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

Simulating the effect of weak measurements by a phase damping channel and extraction of bipartite correlations in nuclear magnetic resonance

Akanksha Gautam, Varad R. Pande, Amandeep Singh, Kavita Dorai, Arvind Arvind

Published Apr 2, 2020• 0 citations
OpenAlex

Abstract

Quantum discord is a measure based on local projective measurements which captures quantum correlations that go beyond entanglement. A change in the measurement process, achieved by replacing rank-one projectors with a weak positive operator-valued measure (POVM), allows one to define a quantity termed as weak quantum discord. In this work, we experimentally simulate the effect of a weak POVM on a nuclear magnetic resonance quantum information processor. The two-qubit system under investigation is part of a three-qubit system, where one of the qubits is used as an ancillary to implement the phase damping channel. The strength of the weak POVM is controlled by varying the strength of the phase damping channel. We experimentally observed weak discord in two-qubit states and computed a cost function whose purpose is to optimally extract correlations representing the difference between weak and strong quantum discord. The resultant dynamics of the states is investigated as a function of the measurement strength.

Related papers

Dynamics of the Quantum Discord with Weak Measurement for a Two-atom System in Thermal Reservoirs

Mei Bai, Hong Jia Xu, Xue Qun Yan

Weak measurement is a kind of state partial collapse measurement developed on the basis of von Neumann measurement and positive operator value measurement, which allows us to explore the quantum world which has the least influence on the research system. Based on the weak measurement theory, the dynamics of quantum discord for two isolated atoms in their own thermal reservoirs is presented. We examine the time evolution of both standard quantum discord and quantum discord with weak measurement for the two-atom system, and analyzes the differences between the standard quantum discord and quantum discord with weak measurement in the evolution process with time, as well as the general role of the strength parameter in determing the discord and affecting its dynamic evolution. We show that quantum discords depend on how weak or strong one perturbs the quantum system. We also show that the difference of the standard quantum discord and the quantum discord with weak measurements increases as the strength parameter decreases. This means that the weak measurements can capture more quantum discord of a bipartite system. Our results show that the weak measurement performed on one of the subsystems can lead to the quantum discord that is a more natural measure of quantum correlations than the standard quantum discord captured by the projective measurements.

American Journal of Modern Physics•Jan 1, 2020•2 citations

Medida da dinâmica de correlações quânticas em ressonância magnética nuclear

Isabela Almeida Silva

We present a study of the decoherence processes in Nuclear Magnetic Resonance (NMR) quantum systems and their effects on the temporal evolution of non-classical correlations.For that, we review some quantum discord quantifiers, such as entropic and geometric discord as well as negativity of quantumness.To describe the relaxation of NMR systems, we use Kraus operators phase and generalized amplitude damping channels.The experimental demonstrations were achieved in 2 qubits systems implemented by J coupled spins 1/2 as well as spins 3/2 subject to quadrupolar interaction.We demonstrate the freezing phenomenon of quantum discord in a 2 spins 1/2 system, subject to phase and amplitude damping channel, and the phenomenon of double sudden-change in a spin 3/2 system, subject to amplitude damping channel.Furthermore, for spin 1/2 system, we introduce a method to selectively measure density matrix elements, that provide the necessary information to calculate discord quantifiers, without needing the full reconstruction provided by usual quantum state tomography.

