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Sönnerborn, O. (2024). Estimate of the time required to perform a nonadiabatic holonomic quantum computation. Physical Review A: covering atomic, molecular, and optical physics and quantum information, 109, Article ID 062433.
Open this publication in new window or tab >>Estimate of the time required to perform a nonadiabatic holonomic quantum computation
2024 (English)In: Physical Review A: covering atomic, molecular, and optical physics and quantum information, ISSN 2469-9926, E-ISSN 2469-9934, Vol. 109, article id 062433Article in journal (Refereed) Published
Abstract [en]

Nonadiabatic holonomic quantum computation has been proposed as a method to implement quantum logic gates with robustness comparable to that of adiabatic holonomic gates but with shorter execution times. In this paper, we establish an isoholonomic inequality for quantum gates, which provides a lower bound on the lengths of cyclic transformations of the computational space that generate a specific gate. Then, as a corollary, we derive a nonadiabatic execution time estimate for holonomic gates. In addition, we demonstrate that under certain dimensional conditions, the isoholonomic inequality is tight in the sense that every gate on the computational space can be implemented holonomically and unitarily in a time-optimal way. We illustrate the results by showing that the procedures for implementing a universal set of holonomic gates proposed in a pioneering paper on nonadiabatic holonomic quantum computation saturate the isoholonomic inequality and are thus time optimal.

Place, publisher, year, edition, pages
American Physical Society, 2024
National Category
Atom and Molecular Physics and Optics Other Physics Topics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-100632 (URN)10.1103/PhysRevA.109.062433 (DOI)001255358200002 ()2-s2.0-85196903770 (Scopus ID)
Available from: 2024-06-25 Created: 2024-06-25 Last updated: 2024-07-12Bibliographically approved
Hörnedal, N. & Sönnerborn, O. (2023). Closed systems refuting quantum-speed-limit hypotheses. Physical Review A: covering atomic, molecular, and optical physics and quantum information, 108(5), Article ID 052421.
Open this publication in new window or tab >>Closed systems refuting quantum-speed-limit hypotheses
2023 (English)In: Physical Review A: covering atomic, molecular, and optical physics and quantum information, ISSN 2469-9926, E-ISSN 2469-9934, Vol. 108, no 5, article id 052421Article in journal (Refereed) Published
Abstract [en]

Many quantum speed limits for isolated systems can be generalized to also apply to closed systems. This is, for example, the case with the well-known Mandelstam-Tamm quantum speed limit. Margolus and Levitin derived an equally well-known and ostensibly related quantum speed limit, and it seems to be widely believed that the Margolus-Levitin quantum speed limit can be similarly generalized to closed systems. However, a recent geometrical examination of this limit reveals that it differs significantly from most known quantum speed limits. In this paper, we show that, contrary to the common belief, the Margolus-Levitin quantum speed limit does not extend to closed systems in an obvious way. More precisely, we show that for every hypothetical bound of Margolus-Levitin type, there are closed systems that evolve with a conserved normalized expected energy between states with any given fidelity in a time shorter than the bound. We also show that for isolated systems, the Mandelstam-Tamm quantum speed limit and a slightly weakened version of this limit that we call the Bhatia-Davies quantum speed limit always saturate simultaneously. Both of these evolution time estimates extend straightforwardly to closed systems. We demonstrate that there are closed systems that saturate the Mandelstam-Tamm but not the Bhatia-Davies quantum speed limit. 

Place, publisher, year, edition, pages
American Physical Society, 2023
Keywords
Closed systems, Evolution time, Expected energy, Isolated systems, Speed limit, Quantum theory
National Category
Physical Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-97684 (URN)10.1103/PhysRevA.108.052421 (DOI)2-s2.0-85178150097 (Scopus ID)
Available from: 2023-12-11 Created: 2023-12-11 Last updated: 2023-12-11Bibliographically approved
Hörnedal, N. & Sönnerborn, O. (2023). Margolus-Levitin quantum speed limit for an arbitrary fidelity. Physical Review Research, 5(4), Article ID 043234.
Open this publication in new window or tab >>Margolus-Levitin quantum speed limit for an arbitrary fidelity
2023 (English)In: Physical Review Research, E-ISSN 2643-1564, Vol. 5, no 4, article id 043234Article in journal (Refereed) Published
Abstract [en]

