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:1606.00148 · New Journal of Physics

Observation of non-classical correlations in sequential measurements of photon polarization

Yutaro Suzuki, M. Iinuma, Holger Friedrich Hofmann

Published Oct 25, 2016• 18 citations
arXivHTMLPDF

Abstract

A sequential measurement of two non-commuting quantum observables results in a joint probability distribution for all output combinations that can be explained in terms of an initial joint quasi-probability of the non-commuting observables, modified by the resolution errors and back-action of the initial measurement. Here, we show that the error statistics of a sequential measurement of photon polarization performed at different measurement strengths can be described consistently by an imaginary correlation between the statistics of resolution and back-action. The experimental setup was designed to realize variable strength measurements with well-controlled imaginary correlation between the statistical errors caused by the initial measurement of diagonal polarizations, followed by a precise measurement of the horizontal/vertical polarization. We perform the experimental characterization of an elliptically polarized input state and show that the same complex joint probability distribution is obtained at any measurement strength.

DOI
10.1088/1367-2630/18/10/103045

Related papers

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

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

Violation of Leggett–Garg inequalities in quantum measurements with variable resolution and back-action

Yutaro Suzuki, M. Iinuma, Holger Friedrich Hofmann

Quantum mechanics violates Leggett–Garg inequalities because the operator formalism predicts correlations between different spin components that would correspond to negative joint probabilities for the outcomes of joint measurements. However, the uncertainty principle ensures that such joint measurements cannot be implemented without errors. In a sequential measurement of the spin components, the resolution and back-action errors of the intermediate measurement can be described by random spin flips acting on an intrinsic joint probability. If the error rates are known, the intrinsic joint probability can be reconstructed from the noisy statistics of the actual measurement outcomes. In this paper, we use the spin-flip model of measurement errors to analyze experimental data on photon polarization obtained with an interferometric setup that allows us to vary the measurement strength and hence the balance between resolution and back-action errors. We confirm that the intrinsic joint probability obtained from the experimental data is independent of measurement strength, and show that the same violation of the Leggett–Garg inequality can be obtained for any combination of measurement resolution and back-action.

arXiv:1206.6954•New Journal of Physics•Oct 16, 2012•97 citations

Experimental observation of quantum correlations between measurement errors using entangled photon pairs as a probe

M. Iinuma, Masayuki Nakano, Holger Friedrich Hofmann +1 more

In order to evaluate a quantum correlation between two measurement errors in a joint measurement, we performed correlation measurements of entangled photon pairs with two identified joint measurements, where two different non-commuting polarizations are jointly measured for each photon. The joint measurements were realized by filtering the polarization oriented the direction, which is halfway in two observables. The experimentally observed correlations corresponded to the ideal correlations expected for the entangled state, except for the correlation between the products of the two non-commuting polarizations. This result exceeds the limits that apply to classical error statistics and suggests that the correlation between the measurement errors in each local measurement is imaginary.

•Jan 1, 2018•0 citations

Correlation between initial and final result in a sequential quantum measurement

M. Iinuma, Yutaro Suzuki, Taiki Nii +2 more

Measurement error can be evaluated using the concepts introduced by Ozawa in 2003. Importantly, this evaluation takes into account the non-classical effects of quantum correlations. We investigate this effect by using a sequence of non-commuting measurements of photon polarization with a variable measurement resolution for the intermediate measurement. It is shown that quantum correlations between the initial and the final measurement outcomes result in a significant reduction of the measurement errors for the target observable, even though the final measurement is not sensitive to the polarization component of interest.

Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)•Aug 1, 2015•0 citations

Weak measurement of photon polarization by back-action-induced path interference

M. Iinuma, Yutaro Suzuki, Gen Taguchi +2 more

An essential feature of weak measurements on quantum systems is the reduction of measurement back-action to negligible levels. To observe the non-classical features of weak measurements, it is therefore more important to avoid additional back-action errors than it is to avoid errors in the actual measurement outcome. In this paper, it is shown how an optical weak measurement of diagonal (PM) polarization can be realized by path interference between the horizontal (H) and vertical (V) polarization components of the input beam. The measurement strength can then be controlled by rotating the H and V polarizations towards each other. This well-controlled operation effectively generates the back-action without additional decoherence, while the visibility of the interference between the two beams only limits the measurement resolution. As the experimental results confirm, we can obtain extremely high weak values, even at rather low visibilities. Our method therefore provides a realization of weak measurements that is extremely robust against experimental imperfections.

arXiv:1012.0896•New Journal of Physics•Mar 31, 2011•41 citations
A sequential measurement of two non-commuting quantum observables results in a joint probability distribution for all output combinations that can be explained in terms of an initial joint quasi-probability of the non-commuting observables, modified by the resolution errors and back-action of the initial measurement. Here, we show that the error statistics of a sequential measurement of photon polarization performed at different measurement strengths can be described consistently by an imaginary correlation between the statistics of resolution and back-action. The experimental setup was designed to realize variable strength measurements with well-controlled imaginary correlation between the statistical errors caused by the initial measurement of diagonal polarizations, followed by a precise measurement of the horizontal/vertical polarization. We perform the experimental characterization of an elliptically polarized input state and show that the same complex joint probability distribution is obtained at any measurement strength.
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.
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.
Quantum mechanics violates Leggett–Garg inequalities because the operator formalism predicts correlations between different spin components that would correspond to negative joint probabilities for the outcomes of joint measurements. However, the uncertainty principle ensures that such joint measurements cannot be implemented without errors. In a sequential measurement of the spin components, the resolution and back-action errors of the intermediate measurement can be described by random spin flips acting on an intrinsic joint probability. If the error rates are known, the intrinsic joint probability can be reconstructed from the noisy statistics of the actual measurement outcomes. In this paper, we use the spin-flip model of measurement errors to analyze experimental data on photon polarization obtained with an interferometric setup that allows us to vary the measurement strength and hence the balance between resolution and back-action errors. We confirm that the intrinsic joint probability obtained from the experimental data is independent of measurement strength, and show that the same violation of the Leggett–Garg inequality can be obtained for any combination of measurement resolution and back-action.
In order to evaluate a quantum correlation between two measurement errors in a joint measurement, we performed correlation measurements of entangled photon pairs with two identified joint measurements, where two different non-commuting polarizations are jointly measured for each photon. The joint measurements were realized by filtering the polarization oriented the direction, which is halfway in two observables. The experimentally observed correlations corresponded to the ideal correlations expected for the entangled state, except for the correlation between the products of the two non-commuting polarizations. This result exceeds the limits that apply to classical error statistics and suggests that the correlation between the measurement errors in each local measurement is imaginary.
Measurement error can be evaluated using the concepts introduced by Ozawa in 2003. Importantly, this evaluation takes into account the non-classical effects of quantum correlations. We investigate this effect by using a sequence of non-commuting measurements of photon polarization with a variable measurement resolution for the intermediate measurement. It is shown that quantum correlations between the initial and the final measurement outcomes result in a significant reduction of the measurement errors for the target observable, even though the final measurement is not sensitive to the polarization component of interest.
An essential feature of weak measurements on quantum systems is the reduction of measurement back-action to negligible levels. To observe the non-classical features of weak measurements, it is therefore more important to avoid additional back-action errors than it is to avoid errors in the actual measurement outcome. In this paper, it is shown how an optical weak measurement of diagonal (PM) polarization can be realized by path interference between the horizontal (H) and vertical (V) polarization components of the input beam. The measurement strength can then be controlled by rotating the H and V polarizations towards each other. This well-controlled operation effectively generates the back-action without additional decoherence, while the visibility of the interference between the two beams only limits the measurement resolution. As the experimental results confirm, we can obtain extremely high weak values, even at rather low visibilities. Our method therefore provides a realization of weak measurements that is extremely robust against experimental imperfections.