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/0003067

Correlations of measurement information and noise in quantum measurements with finite resolution

Holger Friedrich Hofmann, Takayoshi Kobayashi, Akira Furusawa

Published Mar 17, 2000• 0 citations
arXivHTMLPDF

Abstract

The original purpose of measurements is to provide us with information about a previously unknown physical property of the system observed. In the Hilbert space formalism of quantum mechanics, this physical meaning of measurement information is not immediately apparent. In order to study the relationship between the Hilbert space coherence of the quantum state and the measurement information obtained in the laboratory, we introduce a generalized measurement postulate for finite resolution measurements. With this measurement model, correlations between non-commuting observables can be investigated. These experimentally accessible correlations reveal nonclassical features in their dependence on the operator ordering, reflecting the particular measurement context by which they are determined.

DOI
10.48550/arxiv.quant-ph/0003067

Related papers

Correlations of measurement information and noise in quantum measurements with finite resolution (Analytical Study of Quantum Information and Related Fields)

Holger Friedrich Hofmann, Takayoshi Kobayashi, Akira Furusawa

The original purpose of measurements is to provide us with information about a previously unknown physical property of the systeIn observed.In the Hilbert space formalism of quantum mechanics, this physical meaning of measurement information is not immediately apparent.In order to study the relationship between the Hilbert space coherence of the quantum state and the measurement information obtained in the laboratory, we introduce a generalized measurement postulate for finite resolution measurements.With this measurement model, correlations between non-commuting observables can be investigated.These experimentally accessible correlations reveal nonclassical features in their dependence on the operator ordering, reflecting the particular measurement context by which they are determined.

数理解析研究所講究録•Apr 1, 2001•0 citations

Uncertainty characteristics of generalized quantum measurements

Holger Friedrich Hofmann

The effects of any quantum measurement can be described by a collection of measurement operators ${{M}_{m}}$ acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the measurement results and the physical properties of the measured system. In this paper, a characterization of measurement operators in terms of measurement resolution and disturbance is developed. It is then possible to formulate uncertainty relations for the measurement process that are valid for arbitrary input states. The motivation of these concepts is explained from a quantum communication viewpoint. It is shown that the intuitive interpretation of uncertainty as a relation between measurement resolution and disturbance provides a valid description of measurement back action. Possible applications to quantum cryptography, quantum cloning, and teleportation are discussed.

arXiv:quant-ph/0209162•Physical Review A•Feb 13, 2003•18 citations

Sequential measurements of non-commuting observables with quantum controlled interactions

Holger F Hofmann

The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here, this problem is addressed by investigating the uncertainty trade-off between measurement errors and disturbance for measurement interactions controlled by the state of a single qubit, where the measurement is described by a quantum coherent superposition of a fully projective measurement and the identity operation. It is shown that the measurement statistics obtained from a quantum controlled measurement of followed by a projective measurement of can be explained in terms of a simple combination of resolution and back-action errors acting on an intrinsic joint probability of the non-commuting observables defined by the input state of the system. These intrinsic joint probabilities are consistent with the complex-valued joint probabilities recently observed in weak measurements of quantum systems and provide direct evidence of non-commutativity in the form of imaginary correlations between the non-commuting operators. In quantum controlled measurements, these imaginary correlations can be converted into well-defined contributions to the real measurement statistics, allowing a direct experimental observation of the less intuitive aspects of quantum theory.

arXiv:1212.2683•New Journal of Physics•Jun 24, 2014•31 citations

Nonclassical correlations between photon number and quadrature components of the light field

Holger Friedrich Hofmann

Finite resolution quantum nondemolition (QND) measurements allow a determination of light field properties while preserving some of the original quantum coherence of the input state. It is thus possible to measure correlations between the photon number and a quadrature component of the same light field mode. Nonclassical features emerge as photon number quantization is resolved. In particular, a strong anti-correlation of quantization and coherence is observable in QND measurements of photon number, and a correlation between measurement induced quantum jumps and quadrature component measurement results is obtained in QND measurements of quadrature fluctuations in the photon vacuum. Such nonclassical correlations represent fundamental quantum properties of the light field and may provide new insights into the nature of quantization itself.

arXiv:quant-ph/0004073•Apr 19, 2000•0 citations

Sequential measurements of non-commuting observables with quantum controlled interactions

Holger Friedrich Hofmann

The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here, this problem is addressed by investigating the uncertainty trade-off between measurement errors and disturbance for measurement interactions controlled by the state of a single qubit, where the measurement is described by a quantum coherent superposition of a fully projective measurement and the identity operation. It is shown that the measurement statistics obtained from a quantum controlled measurement of followed by a projective measurement of can be explained in terms of a simple combination of resolution and back-action errors acting on an intrinsic joint probability of the non-commuting observables defined by the input state of the system. These intrinsic joint probabilities are consistent with the complex-valued joint probabilities recently observed in weak measurements of quantum systems and provide direct evidence of non-commutativity in the form of imaginary correlations between the non-commuting operators. In quantum controlled measurements, these imaginary correlations can be converted into well-defined contributions to the real measurement statistics, allowing a direct experimental observation of the less intuitive aspects of quantum theory.

