The Experts below are selected from a list of 276 Experts worldwide ranked by ideXlab platform
Urbasi Sinha - One of the best experts on this subject based on the ideXlab platform.
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Measuring average of non-Hermitian Operator with weak value in a Mach-Zehnder interferometer
Physical Review A, 2019Co-Authors: Gaurav Nirala, Surya Narayan Sahoo, Arun Kumar Pati, Urbasi SinhaAbstract:Quantum theory allows direct measurement of the average of a non-Hermitian Operator using the weak value of the positive semidefinite part of the non-Hermitian Operator. Here, we experimentally demonstrate the measurement of weak value and average of non-Hermitian Operators by a novel interferometric technique. Our scheme is unique as we can directly obtain the weak value from the interference visibility and the phase shift in a Mach Zehnder interferometer without using any weak measurement or post selection. Both the experiments discussed here were performed with laser sources, but the results would be the same with average statistics of single photon experiments. Thus, the present experiment opens up the novel possibility of measuring weak value and the average value of non-Hermitian Operator without weak interaction and post-selection, which can have several technological applications.
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Measuring non-Hermitian Operators via weak values
Physical Review A, 2015Co-Authors: Arun Kumar Pati, Uttam Singh, Urbasi SinhaAbstract:In quantum theory, a physical observable is represented by a Hermitian Operator as it admits real eigenvalues. This stems from the fact that any measuring apparatus that is supposed to measure a physical observable will always yield a real number. However, the reality of an eigenvalue of some Operator does not mean that it is necessarily Hermitian. There are examples of non-Hermitian Operators that may admit real eigenvalues under some symmetry conditions. In general, given a non-Hermitian Operator, its average value in a quantum state is a complex number and there are only very limited methods available to measure it. Following standard quantum mechanics, we provide an experimentally feasible protocol to measure the expectation value of any non-Hermitian Operator via weak measurements. The average of a non-Hermitian Operator in a pure state is a complex multiple of the weak value of the positive-semidefinite part of the non-Hermitian Operator. We also prove an uncertainty relation for any two non-Hermitian Operators and show that the fidelity of a quantum state under a quantum channel can be measured using the average of the corresponding Kraus Operators. The importance of our method is shown in testing the stronger uncertainty relation, verifying the Ramanujan formula, and measuring the product of noncommuting projectors.
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Quantum Theory Allows Measurement of Non-Hermitian Operators
2014Co-Authors: Arun Kumar Pati, Uttam Singh, Urbasi SinhaAbstract:In quantum theory, a physical observable is represented by a Hermitian Operator as it admits real eigenvalues. This stems from the fact that any measuring apparatus that is supposed to measure a physical observable will always yield a real number. However, reality of eigenvalue of some Operator does not mean that it is necessarily Hermitian. There are examples of non-Hermitian Operators which may admit real eigenvalues under some symmetry conditions. However, in general, given a non-Hermitian Operator, its average value in a quantum state is a complex number and there are only very limited methods available to measure it. Following standard quantum mechanics, we provide an experimentally feasible protocol to measure the expectation value of any non-Hermitian Operator via weak measurements. The average of a non-Hermitian Operator in a pure state is a complex multiple of the weak value of the positive semi-definite part of the non-Hermitian Operator. We also prove a new uncertainty relation for any two non-Hermitian Operators and show that the fidelity of a quantum state under quantum channel can be measured using the average of the corresponding Kraus Operators. The importance of our method is shown in testing the stronger uncertainty relation, verifying the Ramanujan formula and in measuring the product of non commuting projectors.
Stefano Cerbelli - One of the best experts on this subject based on the ideXlab platform.
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Spectral analysis of the weighted Laplacian in slip and no-slip flows.
Physical Review E, 2009Co-Authors: Massimiliano Giona, Alessandra Adrover, Stefano CerbelliAbstract:Slip boundary conditions for the velocity field impact on the spectral properties of the advection-diffusion Operator describing transport of passive particles in laminar parallel flows. By considering the Hermitian Operator (referred to as the weighted Laplacian), describing the interplay between axial convection and cross-sectional diffusion of a scalar field, we show that the spectral watershed between slip and no-slip boundary conditions is a qualitatively different scaling behavior of the mean of the normalized eigenfunctions of the weighted Laplacian. The occurrence of slip conditions also influences the scaling of the density of states as regards both the leading and the subleading term in the Weyl's expansion.
Arun Kumar Pati - One of the best experts on this subject based on the ideXlab platform.
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Measuring average of non-Hermitian Operator with weak value in a Mach-Zehnder interferometer
Physical Review A, 2019Co-Authors: Gaurav Nirala, Surya Narayan Sahoo, Arun Kumar Pati, Urbasi SinhaAbstract:Quantum theory allows direct measurement of the average of a non-Hermitian Operator using the weak value of the positive semidefinite part of the non-Hermitian Operator. Here, we experimentally demonstrate the measurement of weak value and average of non-Hermitian Operators by a novel interferometric technique. Our scheme is unique as we can directly obtain the weak value from the interference visibility and the phase shift in a Mach Zehnder interferometer without using any weak measurement or post selection. Both the experiments discussed here were performed with laser sources, but the results would be the same with average statistics of single photon experiments. Thus, the present experiment opens up the novel possibility of measuring weak value and the average value of non-Hermitian Operator without weak interaction and post-selection, which can have several technological applications.
