1
|
Zhu C, Liu Z, Zhu C, Wang X. Limitations of Classically Simulable Measurements for Quantum State Discrimination. PHYSICAL REVIEW LETTERS 2024; 133:010202. [PMID: 39042807 DOI: 10.1103/physrevlett.133.010202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2023] [Accepted: 05/31/2024] [Indexed: 07/25/2024]
Abstract
In the realm of fault-tolerant quantum computing, stabilizer operations play a pivotal role, characterized by their remarkable efficiency in classical simulation. This efficiency sets them apart from nonstabilizer operations within the quantum computational theory. In this Letter, we investigate the limitations of classically simulable measurements in distinguishing quantum states. We demonstrate that any pure magic state and its orthogonal complement of odd prime dimensions cannot be unambiguously distinguished by stabilizer operations, regardless of how many copies of the states are supplied. We also reveal intrinsic similarities and distinctions between the quantum resource theories of magic states and entanglement in quantum state discrimination. The results emphasize the inherent limitations of classically simulable measurements and contribute to a deeper understanding of the quantum-classical boundary.
Collapse
|
2
|
Kuroiwa K, Takagi R, Adesso G, Yamasaki H. Every Quantum Helps: Operational Advantage of Quantum Resources beyond Convexity. PHYSICAL REVIEW LETTERS 2024; 132:150201. [PMID: 38682983 DOI: 10.1103/physrevlett.132.150201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Accepted: 02/05/2024] [Indexed: 05/01/2024]
Abstract
Identifying what quantum-mechanical properties are useful to untap a superior performance in quantum technologies is a pivotal question. Quantum resource theories provide a unified framework to analyze and understand such properties, as successfully demonstrated for entanglement and coherence. While these are examples of convex resources, for which quantum advantages can always be identified, many physical resources are described by a nonconvex set of free states and their interpretation has so far remained elusive. Here we address the fundamental question of the usefulness of quantum resources without convexity assumption, by providing two operational interpretations of the generalized robustness measure in general resource theories. First, we characterize the generalized robustness in terms of a nonlinear resource witness and reveal that any state is more advantageous than a free one in some multicopy channel discrimination task. Next, we consider a scenario where a theory is characterized by multiple constraints and show that the generalized robustness coincides with the worst-case advantage in a single-copy channel discrimination setting. Based on these characterizations, we conclude that every quantum resource state shows a qualitative and quantitative advantage in discrimination problems in a general resource theory even without any specification on the structure of the free states.
Collapse
Affiliation(s)
- Kohdai Kuroiwa
- Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, Ontario N2L 2Y5, Canada
| | - Ryuji Takagi
- Department of Basic Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Gerardo Adesso
- School of Mathematical Sciences and Centre for the Mathematical and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Hayata Yamasaki
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| |
Collapse
|
3
|
Tendick L, Kampermann H, Bruß D. Distributed Quantum Incompatibility. PHYSICAL REVIEW LETTERS 2023; 131:120202. [PMID: 37802938 DOI: 10.1103/physrevlett.131.120202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Revised: 07/03/2023] [Accepted: 08/23/2023] [Indexed: 10/08/2023]
Abstract
Incompatible, i.e., nonjointly measurable quantum measurements are a necessary resource for many information processing tasks. It is known that increasing the number of distinct measurements usually enhances the incompatibility of a measurement scheme. However, it is generally unclear how large this enhancement is and on what it depends. Here, we show that the incompatibility which is gained via additional measurements is upper and lower bounded by certain functions of the incompatibility of subsets of the available measurements. We prove the tightness of some of our bounds by providing explicit examples based on mutually unbiased bases. Finally, we discuss the consequences of our results for the nonlocality that can be gained by enlarging the number of measurements in a Bell experiment.
