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Interplanetary Network Progress Report

Quantum Detection and Channel Capacity Using State-Space Optimization

Chi-Wung Lau, Victor A. Vilnrotter

Published Oct 1, 2001• 8 citations
OpenAlex

Abstract

The fundamental performance limits and channel capacity of optical commu-nications systems operating over the free-space channel will be examined using quantum detection theory. The performance of the optimum quantum receiver for on{ofi keying and optical binary phase-shift keying is flrst examined as a pure-state (no-noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes will be 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, will be evaluated along with the performance of certain dense signal sets. Perfor-mance comparisons with classical techniques show an improvement of over 5 dB 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{ofi keyed modulation and quantum detection is evaluated and shown to exceed the capacity obtained with classical photon counting. I.

Related papers

Quantum Detection and Channel Capacity Using

State-Space Optimization

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{ofi keying and optical binary phase-shift keying is flrst examined as a pure-state (no-noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes will be 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, will be evaluated along with the performance of certain dense signal sets. Performance comparisons with classical techniques show an improvement of over 5 dB 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{ofi keyed modulation and quantum detection is evaluated and shown to exceed the capacity obtained with classical photon counting.

•Jan 1, 2002•0 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.

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Quantum Detection Theory for the Free-Space Channel

Victor A. Vilnrotter, Chi-Wung Lau

The fundamental performance limits of optical communications over the freespace channel are developed using quantum theory, and presented in terms of concepts familiar to communications engineers. The compact Dirac notation generally employed in quantum mechanics is defined, and key concepts necessary for understanding quantum projection measurements are reviewed. A derivation that provides significant insights into the quantum measurement performed by the optimum receiver is developed by interpreting the familiar technique of photon counting in terms of quantum projection operators. The performance of the optimum quantum receiver for on–off keying and optical binary phase-shift-keying (BPSK) modulation is treated first as a noise-free (or pure-state) problem, then extended to include the effects of background radiation. The performance of the optimum quantum receiver is compared to that of classical optical receivers employing photon-counting and coherent detection techniques, and it is shown to be exponentially better in most cases.

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Victor A. Vilnrotter

The mathematical structure of the quantum-optimum detection operators for optical signals is derived, and approximated in a three-dimensional number-state basis for the case of weak optical signals. It is shown that mathematical rotation of the received signal-states in Hilbert-space approaches the quantum-optimum detection performance for optical signals such as On-Off Keying (OOK), BPSK (binary phase-shift keying), and binary Pulse Position Modulation (2-PPM) signaling formats originating from interplanetary or even greater interstellar distances. The approximate three-dimensional number-state model is interpreted to help identify the physical operations required to implement the quantum-optimum receiver with well-known field-preparation and signal-processing techniques for these three modulation formats. Graphs demonstrating the practical performance of receivers approximated by three-dimensional detection operators are evaluated, and compared with the theoretical limit on ideal receiver performance dictated by the laws of quantum mechanics.

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M. A. Vázquez‐Castro, Bunyod Samandarov

We assume information is discrete-modulated over coherent states of the single-mode electromagnetic field and transmitted over space quantum channels. In this letter, we provide a comparison of quantum detection with classical detection for communication using on-off keying (OOK) and binary phase shift keying (BPSK) for illustrative system parameters for LEO, MEO and GEO satellites. To do so, we assume an attenuation-only (pure-loss) channel and compute the Shannon capacities for the following detection methods: classical (shot-noise limited) single-photon and coherent detectors as well as optimal quantum hypothesis-testing (Helstrom) detection. As in classical system engineering design, we also obtain theoretical references for comparison, namely, Shannon capacities and Holevo bounds for the ideal Gaussian optical channel. Our results show the ranges of transmitted power and orbital heights for which either classical or quantum detection is optimal, thus providing useful insights into design guidelines and operations of future space communication systems. We also obtain the remarkable result that the BPSK Holevo bound achieves the ultimate quantum capacity of the considered channel.

