Pub Date : 2024-06-11DOI: 10.22331/q-2024-06-11-1366
Aby Philip, Soorya Rethinasamy, Vincent Russo, Mark M. Wilde
Quantifying entanglement is an important task by which the resourcefulness of a quantum state can be measured. Here, we develop a quantum algorithm that tests for and quantifies the separability of a general bipartite state by using the quantum steering effect, the latter initially discovered by Schrödinger. Our separability test consists of a distributed quantum computation involving two parties: a computationally limited client, who prepares a purification of the state of interest, and a computationally unbounded server, who tries to steer the reduced systems to a probabilistic ensemble of pure product states. To design a practical algorithm, we replace the role of the server with a combination of parameterized unitary circuits and classical optimization techniques to perform the necessary computation. The result is a variational quantum steering algorithm (VQSA), a modified separability test that is implementable on quantum computers that are available today. We then simulate our VQSA on noisy quantum simulators and find favorable convergence properties on the examples tested. We also develop semidefinite programs, executable on classical computers, that benchmark the results obtained from our VQSA. Thus, our findings provide a meaningful connection between steering, entanglement, quantum algorithms, and quantum computational complexity theory. They also demonstrate the value of a parameterized mid-circuit measurement in a VQSA.
{"title":"Schrödinger as a Quantum Programmer: Estimating Entanglement via Steering","authors":"Aby Philip, Soorya Rethinasamy, Vincent Russo, Mark M. Wilde","doi":"10.22331/q-2024-06-11-1366","DOIUrl":"https://doi.org/10.22331/q-2024-06-11-1366","url":null,"abstract":"Quantifying entanglement is an important task by which the resourcefulness of a quantum state can be measured. Here, we develop a quantum algorithm that tests for and quantifies the separability of a general bipartite state by using the quantum steering effect, the latter initially discovered by Schrödinger. Our separability test consists of a distributed quantum computation involving two parties: a computationally limited client, who prepares a purification of the state of interest, and a computationally unbounded server, who tries to steer the reduced systems to a probabilistic ensemble of pure product states. To design a practical algorithm, we replace the role of the server with a combination of parameterized unitary circuits and classical optimization techniques to perform the necessary computation. The result is a variational quantum steering algorithm (VQSA), a modified separability test that is implementable on quantum computers that are available today. We then simulate our VQSA on noisy quantum simulators and find favorable convergence properties on the examples tested. We also develop semidefinite programs, executable on classical computers, that benchmark the results obtained from our VQSA. Thus, our findings provide a meaningful connection between steering, entanglement, quantum algorithms, and quantum computational complexity theory. They also demonstrate the value of a parameterized mid-circuit measurement in a VQSA.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141304349","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 : 2024-06-11DOI: 10.22331/q-2024-06-11-1365
Á. Sáiz, J. Khalouf-Rivera, J. M. Arias, P. Pérez-Fernández, J. Casado-Pascual
Quantum phase transitions encompass a variety of phenomena that occur in quantum systems exhibiting several possible symmetries. Traditionally, these transitions are explored by continuously varying a control parameter that connects two different symmetry configurations. Here we propose an alternative approach where the control parameter undergoes abrupt and time-periodic jumps between only two values. This approach yields results surprisingly similar to those obtained by the traditional one and may prove experimentally useful in situations where accessing the control parameter is challenging.
{"title":"Quantum Phase Transitions in periodically quenched systems","authors":"Á. Sáiz, J. Khalouf-Rivera, J. M. Arias, P. Pérez-Fernández, J. Casado-Pascual","doi":"10.22331/q-2024-06-11-1365","DOIUrl":"https://doi.org/10.22331/q-2024-06-11-1365","url":null,"abstract":"Quantum phase transitions encompass a variety of phenomena that occur in quantum systems exhibiting several possible symmetries. Traditionally, these transitions are explored by continuously varying a control parameter that connects two different symmetry configurations. Here we propose an alternative approach where the control parameter undergoes abrupt and time-periodic jumps between only two values. This approach yields results surprisingly similar to those obtained by the traditional one and may prove experimentally useful in situations where accessing the control parameter is challenging.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141304515","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 : 2024-05-29DOI: 10.22331/q-2024-05-29-1363
A. Z. Goldberg, A. B. Klimov, G. Leuchs, L. L. Sanchez-Soto
Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the basic observables, with the crucial property of behaving well under symplectic transformations. This basis is the analogue of the irreducible tensors widely used in the context of SU(2) symmetry. Given the density matrix of a state, the expansion coefficients in that basis constitute the multipoles, which describe the state in a canonically covariant form that is both concise and explicit. We use these quantities to assess properties such as quantumness or Gaussianity and to furnish direct connections between tomographic measurements and quasiprobability distribution reconstructions.