•Jul 22, 2013•0 citations

Evolution of quantum discord and its stability in two-qubit NMR systems

Hemant Katiyar, Soumya S. Roy, T. S. Mahesh +1 more

We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.

arXiv:1203.1756•Physical Review A•Jul 11, 2012•28 citations

Characterizing the dynamics of quantum discord under phase damping with POVM measurements

Feng-Jian Jiang, Jianfeng Ye, Xin-Hu Yan +1 more

In the analysis of quantum discord, the minimization of average entropy traditionally involved over orthogonal projective measurements may be attained at more optimal decompositions by using the positive-operator-valued measure (POVM) measurements. Taking advantage of the quantum steering ellipsoid in combination with three-element POVM optimization, we show that, for a family of two-qubit X states locally interacting with Markovian non-dissipative environments, the decay rates of quantum discord show smooth dynamical evolutions without any sudden change. This is in contrast to two-element orthogonal projective measurements, in which case the sudden change of the decay rates of quantum and classical decoherences may be a common phenomenon. Notwithstanding this, we find that a subset of X states (including the Bell diagonal states) involving POVM optimization can still preserve the sudden change character as usual.

Chinese Physics B•Sep 29, 2015•1 citation

Measuring Bipartite Quantum Correlations of an Unknown State

I. A. Silva, Davide Girolami, R. Auccaise +6 more

We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance setup and employing geometric discord, we evaluate the quantum correlations of a state without resorting to prior knowledge of its density matrix. The method is applicable to any 2 ⊗ d system and provides, in terms of number of measurements required, an advantage over full state tomography scaling with the dimension d of the unmeasured subsystem. The negativity of quantumness is measured as well for reference. We also observe the phenomenon of sudden transition of quantum correlations when local phase and amplitude damping channels are applied to the state.

arXiv:1212.4262•Physical Review Letters•Apr 3, 2013•80 citations

Effect of weak measurement reversal on quantum correlations in a correlated amplitude damping channel, with a neural network perspective

Venkat Abhignan, Bidyut Bikash Boruah, R. Srikanth +1 more

Abstract We study the evolution of quantum correlations in Bell, Werner, and maximally entangled mixed states of two qubits subjected to correlated amplitude-damping channels. Our primary focus is to evaluate the robustness of entanglement as a resource for quantum information protocols such as dense coding, teleportation, and Einstein–Podolsky–Rosen (EPR) steering under the influence of noise. In addition, we investigate the behaviour of other quantum correlations, including quantum discord and coherence, and analyze their hierarchy under decoherence. To counteract the detrimental effects of the channels, we apply the weak measurement and quantum measurement reversal (WMR) protocol, comparing the effectiveness of single-qubit and two-qubit WMR techniques. Our results show that the two-qubit WMR protocol significantly outperforms the single-qubit approach in preserving quantum correlations. Furthermore, we employ a neural network model to enhance our analysis of the relationship between different quantum correlation measures during the evolution. Using a MATLAB-based artificial neural network with 80 neurons across three hidden layers and trained with the Levenberg–Marquardt algorithm, we successfully predict trace distance discord from other correlations, achieving low prediction errors. Besides, our analysis of the neural network weights suggests that concurrence and EPR steering have the most positive influence on the accurate discord predictions.