The Mandelstam-Tamm and Margolus-Levitin quantum speed limits are two well-known evolution time estimates for isolated quantum systems. These bounds are usually formulated for fully distinguishable initial and final states, but both have tight extensions to systems that evolve between states with an arbitrary fidelity. However, the foundations of these extensions differ in some essential respects. The extended Mandelstam-Tamm quantum speed limit has been proven analytically and has a clear geometric interpretation. Furthermore, which systems saturate the limit is known. The derivation of the extended Margolus-Levitin quantum speed limit, on the other hand, is based on numerical estimates. Moreover, the limit lacks a geometric interpretation, and no complete characterization of the systems reaching it exists. In this paper, we derive the extended Margolus-Levitin quantum speed limit analytically and describe the systems that saturate the limit in detail. We also provide the limit with a symplectic-geometric interpretation, which indicates that it is of a different character than most existing quantum speed limits. At the end of the paper, we analyze the maximum of the extended Mandelstam-Tamm and Margolus-Levitin quantum speed limits and derive a dual version of the extended Margolus-Levitin quantum speed limit. The maximum limit is tight regardless of the fidelity of the initial and final states. However, the conditions under which the maximum limit is saturated differ depending on whether or not the initial state and the final state are fully distinguishable. The dual limit is also tight and follows from a time reversal argument. We describe the systems that saturate the dual quantum speed limit. 

Place, publisher, year, edition, pages
American Physical Society, 2023
Keywords
Closed systems, Evolution time, Expected energy, Isolated systems, Speed limit, Quantum theory
National Category
Physical Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-97813 (URN)10.1103/physrevresearch.5.043234 (DOI)001128791000001 ()2-s2.0-85179628087 (Scopus ID)
Available from: 2023-12-19 Created: 2023-12-19 Last updated: 2024-01-16Bibliographically approved
Hörnedal, N. & Sönnerborn, O. (2023). Tight lower bounds on the time it takes to generate a geometric phase. Physica Scripta, 98(10), Article ID 105108.
Open this publication in new window or tab >>Tight lower bounds on the time it takes to generate a geometric phase
2023 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 98, no 10, article id 105108Article in journal (Refereed) Published
Abstract [en]

Geometric phase is a concept of central importance in virtually every branch of physics. In this paper, we show that the evolution time of a cyclically evolving quantum system is restricted by the system's energy resources and the geometric phase acquired by the state. Specifically, we derive and examine three tight lower bounds on the time required to generate any prescribed Aharonov-Anandan geometric phase. The derivations are based on recent results on the geometric character of the Mandelstam-Tamm and Margolus-Levitin quantum speed limits.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2023
Keywords
geometric phase, quantum speed limit, the Margolus-Levitin quantum speed limit, the Mandelstam-Tamm quantum speed limit, quantum holonomy
National Category
Physical Sciences Mathematics
Research subject
Physics; Mathematics
Identifiers
urn:nbn:se:kau:diva-96816 (URN)10.1088/1402-4896/acf8a2 (DOI)001073294300001 ()2-s2.0-85173581042 (Scopus ID)
Available from: 2023-09-27 Created: 2023-09-27 Last updated: 2023-11-22Bibliographically approved
Hörnedal, N., Allan, D. & Sönnerborn, O. (2022). Extensions of the Mandelstam-Tamm quantum speed limit to systems in mixed states. New Journal of Physics, 24(5), Article ID 055004.
Open this publication in new window or tab >>Extensions of the Mandelstam-Tamm quantum speed limit to systems in mixed states
2022 (English)In: New Journal of Physics, E-ISSN 1367-2630, Vol. 24, no 5, article id 055004Article in journal (Refereed) Published
Abstract [en]

