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

Physical Meaning of the Optimum Measurement Process in Quantum Detection Theory

Masao Osaki, Haruhisa Kozuka, Osamu Hirota

Published Jan 1, 1996• 1 citation
OpenAlex

Abstract

The optimum measurement processes are represented as the optimum detection operators in the quantum detection theory. The error probability by the optimum detection operators goes beyond the standard quantum limit automatically. However the optimum detection operators are given by pure mathematical descriptions. In order to realize a communication system overcoming the standard quantum limit, we try to give the physical meaning of the optimum detection operators.

Related papers

Relationship between optimum quantum detection operators for pure and mixed‐state signals

Yuji Fujihara, Tsuyoshi Sasaki Usuda, Ichi Takumi +1 more

Abstract A significant issue at present in the field of quantum information theory is the implementation of an optimum quantum receiver in which the error probability is minimized. Because a quantum receiver is represented by detection operators, in order to implement an optimum quantum receiver, it is important to derive optimum detection operators that minimize the error probability. Although it is generally difficult to analytically derive such a detection operator, optimum detection operators have been obtained on several specific signal systems in which signals are in the pure state. On the other hand, because mixed‐state signals are associated with more general signals, including classical noise, it is more important to address mixed‐state signals. However, for these signals, only basic optimum detection operators, such as binary signals in a two‐dimensional system and M‐ary symmetric signals, have been obtained. Regarding these optimum detection operators, it has been suggested that optimum detection operators for pure‐state signals can also be a reasonably good signal detection process for mixed‐state signals. Based on this suggestion, this paper examines the extent to which the optimum detection operators for pure‐state signals can be applied to mixed‐state signals. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(10): 8–18, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ecjc.1153

Electronics and Communications in Japan (Part III Fundamental Electronic Science)•Apr 14, 2003•6 citations

Optimizations of quantum measurement processes for signal detection and information transmission in quantum systems

Masashi Ban, Masao Osaki, Osamu Hirota

The calculation method proposed here obtains an optimum detection process for an M-ary signal whose quantum states are linearly independent and nonorthogonal. Optimizations are carried out by minimizing the average probability of error or by maximizing the mutual information in the signal detection process. Quantum detection operators, in terms of which the signal detection process is mathematically described, are assumed to be projection operators defined on a Hilbert space H s spanned by the quantum states of the signal; that is, the best projection operators that describe the signal detection process are obtained. The optimization procedure is equivalent to finding an appropriate unitary transformation in the Hilbert space H s. For a binary quantum state signal, the optimum detection processes in which the average probability of error is minimized and in which the mutual information is maximized are obtained. It is found that the optimum detection process minimizing the average probability of error is the same as that maximizing the mutual information.

Journal of Modern Optics•Nov 1, 1996•13 citations

Optimum phase-shift estimation and the quantum description of the phase difference

Alfredo Luis, Jan Peřina

The problem of a correct quantum description of the phase difference is examined from the perspective of parameter estimation theory. It is shown that an optimum phase-shift measurement defines a phase difference operator which coincides with other approaches to the same problem. We also study the fundamental limit to the accuracy of a phase difference shift detection. We show that this limit can be reached by a measurement having countable outcomes despite the fact that a phase shift can take any value. We show that this is the case of the phase difference operator defined by an optimum phase-shift measurement. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Nov 1, 1996•124 citations

A definition of quantum detection point processes

Christine Bénard

A definition of quantum particle detection point processes is given for normal and locally normal systems. This is realized by building coincidence measurement operators, describing in a thoroughly quantum formalism the coincidence experiments that have been actually performed (photon) or that might be performed (electron, neutron). The quantum mean values of these coincidence operators are shown to be the coincidence probabilities of a mathematically well−defined regular process. Some applications of the latter result are given, in particular in the case of fermion point processes.

Journal of Mathematical Physics•Mar 1, 1975•2 citations

Derivation and physical interpretation of the optimum detection operators for coherent-state signals

Masao Osaki, Masashi Ban, Osamu Hirota

The optimum detection operators are derived for several linearly independent signal sets. The quantum minimax strategy is applied to the M-ary coherent state signals such as binary phase shift, ternary symmetric, ternary phase shift, and quadrature phase shift. It is shown that the detection process induces a kind of quantum interference between signal quantum states and measurement states. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Aug 1, 1996•76 citations

Geometric Interpretation of Quantum-Optimum Detection for Weak Optical Signals

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.

IEEE Aerospace Conference (AERO)•Mar 7, 2026•0 citations
The optimum measurement processes are represented as the optimum detection operators in the quantum detection theory. The error probability by the optimum detection operators goes beyond the standard quantum limit automatically. However the optimum detection operators are given by pure mathematical descriptions. In order to realize a communication system overcoming the standard quantum limit, we try to give the physical meaning of the optimum detection operators.
Abstract A significant issue at present in the field of quantum information theory is the implementation of an optimum quantum receiver in which the error probability is minimized. Because a quantum receiver is represented by detection operators, in order to implement an optimum quantum receiver, it is important to derive optimum detection operators that minimize the error probability. Although it is generally difficult to analytically derive such a detection operator, optimum detection operators have been obtained on several specific signal systems in which signals are in the pure state. On the other hand, because mixed‐state signals are associated with more general signals, including classical noise, it is more important to address mixed‐state signals. However, for these signals, only basic optimum detection operators, such as binary signals in a two‐dimensional system and M‐ary symmetric signals, have been obtained. Regarding these optimum detection operators, it has been suggested that optimum detection operators for pure‐state signals can also be a reasonably good signal detection process for mixed‐state signals. Based on this suggestion, this paper examines the extent to which the optimum detection operators for pure‐state signals can be applied to mixed‐state signals. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(10): 8–18, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ecjc.1153
The calculation method proposed here obtains an optimum detection process for an M-ary signal whose quantum states are linearly independent and nonorthogonal. Optimizations are carried out by minimizing the average probability of error or by maximizing the mutual information in the signal detection process. Quantum detection operators, in terms of which the signal detection process is mathematically described, are assumed to be projection operators defined on a Hilbert space H s spanned by the quantum states of the signal; that is, the best projection operators that describe the signal detection process are obtained. The optimization procedure is equivalent to finding an appropriate unitary transformation in the Hilbert space H s. For a binary quantum state signal, the optimum detection processes in which the average probability of error is minimized and in which the mutual information is maximized are obtained. It is found that the optimum detection process minimizing the average probability of error is the same as that maximizing the mutual information.
The problem of a correct quantum description of the phase difference is examined from the perspective of parameter estimation theory. It is shown that an optimum phase-shift measurement defines a phase difference operator which coincides with other approaches to the same problem. We also study the fundamental limit to the accuracy of a phase difference shift detection. We show that this limit can be reached by a measurement having countable outcomes despite the fact that a phase shift can take any value. We show that this is the case of the phase difference operator defined by an optimum phase-shift measurement. \textcopyright{} 1996 The American Physical Society.
A definition of quantum particle detection point processes is given for normal and locally normal systems. This is realized by building coincidence measurement operators, describing in a thoroughly quantum formalism the coincidence experiments that have been actually performed (photon) or that might be performed (electron, neutron). The quantum mean values of these coincidence operators are shown to be the coincidence probabilities of a mathematically well−defined regular process. Some applications of the latter result are given, in particular in the case of fermion point processes.
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.