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

arXiv:quant-ph/0202119

Quantum Theory and Classical Information

G. Einarsson

Published Feb 21, 2002• 0 citations
arXivHTMLPDF

Abstract

Transmission of classical information using quantum objects such as polarized photons is studied. The classical (Shannon) channel capacity and its relation to quantum (von Neumann) channel capacity is investigated for various receiver arrangements. A quantum channel with transmission impairment caused by attenuation and random polarization noise is considered. It is shown that the maximal (von Neumann) capacity of such a channel can be realized by a simple symbol by symbol detector followed by a classical error correcting decoder. For an intensity limited optical channel capacity is achieved by on-off keying (OOK). The capacity per unit cost is shown to be 1 nat/photon = 1.44 bit/photon, slightly larger than the 1 bit/photon obtained by orthogonal quantum signals.

DOI
10.48550/arxiv.quant-ph/0202119

Related papers

Classical capacity per unit cost for quantum channels

Marcin Jarzyna

In most communication scenarios, sending a symbol encoded in a quantum state requires spending resources such as energy, which can be quantified by a cost of communication. A standard approach in this context is to quantify the performance of communication protocol by classical capacity, quantifying the maximal amount of information that can be transmitted through a quantum channel per single use of the channel. However, different figures of merit are also possible and a particularly well-suited one is the classical capacity per unit cost, which quantifies the maximal amount of information that can be transmitted per unit cost. I generalize this concept to account for the quantum nature of the information carriers and communication channels and show that if there exists a state with cost equal to zero, e.g., a vacuum state, the capacity per unit cost can be expressed by a simple formula containing maximization of the relative entropy between two quantum states. This enables me to analyze the behavior of photon information efficiency for general communication tasks and show simple bounds on the capacity per unit cost in terms of quantities familiar from quantum estimation theory. I calculate also the capacity per unit cost for general Gaussian quantum channels.

arXiv:1704.06696•Physical Review A•Sep 28, 2017•12 citations

von Neumann capacity of noisy quantum channels

Christoph Adami, Nicolas J. Cerf

We discuss the capacity of quantum channels for information transmission and storage. Quantum channels have dual uses: they can be used to transmit known quantum states which code for classical information, and they can be used in a purely quantum manner, for transmitting or storing quantum entanglement. We propose here a definition of the von Neumann capacity of quantum channels, which is a quantum-mechanical extension of the Shannon capacity and reverts to it in the classical limit. As such, the von Neumann capacity assumes the role of a classical or quantum capacity depending on the usage of the channel. In analogy to the classical construction, this capacity is defined as the maximum von Neumann mutual entropy processed by the channel, a measure which reduces to the capacity for classical information transmission through quantum channels (the ``Kholevo capacity'') when known quantum states are sent. The quantum mutual entropy fulfills all basic requirements for a measure of information, and observes quantum data-processing inequalities. We also derive a quantum Fano inequality relating the quantum loss of the channel to the fidelity of the quantum code. The quantities introduced are calculated explicitly for the quantum depolarizing channel. The von Neumann capacity is interpreted within the context of superdense coding, and an extended Hamming bound is derived that is consistent with that capacity.

arXiv:quant-ph/9609024•Physical Review A•Nov 1, 1997•209 citations

Classical information capacity of a quantum channel

Paul A. Hausladen, Richard Jozsa, Benjamin W. Schumacher +2 more

We consider the transmission of classical information over a quantum channel. The channel is defined by an ``alphabet'' of quantum states, e.g., certain photon polarizations, together with a specified set of probabilities with which these states must be sent. If the receiver is restricted to making separate measurements on the received ``letter'' states, then the Kholevo theorem implies that the amount of information transmitted per letter cannot be greater than the von Neumann entropy H of the letter ensemble. In fact the actual amount of transmitted information will usually be significantly less than H. We show, however, that if the sender uses a block coding scheme consisting of a choice of code words that respects the a priori probabilities of the letter states, and the receiver distinguishes whole words rather than individual letters, then the information transmitted per letter can be made arbitrarily close to H and never exceeds H. This provides a precise information-theoretic interpretation of von Neumann entropy in quantum mechanics. We apply this result to ``superdense'' coding, and we consider its extension to noisy channels. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Sep 1, 1996•497 citations

