Pub Date : 2024-11-14DOI: 10.22331/q-2024-11-14-1523
Alice Barthe, Adrián Pérez-Salinas
Quantum re-uploading models have been extensively investigated as a form of machine learning within the context of variational quantum algorithms. Their trainability and expressivity are not yet fully understood and are critical to their performance. In this work, we address trainability through the lens of the magnitude of the gradients of the cost function. We prove bounds for the differences between gradients of the better-studied data-less parameterized quantum circuits and re-uploading models. We coin the concept of $textit{absorption witness}$ to quantify such difference. For the expressivity, we prove that quantum re-uploading models output functions with vanishing high-frequency components and upper-bounded derivatives with respect to data. As a consequence, such functions present limited sensitivity to fine details, which protects against overfitting. We performed numerical experiments extending the theoretical results to more relaxed and realistic conditions. Overall, future designs of quantum re-uploading models will benefit from the strengthened knowledge delivered by the uncovering of absorption witnesses and vanishing high frequencies.
{"title":"Gradients and frequency profiles of quantum re-uploading models","authors":"Alice Barthe, Adrián Pérez-Salinas","doi":"10.22331/q-2024-11-14-1523","DOIUrl":"https://doi.org/10.22331/q-2024-11-14-1523","url":null,"abstract":"Quantum re-uploading models have been extensively investigated as a form of machine learning within the context of variational quantum algorithms. Their trainability and expressivity are not yet fully understood and are critical to their performance. In this work, we address trainability through the lens of the magnitude of the gradients of the cost function. We prove bounds for the differences between gradients of the better-studied data-less parameterized quantum circuits and re-uploading models. We coin the concept of $textit{absorption witness}$ to quantify such difference. For the expressivity, we prove that quantum re-uploading models output functions with vanishing high-frequency components and upper-bounded derivatives with respect to data. As a consequence, such functions present limited sensitivity to fine details, which protects against overfitting. We performed numerical experiments extending the theoretical results to more relaxed and realistic conditions. Overall, future designs of quantum re-uploading models will benefit from the strengthened knowledge delivered by the uncovering of absorption witnesses and vanishing high frequencies.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"11 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142610315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-14DOI: 10.22331/q-2024-11-14-1524
Ge Bai, Dominik Šafránek, Joseph Schindler, Francesco Buscemi, Valerio Scarani
Observational entropy captures both the intrinsic uncertainty of a thermodynamic state and the lack of knowledge due to coarse-graining. We demonstrate two interpretations of observational entropy, one as the statistical deficiency resulting from a measurement, the other as the difficulty of inferring the input state from the measurement statistics by quantum Bayesian retrodiction. These interpretations show that the observational entropy implicitly includes a uniform reference prior. Since the uniform prior cannot be used when the system is infinite-dimensional or otherwise energy-constrained, we propose generalizations by replacing the uniform prior with arbitrary quantum states that may not even commute with the state of the system. We propose three candidates for this generalization, discuss their properties, and show that one of them gives a unified expression that relates both interpretations.