arXiv:2506.05642•Physica Scripta•Jun 5, 2025•2 citations
Quantum discord is a measure based on local projective measurements which captures quantum correlations that go beyond entanglement. A change in the measurement process, achieved by replacing rank-one projectors with a weak positive operator-valued measure (POVM), allows one to define a quantity termed as weak quantum discord. In this work, we experimentally simulate the effect of a weak POVM on a nuclear magnetic resonance quantum information processor. The two-qubit system under investigation is part of a three-qubit system, where one of the qubits is used as an ancillary to implement the phase damping channel. The strength of the weak POVM is controlled by varying the strength of the phase damping channel. We experimentally observed weak discord in two-qubit states and computed a cost function whose purpose is to optimally extract correlations representing the difference between weak and strong quantum discord. The resultant dynamics of the states is investigated as a function of the measurement strength.
Weak measurement is a kind of state partial collapse measurement developed on the basis of von Neumann measurement and positive operator value measurement, which allows us to explore the quantum world which has the least influence on the research system. Based on the weak measurement theory, the dynamics of quantum discord for two isolated atoms in their own thermal reservoirs is presented. We examine the time evolution of both standard quantum discord and quantum discord with weak measurement for the two-atom system, and analyzes the differences between the standard quantum discord and quantum discord with weak measurement in the evolution process with time, as well as the general role of the strength parameter in determing the discord and affecting its dynamic evolution. We show that quantum discords depend on how weak or strong one perturbs the quantum system. We also show that the difference of the standard quantum discord and the quantum discord with weak measurements increases as the strength parameter decreases. This means that the weak measurements can capture more quantum discord of a bipartite system. Our results show that the weak measurement performed on one of the subsystems can lead to the quantum discord that is a more natural measure of quantum correlations than the standard quantum discord captured by the projective measurements.
We present a study of the decoherence processes in Nuclear Magnetic Resonance (NMR) quantum systems and their effects on the temporal evolution of non-classical correlations.For that, we review some quantum discord quantifiers, such as entropic and geometric discord as well as negativity of quantumness.To describe the relaxation of NMR systems, we use Kraus operators phase and generalized amplitude damping channels.The experimental demonstrations were achieved in 2 qubits systems implemented by J coupled spins 1/2 as well as spins 3/2 subject to quadrupolar interaction.We demonstrate the freezing phenomenon of quantum discord in a 2 spins 1/2 system, subject to phase and amplitude damping channel, and the phenomenon of double sudden-change in a spin 3/2 system, subject to amplitude damping channel.Furthermore, for spin 1/2 system, we introduce a method to selectively measure density matrix elements, that provide the necessary information to calculate discord quantifiers, without needing the full reconstruction provided by usual quantum state tomography.
We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.
In the analysis of quantum discord, the minimization of average entropy traditionally involved over orthogonal projective measurements may be attained at more optimal decompositions by using the positive-operator-valued measure (POVM) measurements. Taking advantage of the quantum steering ellipsoid in combination with three-element POVM optimization, we show that, for a family of two-qubit X states locally interacting with Markovian non-dissipative environments, the decay rates of quantum discord show smooth dynamical evolutions without any sudden change. This is in contrast to two-element orthogonal projective measurements, in which case the sudden change of the decay rates of quantum and classical decoherences may be a common phenomenon. Notwithstanding this, we find that a subset of X states (including the Bell diagonal states) involving POVM optimization can still preserve the sudden change character as usual.
We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance setup and employing geometric discord, we evaluate the quantum correlations of a state without resorting to prior knowledge of its density matrix. The method is applicable to any 2 ⊗ d system and provides, in terms of number of measurements required, an advantage over full state tomography scaling with the dimension d of the unmeasured subsystem. The negativity of quantumness is measured as well for reference. We also observe the phenomenon of sudden transition of quantum correlations when local phase and amplitude damping channels are applied to the state.
Abstract We study the evolution of quantum correlations in Bell, Werner, and maximally entangled mixed states of two qubits subjected to correlated amplitude-damping channels. Our primary focus is to evaluate the robustness of entanglement as a resource for quantum information protocols such as dense coding, teleportation, and Einstein–Podolsky–Rosen (EPR) steering under the influence of noise. In addition, we investigate the behaviour of other quantum correlations, including quantum discord and coherence, and analyze their hierarchy under decoherence. To counteract the detrimental effects of the channels, we apply the weak measurement and quantum measurement reversal (WMR) protocol, comparing the effectiveness of single-qubit and two-qubit WMR techniques. Our results show that the two-qubit WMR protocol significantly outperforms the single-qubit approach in preserving quantum correlations. Furthermore, we employ a neural network model to enhance our analysis of the relationship between different quantum correlation measures during the evolution. Using a MATLAB-based artificial neural network with 80 neurons across three hidden layers and trained with the Levenberg–Marquardt algorithm, we successfully predict trace distance discord from other correlations, achieving low prediction errors. Besides, our analysis of the neural network weights suggests that concurrence and EPR steering have the most positive influence on the accurate discord predictions.