Quantum detection and channel capacity for communications applications

Victor A. Vilnrotter, Chi-Wung Lau

The fundamental performance limits and channel capacity of optical communications systems operating over the free space channel will be examined using quantum detection theory. The performance of the optimum quantum receiver for on-off keying (OOK) and optical binary phase shift keying (BPSK) is first examined as a pure state (no noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes is then evaluated for the optimum quantum receiver by making use of the concept of quantum measurement states. The performance of M-ary pulse position modulation, which requires a product state representation, is evaluated along with the performance of certain 'dense signal sets.' Performance comparisons with classical techniques shows over 5 dB improvement in some cases when quantum detection is employed. As a further application of the quantum detection theory, the capacity of the binary channel with on-off keyed modulation and quantum detection is evaluated, and shown to exceed the capacity obtained with classical photon counting.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 30, 2002•21 citations

The Capacity of the Quantum Multiple Access Channel

Andreas Winter

We define classical quantum multiway channels for transmission of classical information, after recent work by Allahverdyan and Saakian. Bounds on the capacity region are derived in a uniform way, which are analogous to the classically known ones, simply replacing Shannon entropy with von Neumann entropy. For the single receiver case (multiple-access channel) the exact capacity region is determined. These results are applied to the case of noisy channels, with arbitrary input signal states. A second issue of this work is the presentation of a calculus of quantum information quantities, based on the algebraic formulation of quantum theory.

•Jul 7, 1998•66 citations

Photonic Communications and Quantum Information Storage Capacities

William C. Lindsey

This paper presents photonic communications and data storage capacitates for classical and quantum communications over a quantum channel. These capacities represent a generalization of Shannon’s classical channel capacity and coding theorem in two ways. First, it extends classical results for bit communication transport to all frequencies in the electromagnetic spectrum. Second, it extends the results to quantum bit (qubit) transport as well as a hybrid of classical and quantum communications. Nature’s limits on the rate at which classical and/or quantum information can be sent error-free over a quantum channel using classical and/or quantum error-correcting codes are presented as a function of the thermal background light level and Einstein zero-point energy. Graphical results are given as well as numerical results regarding communication rate limits using Planck’s natural frequency and time-interval units!