{"title":"Observational entropy with general quantum priors","authors":"Ge Bai, Dominik Šafránek, Joseph Schindler, Francesco Buscemi, Valerio Scarani","doi":"10.22331/q-2024-11-14-1524","DOIUrl":"https://doi.org/10.22331/q-2024-11-14-1524","url":null,"abstract":"Observational entropy captures both the intrinsic uncertainty of a thermodynamic state and the lack of knowledge due to coarse-graining. We demonstrate two interpretations of observational entropy, one as the statistical deficiency resulting from a measurement, the other as the difficulty of inferring the input state from the measurement statistics by quantum Bayesian retrodiction. These interpretations show that the observational entropy implicitly includes a uniform reference prior. Since the uniform prior cannot be used when the system is infinite-dimensional or otherwise energy-constrained, we propose generalizations by replacing the uniform prior with arbitrary quantum states that may not even commute with the state of the system. We propose three candidates for this generalization, discuss their properties, and show that one of them gives a unified expression that relates both interpretations.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"98 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142637867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-13DOI: 10.22331/q-2024-11-13-1521
Yanic Cardin, Nicolás Quesada
We develop closed-form expressions for the moments and cumulants of Gaussian states when measured in the photon-number basis. We express the photon-number moments of a Gaussian state in terms of the loop Hafnian, a function that when applied to a $(0,1)$-matrix representing the adjacency of a graph, counts the number of its perfect matchings. Similarly, we express the photon-number cumulants in terms of the Montrealer, a newly introduced matrix function that when applied to a $(0,1)$-matrix counts the number of Hamiltonian cycles of that graph. Based on these graph-theoretic connections, we show that the calculation of photon-number moments and cumulants are #P-hard. Moreover, we provide an exponential time algorithm to calculate Montrealers (and thus cumulants), matching well-known results for Hafnians. We then demonstrate that when a uniformly lossy interferometer is fed in every input with identical single-mode Gaussian states with zero displacement, all the odd-order cumulants but the first one are zero. Finally, we employ the expressions we derive to study the distribution of cumulants up to the fourth order for different input states in a Gaussian boson sampling setup where $K$ identical states are fed into an $ell$-mode interferometer. We analyze the dependence of the cumulants as a function of the type of input state, squeezed, lossy squeezed, squashed, or thermal, and as a function of the number of non-vacuum inputs. We find that thermal states perform much worse than other classical states, such as squashed states, at mimicking the photon-number cumulants of lossy or lossless squeezed states.
{"title":"Photon-number moments and cumulants of Gaussian states","authors":"Yanic Cardin, Nicolás Quesada","doi":"10.22331/q-2024-11-13-1521","DOIUrl":"https://doi.org/10.22331/q-2024-11-13-1521","url":null,"abstract":"We develop closed-form expressions for the moments and cumulants of Gaussian states when measured in the photon-number basis. We express the photon-number moments of a Gaussian state in terms of the loop Hafnian, a function that when applied to a $(0,1)$-matrix representing the adjacency of a graph, counts the number of its perfect matchings. Similarly, we express the photon-number cumulants in terms of the Montrealer, a newly introduced matrix function that when applied to a $(0,1)$-matrix counts the number of Hamiltonian cycles of that graph. Based on these graph-theoretic connections, we show that the calculation of photon-number moments and cumulants are #P-hard. Moreover, we provide an exponential time algorithm to calculate Montrealers (and thus cumulants), matching well-known results for Hafnians. We then demonstrate that when a uniformly lossy interferometer is fed in every input with identical single-mode Gaussian states with zero displacement, all the odd-order cumulants but the first one are zero. Finally, we employ the expressions we derive to study the distribution of cumulants up to the fourth order for different input states in a Gaussian boson sampling setup where $K$ identical states are fed into an $ell$-mode interferometer. We analyze the dependence of the cumulants as a function of the type of input state, squeezed, lossy squeezed, squashed, or thermal, and as a function of the number of non-vacuum inputs. We find that thermal states perform much worse than other classical states, such as squashed states, at mimicking the photon-number cumulants of lossy or lossless squeezed states.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"80 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142600966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-13DOI: 10.22331/q-2024-11-13-1522
Álvaro Gómez-León
Floquet topological phases emerge when systems are periodically driven out-of-equilibrium. They gained attention due to their external control, which allows to simulate a wide variety of static systems by just tuning the external field in the high frequency regime. However, it was soon clear that their relevance goes beyond that, as for lower frequencies, anomalous phases without a static counterpart are present and the bulk-to-boundary correspondence can fail. In this work we discuss the important role of resonances in Floquet phases. For that, we present a method to find analytical solutions when the frequency of the drive matches the band gap, extending the well-known high frequency analysis of Floquet systems. With this formalism, we show that the topology of Floquet phases with resonances can be accurately captured in analytical terms. We also find a bulk-to-boundary correspondence between the number of edge states in finite systems and a set of topological invariants in different frames of reference, which crucially do not explicitly involve the micromotion. To illustrate our results, we periodically drive a SSH chain and a $pi$-flux lattice, showing that our findings remain valid in various two-band systems and in different dimensions. In addition, we notice that the competition between rotating and counter-rotating terms must be carefully treated when the undriven system is a semi-metal. To conclude, we discuss the implications to experimental setups, including the direct detection of anomalous topological phases and the measurement of their invariants.