{"title":"Covariant operator bases for continuous variables","authors":"A. Z. Goldberg, A. B. Klimov, G. Leuchs, L. L. Sanchez-Soto","doi":"10.22331/q-2024-05-29-1363","DOIUrl":"https://doi.org/10.22331/q-2024-05-29-1363","url":null,"abstract":"Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the basic observables, with the crucial property of behaving well under symplectic transformations. This basis is the analogue of the irreducible tensors widely used in the context of SU(2) symmetry. Given the density matrix of a state, the expansion coefficients in that basis constitute the multipoles, which describe the state in a canonically covariant form that is both concise and explicit. We use these quantities to assess properties such as quantumness or Gaussianity and to furnish direct connections between tomographic measurements and quasiprobability distribution reconstructions.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141177737","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 : 2024-05-27DOI: 10.22331/q-2024-05-27-1362
Valérie Bettaque, Brian Swingle
Motivated by the ground state structure of quantum models with all-to-all interactions such as mean-field quantum spin glass models and the Sachdev-Ye-Kitaev (SYK) model, we propose a tensor network architecture which can accomodate volume law entanglement and a large ground state degeneracy. We call this architecture the non-local renormalization ansatz (NoRA) because it can be viewed as a generalization of MERA, DMERA, and branching MERA networks with the constraints of spatial locality removed. We argue that the architecture is potentially expressive enough to capture the entanglement and complexity of the ground space of the SYK model, thus making it a suitable variational ansatz, but we leave a detailed study of SYK to future work. We further explore the architecture in the special case in which the tensors are random Clifford gates. Here the architecture can be viewed as the encoding map of a random stabilizer code. We introduce a family of codes inspired by the SYK model which can be chosen to have constant rate and linear distance at the cost of some high weight stabilizers. We also comment on potential similarities between this code family and the approximate code formed from the SYK ground space.
{"title":"NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians","authors":"Valérie Bettaque, Brian Swingle","doi":"10.22331/q-2024-05-27-1362","DOIUrl":"https://doi.org/10.22331/q-2024-05-27-1362","url":null,"abstract":"Motivated by the ground state structure of quantum models with all-to-all interactions such as mean-field quantum spin glass models and the Sachdev-Ye-Kitaev (SYK) model, we propose a tensor network architecture which can accomodate volume law entanglement and a large ground state degeneracy. We call this architecture the non-local renormalization ansatz (NoRA) because it can be viewed as a generalization of MERA, DMERA, and branching MERA networks with the constraints of spatial locality removed. We argue that the architecture is potentially expressive enough to capture the entanglement and complexity of the ground space of the SYK model, thus making it a suitable variational ansatz, but we leave a detailed study of SYK to future work. We further explore the architecture in the special case in which the tensors are random Clifford gates. Here the architecture can be viewed as the encoding map of a random stabilizer code. We introduce a family of codes inspired by the SYK model which can be chosen to have constant rate and linear distance at the cost of some high weight stabilizers. We also comment on potential similarities between this code family and the approximate code formed from the SYK ground space.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141156663","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 : 2024-05-23DOI: 10.22331/q-2024-05-23-1355
Leonardo Assis Morais, Till Weinhold, Marcelo Pereira de Almeida, Joshua Combes, Markus Rambach, Adriana Lita, Thomas Gerrits, Sae Woo Nam, Andrew G. White, Geoff Gillett
Superconducting transition-edge sensors (TES) are extremely sensitive microcalorimeters used as photon detectors with unparalleled energy resolution. They have found application from measuring astronomical spectra through to determining the quantum property of photon-number, $hat{n} {=} hat{a}^† hat{a}$, for energies from 0.6-2.33eV. However, achieving optimal energy resolution requires considerable data acquisition – on the order of 1GB/min – followed by post-processing, which does not allow access to energy information in real time. Here we use a custom hardware processor to process TES pulses while new detections are still being registered, allowing photon-number to be measured in real time as well as reducing data requirements by orders-of-magnitude. We resolve photon number up to $n=16$ – achieving up to parts-per-billion discrimination for low photon numbers on the fly – providing transformational capacity for applications of TES detectors from astronomy through to quantum technology.
