Quantum information with continuous variables
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Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement. This article reviews the progress in quantum information based on continuous quantum variables, with emphasis on quantum optical implementations in terms of the quadrature amplitudes of the electromagnetic field.
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In quantum optics, the amplitude and phase quadratures of the vacuum state are represented by a pair of non-commuting operators (X and P with [X,P]=i/2), which cannot be determined simultaneously with an arbitrarily high precision.
“In quantum optics, the amplitude and phase quadratures of the vacuum state are represented by a pair of non-commuting operators ( X and P with [ X, P ] = i/ 2), which cannot be determined simultaneously with an arbitrarily high precision 33 -i.e., 〈 ( Δ X ) 2 〉 × 〈 ( Δ P ) 2 〉 ⩾ 1 / 16, with Δ O de fi ned by O -〈 O 〉 and 〈 O 〉 denoting the average of O .”
From Quantum random number generation (2016) · cites this paper as [33]
Quantum teleportation of continuous-variable states has the advantage that full Bell-state analysis is possible with linear optics within the experimental bandwidth, but it is hard to extend to long-distance because squeezed-state entanglement degrades during longer-distance transfers.
“Quantum teleportation of continuous-variable states (Furusawa et al., 1998;Braunstein and van Loock, 2005) has the advantage that full Bell-state analysis is possible with linear optics (within the experimental bandwidth).Yet, it is hard to extend to a long-distance case.The unavoidable degradation of squeezed-states sets in during longer-distance transfers.This consequently leads to a rapid”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Braunstein and van Loock, 2005
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Purification via entanglement swapping and conserved entanglement
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Demonstration of a quantum teleportation network for continuous variables
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Experimental investigation of continuous-variable quantum teleportation
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Entanglement as a Precondition for Secure Quantum Key Distribution
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Entanglement of Formation for Symmetric Gaussian States
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Separable States Are More Disordered Globally than Locally
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Quantum Communication between Atomic Ensembles Using Coherent Light
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Quantum Information with Continuous Variables
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Separability and Distillability of Multiparticle Quantum Systems
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Polarization squeezing and continuous-variable polarization entanglement
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Bell inequality, Bell states and maximally entangled states for n qubits
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Teleportation with Bright Squeezed Light
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Error Correction for Continuous Quantum Variables
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Quantum error correction for communication with linear optics
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Quantum Effects in Communications Systems
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Driving non-Gaussian to Gaussian states with linear optics
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Criteria for continuous-variable quantum teleportation
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Self-citationGaussian entanglement of formation
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Experimental Demonstration of Continuous Variable Polarization Entanglement
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Ultimate information carrying limit of quantum systems
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Entangling Power of Passive Optical Elements
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Quantum Benchmark for Storage and Transmission of Coherent States
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Postselected versus nonpostselected quantum teleportation using parametric down-conversion
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Continuous Variable Entanglement Swapping
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Analog Quantum Error Correction
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Measuring the Quantum State of Light
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Maximal violation of Bell inequalities using continuous-variable measurements
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Atomic Quantum State Teleportation and Swapping
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Telecloning of Continuous Quantum Variables
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Universal Teleportation with a Twist
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Unconditional teleportation of continuous-variable entanglement
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Self-citationShor, P. W., Smolin, J. A., & Terhal, B. M. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.2681 · Cited by 147 · see citing works
Quantum Key Distribution with Bright Entangled Beams
Silberhorn, C., Korolkova, N., & Leuchs, G. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.167902 · Cited by 145 · see citing works
Nonideal quantum nondemolition measurements
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Optimal Cloning of Coherent States with a Linear Amplifier and Beam Splitters
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Self-citationSqueezing of quantum solitons (A)
Carter, S. J., Drummond, P. D., Reid, M. D., et al. (1987) · Journal of the Optical Society of America B · Cited by 142 · see citing works
Quantum cryptography using pulsed homodyne detection
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Sampling entropies and operational phase-space measurement. I. General formalism
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Interdisciplinary Physics: Biological Physics, Quantum Information, etc.
Kempe, J., & Nielsen, M. A. (2001) · Technische Universität Dortmund Eldorado (Technische Universität Dortmund) · doi:10.17877/de290r-1702 · Cited by 137 · see citing works
Quantum versus classical domains for teleportation with continuous variables
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Self-citationQuantum dense coding via a two-mode squeezed-vacuum state
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Security of continuous-variable quantum cryptography
Ralph, T. C. (2000) · Physical Review A · doi:10.1103/physreva.62.062306 · Cited by 129 · see citing works
How to share a continuous-variable quantum secret by optical interferometry
Tyc, T., & Sanders, B. C. (2002) · Physical Review A · doi:10.1103/physreva.65.042310 · Cited by 126 · see citing works
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- Authors
- Braunstein, S. L., & van Loock, P.
- Affiliations
- University of York (GB)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2005-06-29
- Volume
- 77
- Issue
- 2
- Pages
- 513-577
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W2142739935
- Semantic Scholar
- 7778cbc7541e726865bac18aeb4f9ff3ebfcfe0b
- Cited by
- 3,858
- References
- 282
- Citations by year
- 2026: 177 · 2025: 275 · 2024: 229 · 2023: 244 · 2022: 252 · 2021: 250 · 2020: 230 · 2019: 232 · 2018: 193 · 2017: 175 · 2016: 185 · 2015: 171 · 2014: 138 · 2013: 146 · 2012: 137
- FWCI
- 137.86
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Max Planck Digital Library (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- continuous-variable quantum information, quantum optics, electromagnetic fields, entanglement, non-orthogonality, quantum communication, quantum computing
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