{"title":"Anomalous Floquet Phases. A resonance phenomena","authors":"Álvaro Gómez-León","doi":"10.22331/q-2024-11-13-1522","DOIUrl":"https://doi.org/10.22331/q-2024-11-13-1522","url":null,"abstract":"Floquet topological phases emerge when systems are periodically driven out-of-equilibrium. They gained attention due to their external control, which allows to simulate a wide variety of static systems by just tuning the external field in the high frequency regime. However, it was soon clear that their relevance goes beyond that, as for lower frequencies, anomalous phases without a static counterpart are present and the bulk-to-boundary correspondence can fail. In this work we discuss the important role of resonances in Floquet phases. For that, we present a method to find analytical solutions when the frequency of the drive matches the band gap, extending the well-known high frequency analysis of Floquet systems. With this formalism, we show that the topology of Floquet phases with resonances can be accurately captured in analytical terms. We also find a bulk-to-boundary correspondence between the number of edge states in finite systems and a set of topological invariants in different frames of reference, which crucially do not explicitly involve the micromotion. To illustrate our results, we periodically drive a SSH chain and a $pi$-flux lattice, showing that our findings remain valid in various two-band systems and in different dimensions. In addition, we notice that the competition between rotating and counter-rotating terms must be carefully treated when the undriven system is a semi-metal. To conclude, we discuss the implications to experimental setups, including the direct detection of anomalous topological phases and the measurement of their invariants.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"62 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142600968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-11DOI: 10.22331/q-2024-11-11-1520
Zohreh Davoudi, Chung-Chun Hsieh, Saurabh V. Kadam
Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the $Z_2$ and $U(1)$ lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the $Z_2$ lattice gauge theory is built and implemented on the Quantinuum $texttt{H1-1}$ trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics.
{"title":"Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer","authors":"Zohreh Davoudi, Chung-Chun Hsieh, Saurabh V. Kadam","doi":"10.22331/q-2024-11-11-1520","DOIUrl":"https://doi.org/10.22331/q-2024-11-11-1520","url":null,"abstract":"Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the $Z_2$ and $U(1)$ lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the $Z_2$ lattice gauge theory is built and implemented on the Quantinuum $texttt{H1-1}$ trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"71 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-07DOI: 10.22331/q-2024-11-07-1516
Jwo-Sy Chen, Erik Nielsen, Matthew Ebert, Volkan Inlek, Kenneth Wright, Vandiver Chaplin, Andrii Maksymov, Eduardo Páez, Amrit Poudel, Peter Maunz, John Gamble
Quantum computers are rapidly becoming more capable, with dramatic increases in both qubit count [1] and quality [2]. Among different hardware approaches, trapped-ion quantum processors are a leading technology for quantum computing, with established high-fidelity operations and architectures with promising scaling. Here, we demonstrate and thoroughly benchmark the IonQ Forte system: configured as a single-chain 30-qubit trapped-ion quantum computer with all-to-all operations. We assess the performance of our quantum computer operation at the component level via direct randomized benchmarking (DRB) across all 30 choose 2 = 435 gate pairs. We then show the results of application-oriented [3][4] benchmarks and show that the system passes the suite of algorithmic qubit (AQ) benchmarks up to #AQ 29. Finally, we use our component-level benchmarking to build a system-level model to predict the application benchmarking data through direct simulation. While we find that the system-level model correlates with the experiment in predicting application circuit performance, we note quantitative discrepancies indicating significant out-of-model errors, leading to higher predicted performance than what is observed. This highlights that as quantum computers move toward larger and higher-quality devices, characterization becomes more challenging, suggesting future work required to push performance further.