{"title":"Precisely determining photon-number in real time","authors":"Leonardo Assis Morais, Till Weinhold, Marcelo Pereira de Almeida, Joshua Combes, Markus Rambach, Adriana Lita, Thomas Gerrits, Sae Woo Nam, Andrew G. White, Geoff Gillett","doi":"10.22331/q-2024-05-23-1355","DOIUrl":"https://doi.org/10.22331/q-2024-05-23-1355","url":null,"abstract":"Superconducting transition-edge sensors (TES) are extremely sensitive microcalorimeters used as photon detectors with unparalleled energy resolution. They have found application from measuring astronomical spectra through to determining the quantum property of photon-number, $hat{n} {=} hat{a}^† hat{a}$, for energies from 0.6-2.33eV. However, achieving optimal energy resolution requires considerable data acquisition – on the order of 1GB/min – followed by post-processing, which does not allow access to energy information in real time. Here we use a custom hardware processor to process TES pulses while new detections are still being registered, allowing photon-number to be measured in real time as well as reducing data requirements by orders-of-magnitude. We resolve photon number up to $n=16$ – achieving up to parts-per-billion discrimination for low photon numbers on the fly – providing transformational capacity for applications of TES detectors from astronomy through to quantum technology.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141085627","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 : 2024-05-23DOI: 10.22331/q-2024-05-23-1356
Roberto Ruiz, Alejandro Sopena, Max Hunter Gordon, Germán Sierra, Esperanza López
The Bethe ansatz represents an analytical method enabling the exact solution of numerous models in condensed matter physics and statistical mechanics. When a global symmetry is present, the trial wavefunctions of the Bethe ansatz consist of plane wave superpositions. Previously, it has been shown that the Bethe ansatz can be recast as a deterministic quantum circuit. An analytical derivation of the quantum gates that form the circuit was lacking however. Here we present a comprehensive study of the transformation that brings the Bethe ansatz into a quantum circuit, which leads us to determine the analytical expression of the circuit gates. As a crucial step of the derivation, we present a simple set of diagrammatic rules that define a novel Matrix Product State network building Bethe wavefunctions. Remarkably, this provides a new perspective on the equivalence between the coordinate and algebraic versions of the Bethe ansatz.
{"title":"The Bethe Ansatz as a Quantum Circuit","authors":"Roberto Ruiz, Alejandro Sopena, Max Hunter Gordon, Germán Sierra, Esperanza López","doi":"10.22331/q-2024-05-23-1356","DOIUrl":"https://doi.org/10.22331/q-2024-05-23-1356","url":null,"abstract":"The Bethe ansatz represents an analytical method enabling the exact solution of numerous models in condensed matter physics and statistical mechanics. When a global symmetry is present, the trial wavefunctions of the Bethe ansatz consist of plane wave superpositions. Previously, it has been shown that the Bethe ansatz can be recast as a deterministic quantum circuit. An analytical derivation of the quantum gates that form the circuit was lacking however. Here we present a comprehensive study of the transformation that brings the Bethe ansatz into a quantum circuit, which leads us to determine the analytical expression of the circuit gates. As a crucial step of the derivation, we present a simple set of diagrammatic rules that define a novel Matrix Product State network building Bethe wavefunctions. Remarkably, this provides a new perspective on the equivalence between the coordinate and algebraic versions of the Bethe ansatz.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141085601","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 : 2024-05-23DOI: 10.22331/q-2024-05-23-1357
Charlie R. Hogg, Federico Cerisola, James D. Cresser, Simon A. R. Horsley, Janet Anders
The spin-boson model usually considers a spin coupled to a single bosonic bath. However, some physical situations require coupling of the spin to multiple environments. For example, spins interacting with phonons in three-dimensional magnetic materials. Here, we consider a spin coupled isotropically to three independent baths. We show that coupling to multiple baths can significantly increase entanglement between the spin and its environment at zero temperature. The effect of this is to reduce the spin's expectation values in the mean force equilibrium state. In contrast, the classical three-bath spin equilibrium state turns out to be entirely independent of the environmental coupling. These results reveal purely quantum effects that can arise from multi-bath couplings, with potential applications in a wide range of settings, such as magnetic materials.
{"title":"Enhanced entanglement in multi-bath spin-boson models","authors":"Charlie R. Hogg, Federico Cerisola, James D. Cresser, Simon A. R. Horsley, Janet Anders","doi":"10.22331/q-2024-05-23-1357","DOIUrl":"https://doi.org/10.22331/q-2024-05-23-1357","url":null,"abstract":"The spin-boson model usually considers a spin coupled to a single bosonic bath. However, some physical situations require coupling of the spin to multiple environments. For example, spins interacting with phonons in three-dimensional magnetic materials. Here, we consider a spin coupled isotropically to three independent baths. We show that coupling to multiple baths can significantly increase entanglement between the spin and its environment at zero temperature. The effect of this is to reduce the spin's expectation values in the mean force equilibrium state. In contrast, the classical three-bath spin equilibrium state turns out to be entirely independent of the environmental coupling. These results reveal purely quantum effects that can arise from multi-bath couplings, with potential applications in a wide range of settings, such as magnetic materials.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141085495","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 : 2024-05-22DOI: 10.22331/q-2024-05-22-1352
Adam Bene Watts, Anirban Chowdhury, Aidan Epperly, J. William Helton, Igor Klep
The Quantum Max Cut (QMC) problem has emerged as a test-problem for designing approximation algorithms for local Hamiltonian problems. In this paper we attack this problem using the algebraic structure of QMC, in particular the relationship between the quantum max cut Hamiltonian and the representation theory of the symmetric group.