Collapse
Affiliation(s)
- Lucas Tendick
- Institute for Theoretical Physics III, Heinrich Heine University Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hermann Kampermann
- Institute for Theoretical Physics III, Heinrich Heine University Düsseldorf, D-40225 Düsseldorf, Germany
| | - Dagmar Bruß
- Institute for Theoretical Physics III, Heinrich Heine University Düsseldorf, D-40225 Düsseldorf, Germany
| |
Collapse
|
4
|
Ioannou M, Sekatski P, Designolle S, Jones BDM, Uola R, Brunner N. Simulability of High-Dimensional Quantum Measurements. PHYSICAL REVIEW LETTERS 2022; 129:190401. [PMID: 36399736 DOI: 10.1103/physrevlett.129.190401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Accepted: 09/07/2022] [Indexed: 06/16/2023]
Abstract
We investigate the compression of quantum information with respect to a given set M of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from M and an arbitrary quantum state ρ are recovered exactly by first compressing ρ into a lower-dimensional space, followed by some quantum measurements. A full quantum compression is possible, i.e., leaving only classical information, if and only if the set M is jointly measurable. Our notion of simulability can thus be seen as a quantification of measurement incompatibility in terms of dimension. After defining these concepts, we provide an illustrative example involving mutually unbiased bases, and develop a method based on semidefinite programming for constructing simulation models. In turn we analytically construct optimal simulation models for all projective measurements subjected to white noise or losses. Finally, we discuss how our approach connects with other concepts introduced in the context of quantum channels and quantum correlations.
Collapse
Affiliation(s)
- Marie Ioannou
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Pavel Sekatski
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | | | - Benjamin D M Jones
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
- Quantum Engineering Centre for Doctoral Training, University of Bristol, Bristol BS8 1FD, United Kingdom
| | - Roope Uola
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Nicolas Brunner
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| |
Collapse
|
5
|
Ahnefeld F, Theurer T, Egloff D, Matera JM, Plenio MB. Coherence as a Resource for Shor's Algorithm. PHYSICAL REVIEW LETTERS 2022; 129:120501. [PMID: 36179183 DOI: 10.1103/physrevlett.129.120501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2022] [Revised: 07/10/2022] [Accepted: 08/01/2022] [Indexed: 06/16/2023]
Abstract
Shor's factoring algorithm provides a superpolynomial speedup over all known classical factoring algorithms. Here, we address the question of which quantum properties fuel this advantage. We investigate a sequential variant of Shor's algorithm with a fixed overall structure and identify the role of coherence for this algorithm quantitatively. We analyze this protocol in the framework of dynamical resource theories, which capture the resource character of operations that can create and detect coherence. This allows us to derive a lower and an upper bound on the success probability of the protocol, which depend on rigorously defined measures of coherence as a dynamical resource. We compare these bounds with the classical limit of the protocol and conclude that within the fixed structure that we consider, coherence is the quantum resource that determines its performance by bounding the success probability from below and above. Therefore, we shine new light on the fundamental role of coherence in quantum computation.
Collapse
Affiliation(s)
- Felix Ahnefeld
- Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11, D-89081 Ulm, Germany
| | - Thomas Theurer
- Department of Mathematics and Statistics, Institute for Quantum Science and Technology, University of Calgary, Alberta T2N 1N4, Canada
| | - Dario Egloff
- Institute of Theoretical Physics, Technical University Dresden, D-01062 Dresden, Germany
| | - Juan Mauricio Matera
- IFLP-CONICET, Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, La Plata 1900, Argentina
| | - Martin B Plenio
- Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11, D-89081 Ulm, Germany
| |
Collapse
|
6
|
Regula B. Probabilistic Transformations of Quantum Resources. PHYSICAL REVIEW LETTERS 2022; 128:110505. [PMID: 35363021 DOI: 10.1103/physrevlett.128.110505] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2021] [Accepted: 02/23/2022] [Indexed: 06/14/2023]
Abstract
The difficulty in manipulating quantum resources deterministically often necessitates the use of probabilistic protocols, but the characterization of their capabilities and limitations has been lacking. We develop a general approach to this problem by introducing a new resource monotone that obeys a very strong type of monotonicity: it can rule out all transformations, probabilistic or deterministic, between states in any quantum resource theory. This allows us to place fundamental limitations on state transformations and restrict the advantages that probabilistic protocols can provide over deterministic ones, significantly strengthening previous findings and extending recent no-go theorems. We apply our results to obtain a substantial improvement in bounds for the errors and overheads of probabilistic distillation protocols, directly applicable to tasks such as entanglement or magic state distillation, and computable through convex optimization. In broad classes of resources, we strengthen our results to show that the monotone completely governs probabilistic transformations-it serves as a necessary and sufficient condition for state convertibility. This endows the monotone with a direct operational interpretation, as it can exactly quantify the highest fidelity achievable in resource distillation tasks by means of any probabilistic manipulation protocol.