{"title":"Benchmarking a trapped-ion quantum computer with 30 qubits","authors":"Jwo-Sy Chen, Erik Nielsen, Matthew Ebert, Volkan Inlek, Kenneth Wright, Vandiver Chaplin, Andrii Maksymov, Eduardo Páez, Amrit Poudel, Peter Maunz, John Gamble","doi":"10.22331/q-2024-11-07-1516","DOIUrl":"https://doi.org/10.22331/q-2024-11-07-1516","url":null,"abstract":"Quantum computers are rapidly becoming more capable, with dramatic increases in both qubit count [1] and quality [2]. Among different hardware approaches, trapped-ion quantum processors are a leading technology for quantum computing, with established high-fidelity operations and architectures with promising scaling. Here, we demonstrate and thoroughly benchmark the IonQ Forte system: configured as a single-chain 30-qubit trapped-ion quantum computer with all-to-all operations. We assess the performance of our quantum computer operation at the component level via direct randomized benchmarking (DRB) across all 30 choose 2 = 435 gate pairs. We then show the results of application-oriented [3][4] benchmarks and show that the system passes the suite of algorithmic qubit (AQ) benchmarks up to #AQ 29. Finally, we use our component-level benchmarking to build a system-level model to predict the application benchmarking data through direct simulation. While we find that the system-level model correlates with the experiment in predicting application circuit performance, we note quantitative discrepancies indicating significant out-of-model errors, leading to higher predicted performance than what is observed. This highlights that as quantum computers move toward larger and higher-quality devices, characterization becomes more challenging, suggesting future work required to push performance further.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"7 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-07DOI: 10.22331/q-2024-11-07-1518
Johannes Fankhauser
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer a predictive advantage while conforming to the Born rule on average. We present a no-go claim combining three aspects: predictive advantage, no-signalling, and reliable intersubjectivity between quantum observers. The results of the analysis lead to the conclusion that there exists a fundamental limitation on genuine predictive advantage. However, we uncover a fascinating possibility: When the assumption of reliable intersubjectivity between different observers is violated, subjective predictive advantage can, in principle, exist. This, in turn, entails an epistemic boundary between different observers of the same theory. The findings reconcile us to quantum uncertainty as an aspect of limits on Nature's predictability.
{"title":"Epistemic Boundaries and Quantum Uncertainty: What Local Observers Can (Not) Predict","authors":"Johannes Fankhauser","doi":"10.22331/q-2024-11-07-1518","DOIUrl":"https://doi.org/10.22331/q-2024-11-07-1518","url":null,"abstract":"One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer a predictive advantage while conforming to the Born rule on average. We present a no-go claim combining three aspects: predictive advantage, no-signalling, and reliable intersubjectivity between quantum observers. The results of the analysis lead to the conclusion that there exists a fundamental limitation on genuine predictive advantage. However, we uncover a fascinating possibility: When the assumption of reliable intersubjectivity between different observers is violated, subjective predictive advantage can, in principle, exist. This, in turn, entails an epistemic boundary between different observers of the same theory. The findings reconcile us to quantum uncertainty as an aspect of limits on Nature's predictability.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"2 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142597176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quantum kernel methods are a proposal for achieving quantum computational advantage in machine learning. They are based on a hybrid classical-quantum computation where a function called the quantum kernel is estimated by a quantum device while the rest of computation is performed classically. Quantum advantages may be achieved through this method only if the quantum kernel function cannot be estimated efficiently on a classical computer. In this paper, we provide sufficient conditions for the efficient classical estimation of quantum kernel functions for bosonic systems. These conditions are based on phase-space properties of data-encoding quantum states associated with the quantum kernels: negative volume, non-classical depth, and excess range, which are shown to be three signatures of phase-space negativity. We consider quantum optical examples involving linear-optical networks with and without adaptive non-Gaussian measurements, and investigate the effects of loss on the efficiency of the classical simulation. Our results underpin the role of the negativity in phase-space quasi-probability distributions as an essential resource in quantum machine learning based on kernel methods.