The first major contribution of this paper is an extension of non-commutative Sum of Squares (ncSoS) optimization techniques to give a new hierarchy of relaxations to Quantum Max Cut. The hierarchy we present is based on optimizations over polynomials in the qubit swap operators. This is in contrast to the "standard" quantum Lasserre Hierarchy, which is based on polynomials expressed in terms of the Pauli matrices. To prove correctness of this hierarchy, we exploit a finite presentation of the algebra generated by the qubit swap operators. This presentation allows for the use of computer algebraic techniques to manipulate and simplify polynomials written in terms of the swap operators, and may be of independent interest. Surprisingly, we find that level-2 of this new hierarchy is numerically exact (up to tolerance $10^{-7}$) on all QMC instances with uniform edge weights on graphs with at most 8 vertices.
The second major contribution of this paper is a polynomial-time algorithm that computes (in exact arithmetic) the maximum eigenvalue of the QMC Hamiltonian for certain graphs, including graphs that can be "decomposed" as a signed combination of cliques. A special case of the latter are complete bipartite graphs with uniform edge-weights, for which exact solutions are known from the work of Lieb and Mattis [33]. Our methods, which use representation theory of the symmetric group, can be seen as a generalization of the Lieb-Mattis result.
{"title":"Relaxations and Exact Solutions to Quantum Max Cut via the Algebraic Structure of Swap Operators","authors":"Adam Bene Watts, Anirban Chowdhury, Aidan Epperly, J. William Helton, Igor Klep","doi":"10.22331/q-2024-05-22-1352","DOIUrl":"https://doi.org/10.22331/q-2024-05-22-1352","url":null,"abstract":"The Quantum Max Cut (QMC) problem has emerged as a test-problem for designing approximation algorithms for local Hamiltonian problems. In this paper we attack this problem using the algebraic structure of QMC, in particular the relationship between the quantum max cut Hamiltonian and the representation theory of the symmetric group.<br/>\u0000<br/> The first major contribution of this paper is an extension of non-commutative Sum of Squares (ncSoS) optimization techniques to give a new hierarchy of relaxations to Quantum Max Cut. The hierarchy we present is based on optimizations over polynomials in the qubit swap operators. This is in contrast to the \"standard\" quantum Lasserre Hierarchy, which is based on polynomials expressed in terms of the Pauli matrices. To prove correctness of this hierarchy, we exploit a finite presentation of the algebra generated by the qubit swap operators. This presentation allows for the use of computer algebraic techniques to manipulate and simplify polynomials written in terms of the swap operators, and may be of independent interest. Surprisingly, we find that level-2 of this new hierarchy is numerically exact (up to tolerance $10^{-7}$) on all QMC instances with uniform edge weights on graphs with at most 8 vertices.<br/>\u0000<br/> The second major contribution of this paper is a polynomial-time algorithm that computes (in exact arithmetic) the maximum eigenvalue of the QMC Hamiltonian for certain graphs, including graphs that can be \"decomposed\" as a signed combination of cliques. A special case of the latter are complete bipartite graphs with uniform edge-weights, for which exact solutions are known from the work of Lieb and Mattis [33]. Our methods, which use representation theory of the symmetric group, can be seen as a generalization of the Lieb-Mattis result.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141079290","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 : 2024-05-22DOI: 10.22331/q-2024-05-22-1353
Chung-Yun Hsieh, Gelo Noel M. Tabia, Yu-Chun Yin, Yeong-Cherng Liang
We introduce the $textit{resource marginal problems}$, which concern the possibility of having a resource-free target subsystem compatible with a $given$ collection of marginal density matrices. By identifying an appropriate choice of resource R and target subsystem T, our problems reduce, respectively, to the well-known $textit{marginal problems}$ for quantum states and the problem of determining if a given quantum system is a resource. More generally, we say that a set of marginal states is $textit{resource-free incompatible}$ with a target subsystem T if all global states compatible with this set must result in a resourceful state in T of type R. We show that this incompatibility $induces$ a resource theory that can be quantified by a monotone and obtain necessary and sufficient conditions for this monotone to be computable as a conic program with finite optimum. We further show, via the corresponding witnesses, that (1) resource-free incompatibility is equivalent to an operational advantage in some channel-discrimination tasks, and (2) some specific cases of such tasks fully characterize the convertibility between marginal density matrices exhibiting resource-free incompatibility. Through our framework, one sees a clear connection between any marginal problem – which implicitly involves some notion of incompatibility – for quantum states and a resource theory for quantum states. We also establish a close connection between the physical relevance of resource marginal problems and the ground state properties of certain many-body Hamiltonians. In terms of application, the universality of our framework leads, for example, to a further quantitative understanding of the incompatibility associated with the recently-proposed entanglement marginal problems and entanglement transitivity problems.
