It is widely accepted that the selection of measurement bases can affect the efficiency of quantum state estimation methods, precision of estimating an unknown state can be improved significantly by simply introduce a set of symmetrical measurement bases. Here we compare the efficiencies of estimations with different numbers of measurement bases by numerical simulation and experiment in optical system. The advantages of using a complete set of symmetrical measurement bases are illustrated more clearly.It is widely accepted that the selection of measurement bases can affect the efficiency of quantum state estimation methods, precision of estimating an unknown state can be improved significantly by simply introduce a set of symmetrical measurement bases. Here we compare the efficiencies of estimations with different numbers of measurement bases by numerical simulation and experiment in optical system. The advantages of using a complete set of symmetrical measurement bases are illustrated more clearly.

Aug 30, 20110 citations

Improving Quantum State Estimation with Mutually Unbiased Bases

Robert B. A. Adamson, Aephraim M. Steinberg

When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state tomography of two-qubit polarization states to take advantage of mutually unbiased bases. We demonstrate improved state estimation as compared to standard measurement strategies and discuss how this can be understood from the structure of the measurements we use. We experimentally compared our method to the standard state estimation method for three different states and observe that the infidelity was up to 1.84 ± 0.06 times lower by using our technique than it was by using standard state estimation methods.When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state tomography of two-qubit polarization states to take advantage of mutually unbiased bases. We demonstrate improved state estimation as compared to standard measurement strategies and discuss how this can be understood from the structure of the measurements we use. We experimentally compared our method to the standard state estimation method for three different states and observe that the infidelity was up to 1.84 ± 0.06 times lower by using our technique than it was by using standard state estimation methods.

arXiv:0808.0944Physical Review LettersJul 16, 2010186 citations

Improved estimation accuracy of the 5-bases-based tomographic method

Leonardo Zambrano, Luciano Pereira, A. Delgado

It has been recently shown that for quantum systems with dimension $d\ensuremath{\ge}4$ unknown pure states can be estimated via measurements on five bases only. Here, we study by means of numerical experiments the estimation accuracy of this method as a function of the dimension and the number of independently, identically prepared copies, that is, ensemble size. We show that the accuracy of this method can be greatly improved by modifying the estimation procedure, without increasing the number of measurement outcomes. The present estimation accuracy becomes approximately $d$ times smaller than the best accuracy achievable by tomographic methods for unknown mixed states. We also study the case of pure states affected by a low level of white noise. We show that the modified version of the method is very robust; that is, it remains to a large extent unaffected by the noise and achieves an accuracy similar to the case without noise.It has been recently shown that for quantum systems with dimension $d\ensuremath{\ge}4$ unknown pure states can be estimated via measurements on five bases only. Here, we study by means of numerical experiments the estimation accuracy of this method as a function of the dimension and the number of independently, identically prepared copies, that is, ensemble size. We show that the accuracy of this method can be greatly improved by modifying the estimation procedure, without increasing the number of measurement outcomes. The present estimation accuracy becomes approximately $d$ times smaller than the best accuracy achievable by tomographic methods for unknown mixed states. We also study the case of pure states affected by a low level of white noise. We show that the modified version of the method is very robust; that is, it remains to a large extent unaffected by the noise and achieves an accuracy similar to the case without noise.

Physical Review AAug 28, 201911 citations

Fast universal performance certification of measurement schemes for quantum tomography

Dominik Koutný, Yong Siah Teo, Z. Hradil +1 more

Prior to a measurement in a quantum-state tomography experiment, it is important to evaluate the performance of this measurement with respect to the average accuracy in state estimation. We propose a fast and reliable numerical certification of measurement performance that is applicable to any known quantum measurement. This numerical method is based on the statistical theory of unbiased estimation that is valid for any physically accessible quantum state that is necessarily full rank in the limit of a large number of measurement copies, and the Hoeffding inequality that applies to bounded statistical quantities in the quantum state space. We present the use of this straightforward certification procedure by illustrating the convergence to optimal pure-state tomography with an increasing number of overcomplete measurement outcomes. Furthermore, we demonstrate that the performances of symmetric informationally complete measurements and mutually unbiased bases, which are commonly regarded as optimal measurements, can be easily beaten in tomographic performance with randomly generated measurements that are only slightly more informationally overcomplete. Two important classes of random measurements are also discussed with the help of our numerical machinery.Prior to a measurement in a quantum-state tomography experiment, it is important to evaluate the performance of this measurement with respect to the average accuracy in state estimation. We propose a fast and reliable numerical certification of measurement performance that is applicable to any known quantum measurement. This numerical method is based on the statistical theory of unbiased estimation that is valid for any physically accessible quantum state that is necessarily full rank in the limit of a large number of measurement copies, and the Hoeffding inequality that applies to bounded statistical quantities in the quantum state space. We present the use of this straightforward certification procedure by illustrating the convergence to optimal pure-state tomography with an increasing number of overcomplete measurement outcomes. Furthermore, we demonstrate that the performances of symmetric informationally complete measurements and mutually unbiased bases, which are commonly regarded as optimal measurements, can be easily beaten in tomographic performance with randomly generated measurements that are only slightly more informationally overcomplete. Two important classes of random measurements are also discussed with the help of our numerical machinery.

Physical Review AAug 15, 20165 citations

Quantum Optical Implementation of Adaptive Quantum State Tomography

Phillip Cornett, Albert B. Dinkins V, Lucas Vogeli +2 more

Quantum state tomography (QST) estimates an unknown quantum state from a measurement process typically performed on identical copies of the target state and plays a core role in characterizing quantum information systems. However, because quantum measurement outcomes are probabilistic, QST methods often require many shots per basis to achieve high-fidelity estimates, which hinders scalability to many-qubit applications and slows the transmission of quantum information. A more efficient procedure is therefore required for modern-day quantum operations in quantum computing, communications, and sensing. We address this need with an adaptive QST approach that measures a single-qubit state in a wide set of bases. We include bases beyond the Pauli triad {X,Y,Z} by leveraging the infinite-dimensional Hilbert space of quantum mechanics, increasing the likelihood of producing highly polarized measurement outcomes and finding an optimally informative basis. With this basis, the state can be identified with fewer measurements by focusing on directions that most reduce uncertainty of the state. In addition to theoretical innovation in [9], we experimentally verify in a simplified photonic realization using 13 bases that having many more available measurement bases than the Pauli triad benefits QST. This engineering implementation demonstrates that adaptive QST is both efficient in performance and practical to implement.Quantum state tomography (QST) estimates an unknown quantum state from a measurement process typically performed on identical copies of the target state and plays a core role in characterizing quantum information systems. However, because quantum measurement outcomes are probabilistic, QST methods often require many shots per basis to achieve high-fidelity estimates, which hinders scalability to many-qubit applications and slows the transmission of quantum information. A more efficient procedure is therefore required for modern-day quantum operations in quantum computing, communications, and sensing. We address this need with an adaptive QST approach that measures a single-qubit state in a wide set of bases. We include bases beyond the Pauli triad {X,Y,Z} by leveraging the infinite-dimensional Hilbert space of quantum mechanics, increasing the likelihood of producing highly polarized measurement outcomes and finding an optimally informative basis. With this basis, the state can be identified with fewer measurements by focusing on directions that most reduce uncertainty of the state. In addition to theoretical innovation in [9], we experimentally verify in a simplified photonic realization using 13 bases that having many more available measurement bases than the Pauli triad benefits QST. This engineering implementation demonstrates that adaptive QST is both efficient in performance and practical to implement.

International Symposium on Wireless Personal Multimedia Communications (WPMC)Nov 9, 20251 citation

Experimental qudit state estimation via point tomography

D. Martínez, Luciano Pereira, K. Sawada +7 more

Point tomography is an approach to the problem of state estimation, which is arguably the most efficient and simple method for modern high-precision quantum information experiments. In this scenario, the experimenter knows the target state that their device should prepare, except that intrinsic systematic errors will create small discrepancies in the state actually produced. By introducing a kind of informationally complete measurement, dubbed Fisher-symmetric measurements, point tomography determines deviations from the expected state with optimal efficiency. Moreover, the number of outcomes of a measurement saturating the Gill-Massar limit for reconstructing d -dimensional quantum states can be greatly reduced from ∼ 4 d − 3 to only 2 d − 1 outcomes. Thus, improving the measurement overhead as the dimension increases. Here we demonstrate the experimental viability of point tomography. Using a modern photonic platform constructed with state-of-the-art multicore optical fiber technology, we generate four-dimensional quantum states and implement seven-outcome Fisher-symmetric measurements. Our experimental results exhibit the main feature of point tomography, namely, a precision close to the Gill-Massar limit with a single few-outcome measurement. Specifically, we achieved a precision of ( 3.81 ± 0.05 ) / N , while the Gill-Massar limit for d = 4 is 3 / N ( N being the ensemble size).Point tomography is an approach to the problem of state estimation, which is arguably the most efficient and simple method for modern high-precision quantum information experiments. In this scenario, the experimenter knows the target state that their device should prepare, except that intrinsic systematic errors will create small discrepancies in the state actually produced. By introducing a kind of informationally complete measurement, dubbed Fisher-symmetric measurements, point tomography determines deviations from the expected state with optimal efficiency. Moreover, the number of outcomes of a measurement saturating the Gill-Massar limit for reconstructing d -dimensional quantum states can be greatly reduced from ∼ 4 d − 3 to only 2 d − 1 outcomes. Thus, improving the measurement overhead as the dimension increases. Here we demonstrate the experimental viability of point tomography. Using a modern photonic platform constructed with state-of-the-art multicore optical fiber technology, we generate four-dimensional quantum states and implement seven-outcome Fisher-symmetric measurements. Our experimental results exhibit the main feature of point tomography, namely, a precision close to the Gill-Massar limit with a single few-outcome measurement. Specifically, we achieved a precision of ( 3.81 ± 0.05 ) / N , while the Gill-Massar limit for d = 4 is 3 / N ( N being the ensemble size).

arXiv:2412.14915Physical Review ResearchJul 14, 20252 citations

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times smaller than the best accuracy achievable by tomographic methods for unknown mixed states. We also study the case of pure states affected by a low level of white noise. We show that the modified version of the method is very robust; that is, it remains to a large extent unaffected by the noise and achieves an accuracy similar to the case without noise.