Collapse
Affiliation(s)
- Bartosz Regula
- Department of Physics, Graduate School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
| |
Collapse
|
7
|
Haapasalo E, Kraft T, Pellonpää JP, Uola R. Operational Characterization of Infinite-Dimensional Quantum Resources. PHYSICAL REVIEW LETTERS 2021; 127:250401. [PMID: 35029426 DOI: 10.1103/physrevlett.127.250401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Revised: 10/11/2021] [Accepted: 10/22/2021] [Indexed: 06/14/2023]
Abstract
Recently, various nonclassical properties of quantum states and channels have been characterized through an advantage they provide in quantum information tasks over their classical counterparts. Such advantage can be typically proven to be quantitative, in that larger amounts of quantum resources lead to better performance in the corresponding tasks. So far, these characterizations have been established only in the finite-dimensional setting, hence, leaving out central resources in continuous variable systems such as entanglement and nonclassicality of states as well as entanglement breaking and broadcasting channels. In this Letter, we present a fully general framework for resource quantification in infinite-dimensional systems. The framework is applicable to a wide range of resources with the only premises being that classical randomness cannot create a resource and that the resourceless objects form a closed set in an appropriate sense. As the latter may be hard to establish for the abstract topologies of continuous variable systems, we provide a relaxation of the condition with no reference to topology. This envelopes the aforementioned resources and various others, hence, giving them an interpretation as performance enhancement in so-called input-output games.
Collapse
Affiliation(s)
- Erkka Haapasalo
- Centre for Quantum Technologies, National University of Singapore, Science Drive 2 Block S15-03-18, Singapore 117543
| | - Tristan Kraft
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany
| | - Juha-Pekka Pellonpää
- Department of Physics and Astronomy, University of Turku, FI-20014 Turun yliopisto, Finland
| | - Roope Uola
- Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland
| |
Collapse
|
8
|
Tan KC, Narasimhachar V, Regula B. Fisher Information Universally Identifies Quantum Resources. PHYSICAL REVIEW LETTERS 2021; 127:200402. [PMID: 34860070 DOI: 10.1103/physrevlett.127.200402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2021] [Revised: 07/31/2021] [Accepted: 09/28/2021] [Indexed: 06/13/2023]
Abstract
We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states with and without a given resource. This shows that all quantum resources confer an advantage in metrology, and establishes the Fisher information as a universal tool to probe the resourcefulness of quantum states. We provide bounds on the extent of this advantage, as well as a simple criterion to test whether different resources are useful for the estimation of unitarily encoded parameters. Finally, we extend the results to show that the Fisher information is also able to identify the dynamical resourcefulness of quantum operations.