我们引入了$textit{资源边际问题}$，这些问题涉及是否可能有一个无资源的目标子系统与$given$边际密度矩阵集合相兼容。通过确定资源 R 和目标子系统 T 的适当选择，我们的问题分别简化为众所周知的量子态$textit{边际问题}$ 和确定给定量子系统是否是资源的问题。更一般地说，如果所有与边际态集兼容的全局态都会在 T 中产生一个 R 类型的资源态，那么我们就说边际态集与目标子系统 T 是 $textit{无资源不兼容}$。我们证明了这种不兼容会引起一个可以用单调来量化的资源理论，并得到了这个单调可以作为具有有限最优的圆锥程序来计算的必要条件和充分条件。通过相应的证明，我们进一步证明：(1) 在某些渠道区分任务中，无资源不相容等同于操作优势；(2) 在此类任务的某些特定情况下，表现出无资源不相容的边际密度矩阵之间的可转换性是完全表征的。通过我们的框架，我们可以看到量子态的任何边际问题（其中隐含着某种不相容的概念）与量子态资源理论之间的明确联系。我们还在资源边际问题的物理意义与某些多体哈密顿的基态性质之间建立了密切联系。在应用方面，我们框架的普遍性导致了对最近提出的纠缠边际问题和纠缠反式问题相关的不相容性的进一步定量理解。
{"title":"Resource Marginal Problems","authors":"Chung-Yun Hsieh, Gelo Noel M. Tabia, Yu-Chun Yin, Yeong-Cherng Liang","doi":"10.22331/q-2024-05-22-1353","DOIUrl":"https://doi.org/10.22331/q-2024-05-22-1353","url":null,"abstract":"We introduce the $textit{resource marginal problems}$, which concern the possibility of having a resource-free target subsystem compatible with a $given$ collection of marginal density matrices. By identifying an appropriate choice of resource R and target subsystem T, our problems reduce, respectively, to the well-known $textit{marginal problems}$ for quantum states and the problem of determining if a given quantum system is a resource. More generally, we say that a set of marginal states is $textit{resource-free incompatible}$ with a target subsystem T if all global states compatible with this set must result in a resourceful state in T of type R. We show that this incompatibility $induces$ a resource theory that can be quantified by a monotone and obtain necessary and sufficient conditions for this monotone to be computable as a conic program with finite optimum. We further show, via the corresponding witnesses, that (1) resource-free incompatibility is equivalent to an operational advantage in some channel-discrimination tasks, and (2) some specific cases of such tasks fully characterize the convertibility between marginal density matrices exhibiting resource-free incompatibility. Through our framework, one sees a clear connection between any marginal problem – which implicitly involves some notion of incompatibility – for quantum states and a resource theory for quantum states. We also establish a close connection between the physical relevance of resource marginal problems and the ground state properties of certain many-body Hamiltonians. In terms of application, the universality of our framework leads, for example, to a further quantitative understanding of the incompatibility associated with the recently-proposed entanglement marginal problems and entanglement transitivity problems.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141079282","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 : 2024-05-21DOI: 10.22331/q-2024-05-21-1350
Beatriz Dias, Robert Koenig
We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian operations. We argue that this problem is analogous to that of simulating Clifford circuits with non-stabilizer initial states: Algorithms for the latter problem immediately translate to the fermionic setting. Our construction is based on an extension of the covariance matrix formalism which permits to efficiently track relative phases in superpositions of Gaussian states. It yields simulation algorithms with polynomial complexity in the number of fermions, the desired accuracy, and certain quantities capturing the degree of non-Gaussianity of the initial state. We study one such quantity, the fermionic Gaussian extent, and show that it is multiplicative on tensor products when the so-called fermionic Gaussian fidelity is. We establish this property for the tensor product of two arbitrary pure states of four fermions with positive parity.
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