Optics and Photonics Journal•Jan 1, 2013•0 citations
Transmission of classical information using quantum objects such as polarized photons is studied. The classical (Shannon) channel capacity and its relation to quantum (von Neumann) channel capacity is investigated for various receiver arrangements. A quantum channel with transmission impairment caused by attenuation and random polarization noise is considered. It is shown that the maximal (von Neumann) capacity of such a channel can be realized by a simple symbol by symbol detector followed by a classical error correcting decoder. For an intensity limited optical channel capacity is achieved by on-off keying (OOK). The capacity per unit cost is shown to be 1 nat/photon = 1.44 bit/photon, slightly larger than the 1 bit/photon obtained by orthogonal quantum signals.
In most communication scenarios, sending a symbol encoded in a quantum state requires spending resources such as energy, which can be quantified by a cost of communication. A standard approach in this context is to quantify the performance of communication protocol by classical capacity, quantifying the maximal amount of information that can be transmitted through a quantum channel per single use of the channel. However, different figures of merit are also possible and a particularly well-suited one is the classical capacity per unit cost, which quantifies the maximal amount of information that can be transmitted per unit cost. I generalize this concept to account for the quantum nature of the information carriers and communication channels and show that if there exists a state with cost equal to zero, e.g., a vacuum state, the capacity per unit cost can be expressed by a simple formula containing maximization of the relative entropy between two quantum states. This enables me to analyze the behavior of photon information efficiency for general communication tasks and show simple bounds on the capacity per unit cost in terms of quantities familiar from quantum estimation theory. I calculate also the capacity per unit cost for general Gaussian quantum channels.
We discuss the capacity of quantum channels for information transmission and storage. Quantum channels have dual uses: they can be used to transmit known quantum states which code for classical information, and they can be used in a purely quantum manner, for transmitting or storing quantum entanglement. We propose here a definition of the von Neumann capacity of quantum channels, which is a quantum-mechanical extension of the Shannon capacity and reverts to it in the classical limit. As such, the von Neumann capacity assumes the role of a classical or quantum capacity depending on the usage of the channel. In analogy to the classical construction, this capacity is defined as the maximum von Neumann mutual entropy processed by the channel, a measure which reduces to the capacity for classical information transmission through quantum channels (the ``Kholevo capacity'') when known quantum states are sent. The quantum mutual entropy fulfills all basic requirements for a measure of information, and observes quantum data-processing inequalities. We also derive a quantum Fano inequality relating the quantum loss of the channel to the fidelity of the quantum code. The quantities introduced are calculated explicitly for the quantum depolarizing channel. The von Neumann capacity is interpreted within the context of superdense coding, and an extended Hamming bound is derived that is consistent with that capacity.
We consider the transmission of classical information over a quantum channel. The channel is defined by an ``alphabet'' of quantum states, e.g., certain photon polarizations, together with a specified set of probabilities with which these states must be sent. If the receiver is restricted to making separate measurements on the received ``letter'' states, then the Kholevo theorem implies that the amount of information transmitted per letter cannot be greater than the von Neumann entropy H of the letter ensemble. In fact the actual amount of transmitted information will usually be significantly less than H. We show, however, that if the sender uses a block coding scheme consisting of a choice of code words that respects the a priori probabilities of the letter states, and the receiver distinguishes whole words rather than individual letters, then the information transmitted per letter can be made arbitrarily close to H and never exceeds H. This provides a precise information-theoretic interpretation of von Neumann entropy in quantum mechanics. We apply this result to ``superdense'' coding, and we consider its extension to noisy channels. \textcopyright{} 1996 The American Physical Society.
The fundamental performance limits and channel capacity of optical communications systems operating over the free space channel will be examined using quantum detection theory. The performance of the optimum quantum receiver for on-off keying (OOK) and optical binary phase shift keying (BPSK) is first examined as a pure state (no noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes is then evaluated for the optimum quantum receiver by making use of the concept of quantum measurement states. The performance of M-ary pulse position modulation, which requires a product state representation, is evaluated along with the performance of certain 'dense signal sets.' Performance comparisons with classical techniques shows over 5 dB improvement in some cases when quantum detection is employed. As a further application of the quantum detection theory, the capacity of the binary channel with on-off keyed modulation and quantum detection is evaluated, and shown to exceed the capacity obtained with classical photon counting.
We define classical quantum multiway channels for transmission of classical information, after recent work by Allahverdyan and Saakian. Bounds on the capacity region are derived in a uniform way, which are analogous to the classically known ones, simply replacing Shannon entropy with von Neumann entropy. For the single receiver case (multiple-access channel) the exact capacity region is determined. These results are applied to the case of noisy channels, with arbitrary input signal states. A second issue of this work is the presentation of a calculus of quantum information quantities, based on the algebraic formulation of quantum theory.
This paper presents photonic communications and data storage capacitates for classical and quantum communications over a quantum channel. These capacities represent a generalization of Shannon’s classical channel capacity and coding theorem in two ways. First, it extends classical results for bit communication transport to all frequencies in the electromagnetic spectrum. Second, it extends the results to quantum bit (qubit) transport as well as a hybrid of classical and quantum communications. Nature’s limits on the rate at which classical and/or quantum information can be sent error-free over a quantum channel using classical and/or quantum error-correcting codes are presented as a function of the thermal background light level and Einstein zero-point energy. Graphical results are given as well as numerical results regarding communication rate limits using Planck’s natural frequency and time-interval units!