Collapse
Affiliation(s)
- Kok Chuan Tan
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Republic of Singapore
| | - Varun Narasimhachar
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Republic of Singapore
| | - Bartosz Regula
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Republic of Singapore
| |
Collapse
|
9
|
Lipka-Bartosik P, Skrzypczyk P. Catalytic Quantum Teleportation. PHYSICAL REVIEW LETTERS 2021; 127:080502. [PMID: 34477432 DOI: 10.1103/physrevlett.127.080502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 07/12/2021] [Indexed: 06/13/2023]
Abstract
In this work, we address fundamental limitations of quantum teleportation-the process of transferring quantum information using classical communication and preshared entanglement. We develop a new teleportation protocol based upon the idea of using ancillary entanglement catalytically, i.e., without depleting it. This protocol is then used to show that catalytic entanglement allows for a noiseless quantum channel to be simulated with a quality that could never be achieved using only entanglement from the shared state, even for catalysts with a small dimension. On the one hand, this allows for a more faithful transmission of quantum information using generic states and fixed amount of consumed entanglement. On the other hand, this shows, for the first time, that entanglement catalysis provides a genuine advantage in a generic quantum-information processing task. Finally, we show that similar ideas can be directly applied to study quantum catalysis for more general problems in quantum mechanics. As an application, we show that catalysts can activate so-called passive states, a concept that finds widespread application, e.g., in quantum thermodynamics.
Collapse
Affiliation(s)
- Patryk Lipka-Bartosik
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Paul Skrzypczyk
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| |
Collapse
|
10
|
Regula B, Lami L, Ferrari G, Takagi R. Operational Quantification of Continuous-Variable Quantum Resources. PHYSICAL REVIEW LETTERS 2021; 126:110403. [PMID: 33798371 DOI: 10.1103/physrevlett.126.110403] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Accepted: 02/08/2021] [Indexed: 06/12/2023]
Abstract
The diverse range of resources which underlie the utility of quantum states in practical tasks motivates the development of universally applicable methods to measure and compare resources of different types. However, many of such approaches were hitherto limited to the finite-dimensional setting or were not connected with operational tasks. We overcome this by introducing a general method of quantifying resources for continuous-variable quantum systems based on the robustness measure, applicable to a plethora of physically relevant resources such as optical nonclassicality, entanglement, genuine non-Gaussianity, and coherence. We demonstrate in particular that the measure has a direct operational interpretation as the advantage enabled by a given state in a class of channel discrimination tasks. We show that the robustness constitutes a well-behaved, bona fide resource quantifier in any convex resource theory, contrary to a related negativity-based measure known as the standard robustness. Furthermore, we show the robustness to be directly observable-it can be computed as the expectation value of a single witness operator-and establish general methods for evaluating the measure. Explicitly applying our results to the relevant resources, we demonstrate the exact computability of the robustness for several classes of states.
Collapse
Affiliation(s)
- Bartosz Regula
- School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
| | - Ludovico Lami
- Institut für Theoretische Physik und IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | - Giovanni Ferrari
- Institut für Theoretische Physik und IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
- Dipartimento di Fisica e Astronomia Galileo Galilei, Università degli studi di Padova, via Marzolo 8, 35131 Padova, Italy
| | - Ryuji Takagi
- School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
- Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| |
Collapse
|
11
|
Uola R, Bullock T, Kraft T, Pellonpää JP, Brunner N. All Quantum Resources Provide an Advantage in Exclusion Tasks. PHYSICAL REVIEW LETTERS 2020; 125:110402. [PMID: 32975968 DOI: 10.1103/physrevlett.125.110402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Revised: 04/24/2020] [Accepted: 08/03/2020] [Indexed: 06/11/2023]
Abstract
A key ingredient in quantum resource theories is a notion of measure. Such as a measure should have a number of fundamental properties, and desirably also a clear operational meaning. Here we show that a natural measure known as the convex weight, which quantifies the resource cost of a quantum device, has all the desired properties. In particular, the convex weight of any quantum resource corresponds exactly to the relative advantage it offers in an exclusion (or antidistinguishability) task. After presenting the general result, we show how the construction works for state assemblages, sets of measurements, and sets of transformations. Moreover, in order to bound the convex weight analytically, we give a complete characterization of the convex components and corresponding weights of such devices.
Collapse
Affiliation(s)
- Roope Uola
- Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland
| | - Tom Bullock
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun yliopisto, Finland
| | - Tristan Kraft
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany
| | - Juha-Pekka Pellonpää
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun yliopisto, Finland
| | - Nicolas Brunner
- Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland
| |
Collapse
|