•Aug 16, 2016•13 citations

Finite-resolution measurement of the nonclassical polarization statistics of entangled photon pairs

Holger Friedrich Hofmann

By limiting the resolution of quantum measurements, measurement-induced changes of the quantum state can be reduced, permitting subsequent measurements of variables that do not commute with the initially measured property. It is then possible to determine correlations between noncommuting variables experimentally. The application of this method to the polarization statistics of entangled photon pairs reveals that negative conditional probabilities between nonorthogonal polarization components are responsible for the violation of Bell's inequalities. Such negative probabilities can also be observed in finite-resolution measurements of the polarization of a single photon. The violation of Bell's inequalities therefore originates from local properties of the quantum statistics of single-photon polarization.

arXiv:quant-ph/0008122•Physical Review A•Mar 16, 2001•4 citations
The original purpose of measurements is to provide us with information about a previously unknown physical property of the system observed. In the Hilbert space formalism of quantum mechanics, this physical meaning of measurement information is not immediately apparent. In order to study the relationship between the Hilbert space coherence of the quantum state and the measurement information obtained in the laboratory, we introduce a generalized measurement postulate for finite resolution measurements. With this measurement model, correlations between non-commuting observables can be investigated. These experimentally accessible correlations reveal nonclassical features in their dependence on the operator ordering, reflecting the particular measurement context by which they are determined.
The original purpose of measurements is to provide us with information about a previously unknown physical property of the systeIn observed.In the Hilbert space formalism of quantum mechanics, this physical meaning of measurement information is not immediately apparent.In order to study the relationship between the Hilbert space coherence of the quantum state and the measurement information obtained in the laboratory, we introduce a generalized measurement postulate for finite resolution measurements.With this measurement model, correlations between non-commuting observables can be investigated.These experimentally accessible correlations reveal nonclassical features in their dependence on the operator ordering, reflecting the particular measurement context by which they are determined.
The effects of any quantum measurement can be described by a collection of measurement operators Mm{{M}_{m}}Mm​ acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the measurement results and the physical properties of the measured system. In this paper, a characterization of measurement operators in terms of measurement resolution and disturbance is developed. It is then possible to formulate uncertainty relations for the measurement process that are valid for arbitrary input states. The motivation of these concepts is explained from a quantum communication viewpoint. It is shown that the intuitive interpretation of uncertainty as a relation between measurement resolution and disturbance provides a valid description of measurement back action. Possible applications to quantum cryptography, quantum cloning, and teleportation are discussed.
The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here, this problem is addressed by investigating the uncertainty trade-off between measurement errors and disturbance for measurement interactions controlled by the state of a single qubit, where the measurement is described by a quantum coherent superposition of a fully projective measurement and the identity operation. It is shown that the measurement statistics obtained from a quantum controlled measurement of followed by a projective measurement of can be explained in terms of a simple combination of resolution and back-action errors acting on an intrinsic joint probability of the non-commuting observables defined by the input state of the system. These intrinsic joint probabilities are consistent with the complex-valued joint probabilities recently observed in weak measurements of quantum systems and provide direct evidence of non-commutativity in the form of imaginary correlations between the non-commuting operators. In quantum controlled measurements, these imaginary correlations can be converted into well-defined contributions to the real measurement statistics, allowing a direct experimental observation of the less intuitive aspects of quantum theory.
Finite resolution quantum nondemolition (QND) measurements allow a determination of light field properties while preserving some of the original quantum coherence of the input state. It is thus possible to measure correlations between the photon number and a quadrature component of the same light field mode. Nonclassical features emerge as photon number quantization is resolved. In particular, a strong anti-correlation of quantization and coherence is observable in QND measurements of photon number, and a correlation between measurement induced quantum jumps and quadrature component measurement results is obtained in QND measurements of quadrature fluctuations in the photon vacuum. Such nonclassical correlations represent fundamental quantum properties of the light field and may provide new insights into the nature of quantization itself.
The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here, this problem is addressed by investigating the uncertainty trade-off between measurement errors and disturbance for measurement interactions controlled by the state of a single qubit, where the measurement is described by a quantum coherent superposition of a fully projective measurement and the identity operation. It is shown that the measurement statistics obtained from a quantum controlled measurement of followed by a projective measurement of can be explained in terms of a simple combination of resolution and back-action errors acting on an intrinsic joint probability of the non-commuting observables defined by the input state of the system. These intrinsic joint probabilities are consistent with the complex-valued joint probabilities recently observed in weak measurements of quantum systems and provide direct evidence of non-commutativity in the form of imaginary correlations between the non-commuting operators. In quantum controlled measurements, these imaginary correlations can be converted into well-defined contributions to the real measurement statistics, allowing a direct experimental observation of the less intuitive aspects of quantum theory.
By limiting the resolution of quantum measurements, measurement-induced changes of the quantum state can be reduced, permitting subsequent measurements of variables that do not commute with the initially measured property. It is then possible to determine correlations between noncommuting variables experimentally. The application of this method to the polarization statistics of entangled photon pairs reveals that negative conditional probabilities between nonorthogonal polarization components are responsible for the violation of Bell's inequalities. Such negative probabilities can also be observed in finite-resolution measurements of the polarization of a single photon. The violation of Bell's inequalities therefore originates from local properties of the quantum statistics of single-photon polarization.