{"title":"Phase-space negativity as a computational resource for quantum kernel methods","authors":"Ulysse Chabaud, Roohollah Ghobadi, Salman Beigi, Saleh Rahimi-Keshari","doi":"10.22331/q-2024-11-07-1519","DOIUrl":"https://doi.org/10.22331/q-2024-11-07-1519","url":null,"abstract":"Quantum kernel methods are a proposal for achieving quantum computational advantage in machine learning. They are based on a hybrid classical-quantum computation where a function called the quantum kernel is estimated by a quantum device while the rest of computation is performed classically. Quantum advantages may be achieved through this method only if the quantum kernel function cannot be estimated efficiently on a classical computer. In this paper, we provide sufficient conditions for the efficient classical estimation of quantum kernel functions for bosonic systems. These conditions are based on phase-space properties of data-encoding quantum states associated with the quantum kernels: negative volume, non-classical depth, and excess range, which are shown to be three signatures of phase-space negativity. We consider quantum optical examples involving linear-optical networks with and without adaptive non-Gaussian measurements, and investigate the effects of loss on the efficiency of the classical simulation. Our results underpin the role of the negativity in phase-space quasi-probability distributions as an essential resource in quantum machine learning based on kernel methods.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"38 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142597178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-07DOI: 10.22331/q-2024-11-07-1517
Masahito Hayashi
A Dicke state and its decohered state are invariant for permutation. However, when another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation. The amount of asymmetry can be measured by the number of distinguishable states under the group action or the mutual information. Generally, the amount of asymmetry of the whole state is larger than the amount of asymmetry of the added state. That is, the asymmetry activation happens in this case. This paper investigates the amount of the asymmetry activation under Dicke states. To address the asymmetry activation asymptotically, we introduce a new type of central limit theorem by using several formulas on hypergeometric functions. We reveal that the amounts of the asymmetry and the asymmetry activation with a Dicke state have a strictly larger order than those with the decohered state in a specific type of the limit.
{"title":"Asymmetry activation and its relation to coherence under permutation operation","authors":"Masahito Hayashi","doi":"10.22331/q-2024-11-07-1517","DOIUrl":"https://doi.org/10.22331/q-2024-11-07-1517","url":null,"abstract":"A Dicke state and its decohered state are invariant for permutation. However, when another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation. The amount of asymmetry can be measured by the number of distinguishable states under the group action or the mutual information. Generally, the amount of asymmetry of the whole state is larger than the amount of asymmetry of the added state. That is, the asymmetry activation happens in this case. This paper investigates the amount of the asymmetry activation under Dicke states. To address the asymmetry activation asymptotically, we introduce a new type of central limit theorem by using several formulas on hypergeometric functions. We reveal that the amounts of the asymmetry and the asymmetry activation with a Dicke state have a strictly larger order than those with the decohered state in a specific type of the limit.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"245 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142597175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-07DOI: 10.22331/q-2024-11-07-1515
Teiko Heinosaari, Oskari Kerppo
A prepare-and-measure scenario is naturally described by a communication matrix that collects all conditional outcome probabilities of the scenario into a row-stochastic matrix. The set of all possible communication matrices is partially ordered via the possibility to transform one matrix to another by pre- and post-processings. By considering maximal elements in this preorder for a subset of matrices implementable in a given theory, it becomes possible to identify communication matrices of maximum utility, i.e., matrices that are not majorized by any other matrices in the theory. The identity matrix of an appropriate size is the greatest element in classical theories, while the maximal elements in quantum theory have remained unknown. We completely characterize the maximal elements in quantum theory, thereby revealing the essential structure of the set of quantum communication matrices. In particular, we show that the identity matrix is the only maximal element in quantum theory but, as opposed to a classical theory, it is not the greatest element. Quantum theory can hence be seen to be distinct from classical theory by the existence of incompatible communication matrices.
{"title":"Maximal Elements of Quantum Communication","authors":"Teiko Heinosaari, Oskari Kerppo","doi":"10.22331/q-2024-11-07-1515","DOIUrl":"https://doi.org/10.22331/q-2024-11-07-1515","url":null,"abstract":"A prepare-and-measure scenario is naturally described by a communication matrix that collects all conditional outcome probabilities of the scenario into a row-stochastic matrix. The set of all possible communication matrices is partially ordered via the possibility to transform one matrix to another by pre- and post-processings. By considering maximal elements in this preorder for a subset of matrices implementable in a given theory, it becomes possible to identify communication matrices of maximum utility, i.e., matrices that are not majorized by any other matrices in the theory. The identity matrix of an appropriate size is the greatest element in classical theories, while the maximal elements in quantum theory have remained unknown. We completely characterize the maximal elements in quantum theory, thereby revealing the essential structure of the set of quantum communication matrices. In particular, we show that the identity matrix is the only maximal element in quantum theory but, as opposed to a classical theory, it is not the greatest element. Quantum theory can hence be seen to be distinct from classical theory by the existence of incompatible communication matrices.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"104 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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