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On quantum limit of optical communications: Concatenated codes and joint-detection receivers

Saikat Guha, Zachary Dutton, Jeffrey H. Shapiro

When classical information is sent over a channel with quantum-state modulation alphabet, such as the free-space optical (FSO) channel, attaining the ultimate (Holevo) limit to channel capacity requires the receiver to make joint measurements over long codeword blocks. In recent work, we showed a receiver for a pure-state channel that can attain the ultimate capacity by applying a single-shot optical (unitary) transformation on the received codeword state followed by simultaneous (but separable) projective measurements on the single-modulation-symbol state spaces. In this paper, we study the ultimate tradeoff between photon efficiency and spectral efficiency for the FSO channel. Based on our general results for the pure-state quantum channel, we show some of the first concrete examples of codes and laboratory-realizable joint-detection optical receivers that can achieve fundamentally higher (superadditive) channel capacity than receivers that physically detect each modulation symbol one at a time, as is done by all conventional (coherent or direct-detection) optical receivers.

arXiv:1102.1963•IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2011•24 citations
The fundamental performance limits and channel capacity of optical commu-nications systems operating over the free-space channel will be examined using quantum detection theory. The performance of the optimum quantum receiver for on{ofi keying and optical binary phase-shift keying is flrst examined as a pure-state (no-noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes will be 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, will be evaluated along with the performance of certain dense signal sets. Perfor-mance comparisons with classical techniques show an improvement of over 5 dB 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{ofi keyed modulation and quantum detection is evaluated and shown to exceed the capacity obtained with classical photon counting. I.
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{ofi keying and optical binary phase-shift keying is flrst examined as a pure-state (no-noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes will be 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, will be evaluated along with the performance of certain dense signal sets. Performance comparisons with classical techniques show an improvement of over 5 dB 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{ofi keyed modulation and quantum detection is evaluated and shown to exceed the capacity obtained with classical photon counting.
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.
The fundamental performance limits of optical communications over the freespace channel are developed using quantum theory, and presented in terms of concepts familiar to communications engineers. The compact Dirac notation generally employed in quantum mechanics is defined, and key concepts necessary for understanding quantum projection measurements are reviewed. A derivation that provides significant insights into the quantum measurement performed by the optimum receiver is developed by interpreting the familiar technique of photon counting in terms of quantum projection operators. The performance of the optimum quantum receiver for on–off keying and optical binary phase-shift-keying (BPSK) modulation is treated first as a noise-free (or pure-state) problem, then extended to include the effects of background radiation. The performance of the optimum quantum receiver is compared to that of classical optical receivers employing photon-counting and coherent detection techniques, and it is shown to be exponentially better in most cases.
The mathematical structure of the quantum-optimum detection operators for optical signals is derived, and approximated in a three-dimensional number-state basis for the case of weak optical signals. It is shown that mathematical rotation of the received signal-states in Hilbert-space approaches the quantum-optimum detection performance for optical signals such as On-Off Keying (OOK), BPSK (binary phase-shift keying), and binary Pulse Position Modulation (2-PPM) signaling formats originating from interplanetary or even greater interstellar distances. The approximate three-dimensional number-state model is interpreted to help identify the physical operations required to implement the quantum-optimum receiver with well-known field-preparation and signal-processing techniques for these three modulation formats. Graphs demonstrating the practical performance of receivers approximated by three-dimensional detection operators are evaluated, and compared with the theoretical limit on ideal receiver performance dictated by the laws of quantum mechanics.
We assume information is discrete-modulated over coherent states of the single-mode electromagnetic field and transmitted over space quantum channels. In this letter, we provide a comparison of quantum detection with classical detection for communication using on-off keying (OOK) and binary phase shift keying (BPSK) for illustrative system parameters for LEO, MEO and GEO satellites. To do so, we assume an attenuation-only (pure-loss) channel and compute the Shannon capacities for the following detection methods: classical (shot-noise limited) single-photon and coherent detectors as well as optimal quantum hypothesis-testing (Helstrom) detection. As in classical system engineering design, we also obtain theoretical references for comparison, namely, Shannon capacities and Holevo bounds for the ideal Gaussian optical channel. Our results show the ranges of transmitted power and orbital heights for which either classical or quantum detection is optimal, thus providing useful insights into design guidelines and operations of future space communication systems. We also obtain the remarkable result that the BPSK Holevo bound achieves the ultimate quantum capacity of the considered channel.
When classical information is sent over a channel with quantum-state modulation alphabet, such as the free-space optical (FSO) channel, attaining the ultimate (Holevo) limit to channel capacity requires the receiver to make joint measurements over long codeword blocks. In recent work, we showed a receiver for a pure-state channel that can attain the ultimate capacity by applying a single-shot optical (unitary) transformation on the received codeword state followed by simultaneous (but separable) projective measurements on the single-modulation-symbol state spaces. In this paper, we study the ultimate tradeoff between photon efficiency and spectral efficiency for the FSO channel. Based on our general results for the pure-state quantum channel, we show some of the first concrete examples of codes and laboratory-realizable joint-detection optical receivers that can achieve fundamentally higher (superadditive) channel capacity than receivers that physically detect each modulation symbol one at a time, as is done by all conventional (coherent or direct-detection) optical receivers.