The Mandelstam-Tamm quantum speed limit (QSL) puts a bound on how fast a closed system in a pure state can evolve. In this paper, we derive several extensions of this QSL to closed systems in mixed states. We also compare the strengths of these extensions and examine their tightness. The most widely used extension of the Mandelstam-Tamm QSL originates in Uhlmann's energy dispersion estimate. We carefully analyze the underlying geometry of this estimate, an analysis that makes apparent that the Bures metric, or equivalently the quantum Fisher information, will rarely give rise to tight extensions. This observation leads us to address whether there is a tightest general extension of the Mandelstam-Tamm QSL. Using a geometric construction similar to that developed by Uhlmann, we prove that this is indeed the case. In addition, we show that tight evolutions of mixed states are typically generated by time-varying Hamiltonians, which contrasts with the case for systems in pure states.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2022
Keywords
quantum speed limit, time-energy uncertainty relation, skew-information, Uhlmann energy dispersion estimate quantum Fisher information, quantum information
National Category
Other Physics Topics
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-90121 (URN)10.1088/1367-2630/ac688a (DOI)000797189200001 ()2-s2.0-85130984169 (Scopus ID)
Available from: 2022-06-07 Created: 2022-06-07 Last updated: 2024-01-17Bibliographically approved
Allan, D., Hörnedal, N. & Andersson, O. (2021). Time-optimal quantum transformations with bounded bandwidth. Quantum, 5, 1-19, Article ID 462.
Open this publication in new window or tab >>Time-optimal quantum transformations with bounded bandwidth
2021 (English)In: Quantum, E-ISSN 2521-327X, Vol. 5, p. 1-19, article id 462Article in journal (Refereed) Published
Abstract [en]

In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is initially in an incoherent state relative to the observable and that the state evolves according to a von Neumann equation with a Hamiltonian whose bandwidth is uniformly bounded. The transformation time depends intricately on the observable's and the initial state's eigenvalue spectrum and the relative constellation of the associated eigenspaces. The problem of finding quantum speed limits consequently divides into different cases requiring different strategies. We derive quantum speed limits in a large number of cases, and we simultaneously develop a method to break down complex cases into manageable ones. The derivations involve both combinatorial and differential geometric techniques. We also study multipartite systems and show that allowing correlations between the parts can speed up the transformation time. In a final section, we use the quantum speed limits to obtain upper bounds on the power with which energy can be extracted from quantum batteries.

Place, publisher, year, edition, pages
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2021
National Category
Mathematics Physical Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-90238 (URN)10.22331/q-2021-05-27-462 (DOI)
Available from: 2022-06-10 Created: 2022-06-10 Last updated: 2022-06-22Bibliographically approved
Andersson, O. & Dumitru, I. (2019). Aligned SICs and embedded tight frames in even dimensions. Journal of Physics A: Mathematical and Theoretical, 52(42), Article ID 425302.
Open this publication in new window or tab >>Aligned SICs and embedded tight frames in even dimensions
2019 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, no 42, article id 425302Article in journal (Refereed) Published
Abstract [en]

Alignment is a geometric relation between pairs of Weyl-Heisenberg SICs, one in dimension d and another in dimension d(d - 2), manifesting a well-founded conjecture about a number-theoretical connection between the SICs. In this paper, we prove that if d is even, the SIC in dimension d(d - 2) of an aligned pair can be partitioned into (d - 2)(2) tight d(2)-frames of rank d(d - 1)/2 and, alternatively, into d(2) tight (d - 2)(2) -frames of rank (d - 1) (d - 2)/2. The corresponding result for odd d is already known, but the proof for odd d relies on results which are not available for even d. We develop methods that allow us to overcome this issue. In addition, we provide a relatively detailed study of parity operators in the Clifford group, emphasizing differences in the theory of parity operators in even and odd dimensions and discussing consequences due to such differences. In a final section, we study implications of alignment for the symmetry of the SIC.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2019
Keywords
SIC-POVM, frame theory, Weyl-Heisenberg group, symmetry, parity operator, Chinese remainder, Physical Sciences, Fysik
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-90731 (URN)10.1088/1751-8121/ab434e (DOI)
Available from: 2022-06-22 Created: 2022-06-22 Last updated: 2022-06-22Bibliographically approved
Andersson, O., Badziąg, P., Dumitru, I. & Cabello, A. (2018). Device-independent certification of two bits of randomness from one entangled bit and Gisin's elegant Bell inequality. Physical Review A. Atomic, Molecular, and Optical Physics, 97(1), Article ID 012314.
Open this publication in new window or tab >>Device-independent certification of two bits of randomness from one entangled bit and Gisin's elegant Bell inequality
2018 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 97, no 1, article id 012314Article in journal (Refereed) Published
Abstract [en]

