to Gaussian entanglement via recoverability theory
• Key distillation from Gaussian states by Gaussian operations
• A Quantum Teleportation Game
• Extendibility of bosonic Gaussian states
• Optimal uniform continuity bound for conditional entropy of classical--quantum states
• Efficiency in Quantum Key Distribution Protocols with Entangled Gaussian States
• Assisted concentration of Gaussian resources
• Teleportation-based collective attacks in Gaussian quantum key distribution
• Gaussian intrinsic entanglement
• The information capacity of entanglement-assisted continuous variable measurement
• Gaussian intrinsic entanglement: An entanglement quantifier based on secret correlations
• Gaussian Operations and Privacy
• Gaussian intrinsic entanglement for states with partial minimum uncertainty

Cited by in corpus (2)

• Quantum communications in continuous variable systems
• All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources