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

PT-symmetric distinction of three states and its implementation on a cloud quantum processor

Yaroslav Balytskyi, Yevgen V. Kotukh, Gennady Khalimov, Sang‐Yoon Chang

Published Feb 24, 2022• 0 citations
Publisher

Abstract

Abstract We present a novel $\mathcal{PT}$-symmetric approach for discriminating three pure qubit states and its implementation by the dilation method. Our approach based on the dilation method manipulating the Hilbert space of the system by two-staged $\mathcal{PT}$-symmetric evolution expedites the three-state discrimination process at the cost of introducing an inconclusive outcome. This modification of the Hilbert space of the qubit makes it possible to eliminate one of three states in the limit $\alpha\rightarrow\pm\frac{\pi}{2}$ in the vicinity of the exceptional point corresponding to coalescing eigenvectors and eigenvalues, effectively reducing the problem to two-state discrimination, or reducing the geometry to the mirror-symmetric states for which an efficient discrimination strategy is developed. To demonstrate the effectiveness of our approach, we implement it on a superconducting quantum processor provided by IBM Quantum Experience employing an ancilla qubit. We conclude our paper by identifying potential applications, including those in quantum communication and cryptography, to facilitate further research and development.

DOI
10.21203/rs.3.rs-1356416/v1

Related papers

PT -symmetric mapping of three states and its implementation on a cloud quantum processor

Yaroslav Balytskyi, Yevgen V. Kotukh, Gennady Khalimov +1 more

PT -symmetric systems have garnered significant attention due to their unconventional properties. Despite the growing interest, there remains an ongoing debate about whether these systems outperform their Hermitian counterparts in practical applications, and if so, by what metrics this performance should be measured. We developed PT -symmetric approach for mapping N=3 pure qubit states to address this, implemented it using the dilation method, and demonstrated it on a superconducting quantum processor from the IBM Quantum Experience. For the first time, we derived exact expressions for the population of the post-selected PT -symmetric subspace for both N=2 and N=3 states. When applied to the discrimination of N=2 pure states, our algorithm provides an equivalent result to the conventional unambiguous quantum state discrimination. For N=3 states, our approach introduces novel capabilities not available in traditional Hermitian systems, enabling the transformation of an arbitrary set of three pure quantum states into another, at the cost of introducing an inconclusive outcome. Our algorithm has the same error rate for the attack on the three-state QKD protocol as the conventional minimum error, maximum confidence, and maximum mutual information strategies. For post-selected quantum metrology, our results provide precise conditions where PT -symmetric quantum sensors outperform their Hermitian counterparts in terms of information-cost rate. Combined with punctuated unstructured quantum database search, our method significantly reduces the qubit readout requirements at the cost of adding an ancilla, while maintaining the same average number of oracle calls as the original punctuated Grover's algorithm. Our work opens new pathways for applying PT symmetry in quantum communications, computing, and cryptography.

arXiv:2312.16680•Quantum•Apr 18, 2025•2 citations

$\mathcal{PT}$-Symmetric Quantum Discrimination of Three States

Yaroslav Balytskyi, Manohar Raavi, Anatoliy O. Pinchuk +1 more

If the system is known to be in one of two non-orthogonal quantum states, $|ψ_1\rangle$ or $|ψ_2\rangle$, it is not possible to discriminate them by a single measurement due to the unitarity constraint. In a regular Hermitian quantum mechanics, the successful discrimination is possible to perform with the probability $p < 1$, while in $\mathcal{PT}$-symmetric quantum mechanics a \textit{simulated single-measurement} quantum state discrimination with the success rate $p$ can be done. We extend the $\mathcal{PT}$-symmetric quantum state discrimination approach for the case of three pure quantum states, $|ψ_1\rangle$, $|ψ_2\rangle$ and $|ψ_3\rangle$ without any additional restrictions on the geometry and symmetry possession of these states. We discuss the relation of our approach with the recent implementation of $\mathcal{PT}$ symmetry on the IBM quantum processor.

arXiv:2012.14897•Dec 29, 2020•2 citations

P T-symmetric Bayesian parameter estimation on a superconducting quantum processor

Yaroslav Balytskyi, Manohar Raavi, Yevgen V. Kotukh +2 more

To realize the computational advantages of quantum mechanics, it is necessary to be able to effectively perform quantum state tomography, and Bayesian methods provide significant opportunities in this regard, being applicable in the uncertainty regimes, where the local approaches based on Cramer-Rao bound become ill-defined. ${\mathcal{P}}{\mathcal{T}}$ -symmetric quantum mechanics provides a unique advantage for Bayesian parameter estimation having an additional degree of freedom, absent in the regular Hermitian case, which significantly enhances the quantum Fisher information and reduces variance of the obtained results. While previous studies have examined ${\mathcal{P}}{\mathcal{T}}$ -symmetric Bayesian parameter estimation in theory, we conduct experimental studies using IBM Quantum Experience and compare them with theoretical calculations. In our approach, the evolution of a qubit controlled by a ${\mathcal{P}}{\mathcal{T}}$-symmetric Hamiltonian is realized by the dilation method using ancilla qubit. We show that our implementation is consistent with the theoretical model and, in particular, we observe a good correspondence between the theoretical and experimental likelihood distributions. Thus we bridge the gap between theory and practical implementations in ${\mathcal{P}}{\mathcal{T}}$-symmetric quantum mechanics and its practical applications in quantum information science.

International Conference on Communications•May 16, 2022•1 citation

PT -symmetric quantum state discrimination

Carl M. Bender, Dorje C. Brody, João Luiz Caldeira +3 more

The objective of this paper is to explain and elucidate the formalism of PT quantum mechanics by applying it to a well-known problem in conventional Hermitian quantum mechanics, namely the problem of state discrimination. Suppose that a system is known to be in one of two quantum states, |ψ(1)> or |ψ(2)>. If these states are not orthogonal, then the requirement of unitarity forbids the possibility of discriminating between these two states with one measurement; that is, determining with one measurement what state the system is in. In conventional quantum mechanics, there is a strategy in which successful state discrimination can be achieved with a single measurement but only with a success probability p that is less than unity. In this paper, the state-discrimination problem is examined in the context of PT quantum mechanics and the approach is based on the fact that a non-Hermitian PT-symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states. It is shown that it is always possible to choose this inner product so that the two states |ψ(1)> and |ψ(2)> are orthogonal. Using PT quantum mechanics, one cannot achieve a better state discrimination than in ordinary quantum mechanics, but one can instead perform a simulated quantum state discrimination, in which with a single measurement a perfect state discrimination is realized with probability p.

arXiv:1011.1871•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Mar 19, 2013•39 citations

Quantum state discrimination in a PT -symmetric system

Dong‐Xu Chen, Yu Zhang, Jun‐Long Zhao +4 more

Nonorthogonal quantum state discrimination (QSD) plays an important role in quantum information and quantum communication. In addition, compared to Hermitian quantum systems, parity-time-($\mathcal{PT}$-)symmetric non-Hermitian quantum systems exhibit novel phenomena and have attracted considerable attention. Here, we experimentally demonstrate QSD in a $\mathcal{PT}$-symmetric system (i.e., $\mathcal{PT}$-symmetric QSD), by having quantum states evolve under a $\mathcal{PT}$-symmetric Hamiltonian in a lossy linear optical setup. We observe that two initially nonorthogonal states can rapidly evolve into orthogonal states and the required evolution time can even be vanishing provided the matrix elements of the Hamiltonian become sufficiently large. We also observe that the cost of such a discrimination is a dissipation of quantum states into the environment. Furthermore, by comparing $\mathcal{PT}$-symmetric QSD with optimal strategies in Hermitian systems, we find that at the critical value, $\mathcal{PT}$-symmetric QSD is equivalent to the optimal unambiguous state discrimination in Hermitian systems. We also extend the $\mathcal{PT}$-symmetric QSD to the case of discriminating three nonorthogonal states. The QSD in a $\mathcal{PT}$-symmetric system opens a new door for quantum state discrimination, which has important applications in quantum computing, quantum cryptography, and quantum communication.

arXiv:2209.02481•Physical Review A•Aug 30, 2022•14 citations

Experimental Demonstration of Non-Destructive Discrimination of Arbitrary Set of Orthogonal Quantum States Using 5-qubit IBM Quantum Computer on Cloud

Ayan Majumder, Anil Kumar

A protocol for non-destructive descrimination of arbitrary set of orthogonal quantum states was proposed by V. S. Manu et al., using an algorithm based on quantum phase estimation. IBM Corporation has released a superconductivity based 5-qubit (5-qubit transmon bowtie chip 3 and IBM 5-qubit real processor) quantum computer named Quantum Experience and placed it on cloud. In this paper we take advantage of the online availability of those real quantum processors(ibmqx2 amd ibmqx4) and carry out the above protocol that has experimentally demonstrated earlier using NMR quantum processor. Here, we set up experiments for arbitrary one-qubit and two-qubit orthogonal quantum states. The experiment confirmed that the arbitrary orthogonal quantum states can be discriminate in a nondestructive manner with a high fidelity. We compare the outcomes of those experiments which are done by ibmqx2 and ibmqx4 processors. Here, we also show the state tomography for the single qubit experiments.

arXiv:1803.06311•Mar 16, 2018•1 citation
Abstract We present a novel PT\mathcal{PT}PT-symmetric approach for discriminating three pure qubit states and its implementation by the dilation method. Our approach based on the dilation method manipulating the Hilbert space of the system by two-staged PT\mathcal{PT}PT-symmetric evolution expedites the three-state discrimination process at the cost of introducing an inconclusive outcome. This modification of the Hilbert space of the qubit makes it possible to eliminate one of three states in the limit α→±π2\alpha\rightarrow\pm\frac{\pi}{2}α→±2π​ in the vicinity of the exceptional point corresponding to coalescing eigenvectors and eigenvalues, effectively reducing the problem to two-state discrimination, or reducing the geometry to the mirror-symmetric states for which an efficient discrimination strategy is developed. To demonstrate the effectiveness of our approach, we implement it on a superconducting quantum processor provided by IBM Quantum Experience employing an ancilla qubit. We conclude our paper by identifying potential applications, including those in quantum communication and cryptography, to facilitate further research and development.
PT -symmetric systems have garnered significant attention due to their unconventional properties. Despite the growing interest, there remains an ongoing debate about whether these systems outperform their Hermitian counterparts in practical applications, and if so, by what metrics this performance should be measured. We developed PT -symmetric approach for mapping N=3 pure qubit states to address this, implemented it using the dilation method, and demonstrated it on a superconducting quantum processor from the IBM Quantum Experience. For the first time, we derived exact expressions for the population of the post-selected PT -symmetric subspace for both N=2 and N=3 states. When applied to the discrimination of N=2 pure states, our algorithm provides an equivalent result to the conventional unambiguous quantum state discrimination. For N=3 states, our approach introduces novel capabilities not available in traditional Hermitian systems, enabling the transformation of an arbitrary set of three pure quantum states into another, at the cost of introducing an inconclusive outcome. Our algorithm has the same error rate for the attack on the three-state QKD protocol as the conventional minimum error, maximum confidence, and maximum mutual information strategies. For post-selected quantum metrology, our results provide precise conditions where PT -symmetric quantum sensors outperform their Hermitian counterparts in terms of information-cost rate. Combined with punctuated unstructured quantum database search, our method significantly reduces the qubit readout requirements at the cost of adding an ancilla, while maintaining the same average number of oracle calls as the original punctuated Grover's algorithm. Our work opens new pathways for applying PT symmetry in quantum communications, computing, and cryptography.
PT\mathcal{PT}PT-Symmetric Quantum Discrimination of Three States
If the system is known to be in one of two non-orthogonal quantum states, ∣ψ1⟩|ψ_1\rangle∣ψ1​⟩ or ∣ψ2⟩|ψ_2\rangle∣ψ2​⟩, it is not possible to discriminate them by a single measurement due to the unitarity constraint. In a regular Hermitian quantum mechanics, the successful discrimination is possible to perform with the probability p<1p < 1p<1, while in PT\mathcal{PT}PT-symmetric quantum mechanics a \textit{simulated single-measurement} quantum state discrimination with the success rate ppp can be done. We extend the PT\mathcal{PT}PT-symmetric quantum state discrimination approach for the case of three pure quantum states, ∣ψ1⟩|ψ_1\rangle∣ψ1​⟩, ∣ψ2⟩|ψ_2\rangle∣ψ2​⟩ and ∣ψ3⟩|ψ_3\rangle∣ψ3​⟩ without any additional restrictions on the geometry and symmetry possession of these states. We discuss the relation of our approach with the recent implementation of PT\mathcal{PT}PT symmetry on the IBM quantum processor.