We prove that as conjectured by Acín et al. [Phys. Rev. A 93, 040102(R) (2016)], two bits of randomness can be certified in a device-independent way from one bit of entanglement using the maximal quantum violation of Gisin's elegant Bell inequality. This suggests a surprising connection between maximal entanglement, complete sets of mutually unbiased bases, and elements of symmetric informationally complete positive operator-valued measures, on one side, and the optimal way of certifying maximal randomness, on the other.

Place, publisher, year, edition, pages
American Physical Society, 2018
Keywords
Other Physics Topics, Annan fysik
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-90727 (URN)10.1103/PhysRevA.97.012314 (DOI)
Available from: 2022-06-22 Created: 2022-06-22 Last updated: 2022-06-22Bibliographically approved
Andersson, O. (2018). Holonomy in Quantum Information Geometry. (Licentiate dissertation). Stockholm University
Open this publication in new window or tab >>Holonomy in Quantum Information Geometry
2018 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we provide a uniform treatment of the two most popular non-adiabatic geometric phases for dynamical systems of mixed quantum states, namely those of Uhlmann and of Sjöqvist et al. We develop a holonomy theory for the latter which we also relate to the already existing theory for the former. This makes it clear what the similarities and differences between the two geometric phases are. We discuss and motivate constraints on the two phases. Furthermore, we discuss some topological properties of the holonomy of `real' quantum systems, and we introduce higher-order geometric phases for not necessarily cyclic dynamical systems of mixed states. In a final chapter we apply the theory developed for the geometric phase of Sjöqvist et al. to geometric uncertainty relations, including some new "quantum speed limits''.

Place, publisher, year, edition, pages
Stockholm University, 2018
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-90779 (URN)
Presentation
2018-03-21, C5:1007, Fysikum, Albanova universitetscentrum, 10:15 (English)
Opponent
Supervisors
Available from: 2022-06-23 Created: 2022-06-23 Last updated: 2022-06-23Bibliographically approved
Andersson, O. & Bengtsson, I. (2017). Clifford tori and unbiased vectors. Reports on mathematical physics, 79(1), 33-51
Open this publication in new window or tab >>Clifford tori and unbiased vectors
2017 (English)In: Reports on mathematical physics, ISSN 0034-4877, E-ISSN 1879-0674, Vol. 79, no 1, p. 33-51Article in journal (Refereed) Published
Abstract [en]

The existence problem for mutually unbiased bases is an unsolved problem in quantum information theory. A related question is whether every pair of bases admits vectors that are unbiased to both. Mathematically this translates to the question whether two Lagrangian Clifford tori intersect, and a body of results exists concerning it. These results are however rather weak from the point of view of the first problem. We make a detailed study of how the intersections behave in the simplest nontrivial case, that of complex projective 2-space (the qutrit), for which the set of pairs of Clifford tori can be usefully parametrized by the unistochastic subset of Birkhoff's polytope. Pairs that do not intersect transversally are located. Some calculations in higher dimensions are included to see which results are special to the qutrit.

Place, publisher, year, edition, pages
Elsevier, 2017
Keywords
mutually unbiased bases, Lagrangian submanifolds, Birkhoff's polytope, Physical Sciences, Fysik
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-90728 (URN)10.1016/S0034-4877(17)30019-8 (DOI)
Available from: 2022-06-22 Created: 2022-06-22 Last updated: 2022-06-22Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-1726-4892

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