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Measuring non-Hermitian Operators via weak values
Physical Review A, 2015Co-Authors: Arun Kumar Pati, Uttam Singh, Urbasi SinhaAbstract:In quantum theory, a physical observable is represented by a Hermitian Operator as it admits real eigenvalues. This stems from the fact that any measuring apparatus that is supposed to measure a physical observable will always yield a real number. However, the reality of an eigenvalue of some Operator does not mean that it is necessarily Hermitian. There are examples of non-Hermitian Operators that may admit real eigenvalues under some symmetry conditions. In general, given a non-Hermitian Operator, its average value in a quantum state is a complex number and there are only very limited methods available to measure it. Following standard quantum mechanics, we provide an experimentally feasible protocol to measure the expectation value of any non-Hermitian Operator via weak measurements. The average of a non-Hermitian Operator in a pure state is a complex multiple of the weak value of the positive-semidefinite part of the non-Hermitian Operator. We also prove an uncertainty relation for any two non-Hermitian Operators and show that the fidelity of a quantum state under a quantum channel can be measured using the average of the corresponding Kraus Operators. The importance of our method is shown in testing the stronger uncertainty relation, verifying the Ramanujan formula, and measuring the product of noncommuting projectors.
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Quantum Theory Allows Measurement of Non-Hermitian Operators
2014Co-Authors: Arun Kumar Pati, Uttam Singh, Urbasi SinhaAbstract:In quantum theory, a physical observable is represented by a Hermitian Operator as it admits real eigenvalues. This stems from the fact that any measuring apparatus that is supposed to measure a physical observable will always yield a real number. However, reality of eigenvalue of some Operator does not mean that it is necessarily Hermitian. There are examples of non-Hermitian Operators which may admit real eigenvalues under some symmetry conditions. However, in general, given a non-Hermitian Operator, its average value in a quantum state is a complex number and there are only very limited methods available to measure it. Following standard quantum mechanics, we provide an experimentally feasible protocol to measure the expectation value of any non-Hermitian Operator via weak measurements. The average of a non-Hermitian Operator in a pure state is a complex multiple of the weak value of the positive semi-definite part of the non-Hermitian Operator. We also prove a new uncertainty relation for any two non-Hermitian Operators and show that the fidelity of a quantum state under quantum channel can be measured using the average of the corresponding Kraus Operators. The importance of our method is shown in testing the stronger uncertainty relation, verifying the Ramanujan formula and in measuring the product of non commuting projectors.
Tomio Petrosky - One of the best experts on this subject based on the ideXlab platform.
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non divergent representation of a non Hermitian Operator near the exceptional point with application to a quantum lorentz gas
Progress of Theoretical and Experimental Physics, 2015Co-Authors: Kazunari Hashimoto, Kazuki Kanki, Hisao Hayakawa, Tomio PetroskyAbstract:Non-divergent representation of a non-Hermitian Operator near the exceptional point with application to a quantum Lorentz gas Kazunari Hashimoto1,∗, Kazuki Kanki1, Hisao Hayakawa2, and Tomio Petrosky3,4 1Department of Physical Science, Osaka Prefecture University, Sakai 599-8531, Japan 2Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8501, Japan 3Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan 4Center for Complex Quantum Systems, The University of Texas at Austin, TX 78712, USA ∗E-mail: kazu.uncertainworld@gmail.com
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non divergent representation of non Hermitian Operator near the exceptional point with application to a quantum lorentz gas
arXiv: Statistical Mechanics, 2014Co-Authors: Kazunari Hashimoto, Kazuki Kanki, Hisao Hayakawa, Tomio PetroskyAbstract:We propose a non-singular representation for a non-Hermitian Operator even if the parameter space contains exceptional points (EPs), at which the Operator cannot be diagonalized and the usual spectral representation ceases to exist. Our representation has a generalized Jordan block form and is written in terms of extended pseudo-eigenstates. Our method is free from a divergence in the spectral representation at EPs, at which multiple eigenvalues and eigenvectors coalesce and the eigenvectors cannot be normalized. Our representation improves the accuracy of numerical calculations of physical quantities near EPs. We also find that our method is applicable to various problems related to EPs in the parameter space of non-Hermitian Operators. We demonstrate the usefulness of our representation by investigating Boltzmann's collision Operator in a one-dimensional quantum Lorentz gas in the weak coupling approximation.
Tzu-chieh Wei - One of the best experts on this subject based on the ideXlab platform.
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Quantum algorithm for spectral projection by measuring an ancilla iteratively
Physical Review A, 2020Co-Authors: Yanzhu Chen, Tzu-chieh WeiAbstract:We propose a quantum algorithm for projecting a quantum system to eigenstates of any Hermitian Operator, provided one can access the associated control-unitary evolution for the ancilla and the system, as well as the measurement of the controlling ancillary qubit. Such a Hadamard-test-like primitive is iterated so as to achieve the spectral projection, and the distribution of the projected eigenstates obeys the Born rule. This algorithm can be used as a subroutine in the quantum annealing procedure by measurement to drive the system to the ground state of a final Hamiltonian, and we simulate this for quantum many-body spin chains.
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Quantum algorithm for spectral projection by measuring an ancilla
arXiv: Quantum Physics, 2019Co-Authors: Yanzhu Chen, Tzu-chieh WeiAbstract:We propose a quantum algorithm for projecting to eigenstates of any Hermitian Operator, provided one can access the associated control-unitary evolution and measurement of the ancilla of the control. The procedure is iterative and the distribution of the projected eigenstates obeys the Born rule. This algorithm can be used as a subroutine in the quantum annealing procedure by measurement to drive the system to the ground state, and we demonstrate its feasibility by simulating the procedure