To realize the computational advantages of quantum mechanics, it is necessary to be able to effectively perform quantum state tomography, and Bayesian methods provide significant opportunities in this regard, being applicable in the uncertainty regimes, where the local approaches based on Cramer-Rao bound become ill-defined. PT{\mathcal{P}}{\mathcal{T}}PT -symmetric quantum mechanics provides a unique advantage for Bayesian parameter estimation having an additional degree of freedom, absent in the regular Hermitian case, which significantly enhances the quantum Fisher information and reduces variance of the obtained results. While previous studies have examined PT{\mathcal{P}}{\mathcal{T}}PT -symmetric Bayesian parameter estimation in theory, we conduct experimental studies using IBM Quantum Experience and compare them with theoretical calculations. In our approach, the evolution of a qubit controlled by a PT{\mathcal{P}}{\mathcal{T}}PT-symmetric Hamiltonian is realized by the dilation method using ancilla qubit. We show that our implementation is consistent with the theoretical model and, in particular, we observe a good correspondence between the theoretical and experimental likelihood distributions. Thus we bridge the gap between theory and practical implementations in PT{\mathcal{P}}{\mathcal{T}}PT-symmetric quantum mechanics and its practical applications in quantum information science.
The objective of this paper is to explain and elucidate the formalism of PT quantum mechanics by applying it to a well-known problem in conventional Hermitian quantum mechanics, namely the problem of state discrimination. Suppose that a system is known to be in one of two quantum states, |ψ(1)> or |ψ(2)>. If these states are not orthogonal, then the requirement of unitarity forbids the possibility of discriminating between these two states with one measurement; that is, determining with one measurement what state the system is in. In conventional quantum mechanics, there is a strategy in which successful state discrimination can be achieved with a single measurement but only with a success probability p that is less than unity. In this paper, the state-discrimination problem is examined in the context of PT quantum mechanics and the approach is based on the fact that a non-Hermitian PT-symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states. It is shown that it is always possible to choose this inner product so that the two states |ψ(1)> and |ψ(2)> are orthogonal. Using PT quantum mechanics, one cannot achieve a better state discrimination than in ordinary quantum mechanics, but one can instead perform a simulated quantum state discrimination, in which with a single measurement a perfect state discrimination is realized with probability p.
Nonorthogonal quantum state discrimination (QSD) plays an important role in quantum information and quantum communication. In addition, compared to Hermitian quantum systems, parity-time-(PT\mathcal{PT}PT-)symmetric non-Hermitian quantum systems exhibit novel phenomena and have attracted considerable attention. Here, we experimentally demonstrate QSD in a PT\mathcal{PT}PT-symmetric system (i.e., PT\mathcal{PT}PT-symmetric QSD), by having quantum states evolve under a PT\mathcal{PT}PT-symmetric Hamiltonian in a lossy linear optical setup. We observe that two initially nonorthogonal states can rapidly evolve into orthogonal states and the required evolution time can even be vanishing provided the matrix elements of the Hamiltonian become sufficiently large. We also observe that the cost of such a discrimination is a dissipation of quantum states into the environment. Furthermore, by comparing PT\mathcal{PT}PT-symmetric QSD with optimal strategies in Hermitian systems, we find that at the critical value, PT\mathcal{PT}PT-symmetric QSD is equivalent to the optimal unambiguous state discrimination in Hermitian systems. We also extend the PT\mathcal{PT}PT-symmetric QSD to the case of discriminating three nonorthogonal states. The QSD in a PT\mathcal{PT}PT-symmetric system opens a new door for quantum state discrimination, which has important applications in quantum computing, quantum cryptography, and quantum communication.
A protocol for non-destructive descrimination of arbitrary set of orthogonal quantum states was proposed by V. S. Manu et al., using an algorithm based on quantum phase estimation. IBM Corporation has released a superconductivity based 5-qubit (5-qubit transmon bowtie chip 3 and IBM 5-qubit real processor) quantum computer named Quantum Experience and placed it on cloud. In this paper we take advantage of the online availability of those real quantum processors(ibmqx2 amd ibmqx4) and carry out the above protocol that has experimentally demonstrated earlier using NMR quantum processor. Here, we set up experiments for arbitrary one-qubit and two-qubit orthogonal quantum states. The experiment confirmed that the arbitrary orthogonal quantum states can be discriminate in a nondestructive manner with a high fidelity. We compare the outcomes of those experiments which are done by ibmqx2 and ibmqx4 processors. Here, we also show the state tomography for the single qubit experiments.