Abstract Quantum speed limit (QSL), the lower bound of the time for transferring an initial state to a target one, is of fundamental interest in quantum information processing. Despite that the speed limit of a unitary evolution could be well analyzed by either the Mandelstam–Tamm or the Margolus–Levitin bound, there are still many unknowns for the QSL in open systems. A particularly exciting result is about that the evolution time can be made arbitrarily small without violating the time-energy uncertainty principle, whenever the dynamics is governed by a parity-time ( P T ) symmetric Hamiltonian. Here we study the QSLs with both P T and anti- P T Hamiltonians, and pose the QSL as a brachistochrone problem on a non-Hermitian Bloch sphere. We then use dissipative trapped-ion qubits to construct the Hamiltonians, where the state evolutions reach the QSL governed by a generalized Margolus-Levitin bound of the non-Hermitian system. We find that the evolution time monotonously decreases with the increase of the dissipation strength and exhibits chiral dependence on the Bloch sphere. These results enable a well-controlled knob for speeding up the state manipulation in open quantum systems, which could be used for quantum control and simulation with non-unitary dynamics.
Abstract Quantum speed limit (QSL), the lower bound of the time for transferring an initial state to a target one, is of fundamental interest in quantum information processing. Despite that the speed limit of a unitary evolution could be well analyzed by either the Mandelstam–Tamm or the Margolus–Levitin bound, there are still many unknowns for the QSL in open systems. A particularly exciting result is about that the evolution time can be made arbitrarily small without violating the time-energy uncertainty principle, whenever the dynamics is governed by a parity-time ( P T ) symmetric Hamiltonian. Here we study the QSLs with both P T and anti- P T Hamiltonians, and pose the QSL as a brachistochrone problem on a non-Hermitian Bloch sphere. We then use dissipative trapped-ion qubits to construct the Hamiltonians, where the state evolutions reach the QSL governed by a generalized Margolus-Levitin bound of the non-Hermitian system. We find that the evolution time monotonously decreases with the increase of the dissipation strength and exhibits chiral dependence on the Bloch sphere. These results enable a well-controlled knob for speeding up the state manipulation in open quantum systems, which could be used for quantum control and simulation with non-unitary dynamics.
The quantum speed limit (QSL) refers to the maximum speed of a quantum system to evolve from an initial state to its orthogonal states. The bound on the QSL for Hermitian systems, for example the Mandelstam-Tamm (MT) and Margolus-Levitin (ML) as well as Sun-Zheng(SZ) bound, was studied respectively from the perspectives of average value and variance of the system Hamiltonian as well as the geometry of the system. While the compactness of the MT-type, ML-type and SZ-type bounds has been examined well for Hermitian systems, a compact QSL for non-Hermitian systems has not been well studied. In this work, based on the biorthogonal basis theory we derive two distinct and tighter bounds on the QSL for non-Hermitian systems, which correspond to the MT and ML bounds for Hermitian systems. We show that the shortest evolution time corresponding to the two bounds of the non-Hermitian system can be attained by certain initial states, showing the compactness and tightness of our bounds. These initial states dubbed fastest initial states(FIS) are different from that in Hermitian systems. A bound close to QSL for non-FIS is presented and comparison of our bound with others in literature is performed. To illustrate our results, we present a minimal non-Hermitian system to show QSL, and the condition for the shortest evolution time is derived analytically using the present theory.
Abstract Quantum speed limit (QSL) is the study of fundamental limits on the evolution time of quantum systems. For instance, under the action of a time-independent Hamiltonian, the evolution time between an initial and a final quantum state obeys various mutually complementary lower bounds. They include the Mandelstam–Tamm (MT) bound, the Margolus–Levitin (ML) bound, the Luo–Zhang bound, the Lee–Chau (LC) bound together with the dual ML bound introduced by Ness and coworkers. Here we show that the MT bound can be obtained by optimizing the LC bound over a certain parameter. More importantly, we report a QSL that includes all the above bounds as special cases before optimizing over the physically meaningless reference energy level of a quantum system. This unifying bound depends on a certain parameter p. For any fixed p, we find all pairs of time-independent Hamiltonian and initial pure quantum state that saturate this unifying bound. More importantly, these pairs allow us to compute this bound accurately and efficiently using an oracle that returns certain pth moments related to the absolute value of energy of the quantum state. Moreover, this oracle can be simulated by a computationally efficient and accurate algorithm for finite-dimensional quantum systems as well as for certain infinite-dimensional quantum states with bounded and continuous energy spectra. This makes our computational method feasible in a lot of practical situations. We further compare the performance of this bound for the case of a fixed p as well as the case of optimizing over p with existing QSLs. We find that if the dimension of the underlying Hilbert space is ≲ 2000 , our unifying bound optimized over p can be computed accurately in a few minutes using Mathematica code with just-in-time compilation in a typical desktop. Besides, this optimized unifying QSL is at least as good as all the existing ones combined and can occasionally be a few percent to a few times better.
Quantum speed limits describe how fast a system can evolve from one state to another. There are several well-known quantum speed limits such as the Mandelstam–Tamm and Margolus–Levitin bounds which were originally derived for pure states and are not always tight for mixed states. In this thesis a stronger bound is derived for mixed qubit states, which has been shown to be tight, by using additional information about the system. We chose to focus on a single qubit and use the Bloch representation to describe its evolution geometrically. Due to both the energy and the purity of the system being conserved under unitary time evolution, the Bloch vector moves in a circle. By expressing the fidelity between the initial and final state in terms of Bloch vectors, we can derive a stricter quantum speed limit for mixed qubit states. This new lower bound depends on both fidelity and purity and is tighter than the Margolus–Levitin bound. The result shows that taking conserved quantities like purity into account can lead to improved quantum speed limits and similar ideas might be useful for more complex systems as well.
Quantum speed limits (QSLs) constrain the minimum time for quantum state evolution, typically derived from energy bounds like the Margolus-Levitin (ML) and Mandelstam-Tamm (MT) relations. In open systems, decoherence—driven by environmental interactions—may impose additional constraints. This work investigates whether decoherence times fundamentally limit QSLs in spin-chain systems, extending ML/MT bounds to open dynamics. By modeling spin chains with Lindblad equations and simulating Heisenberg-type interactions, we analyze the interplay between energy fluctuations, decoherence rates, and evolution times. Experimental validation via trapped-ion or superconducting-qubit arrays could test energy-time uncertainty in many-body systems. Results suggest decoherence times establish a lower QSL bound proportional to [to verify], offering a platform to probe open-system quantum dynamics. ## 1. Introduction Quantum speed limits (QSLs) define the fastest possible evolution between distinguishable quantum states, critical for quantum computing and information processing. Closed-system QSLs, such as the ML [arXiv:quant-ph/9804014] and MT [DOI:10.1103/PhysRev.41.1019] bounds, rely on energy constraints. However, open systems—subject to decoherence—require extended frameworks. Decoherence times, governed by environmental couplings, may impose additional QSLs, yet their interplay with ML/MT bounds remains unexplored. Spin chains, realizable in trapped ions [DOI:10.1038/s41586-019-1394-6] and superconducting circuits, offer a many-body testbed for studying these effects. This work bridges open-system dynamics with QSL theory, assessing whether decoherence times set a fundamental lower bound and enabling experimental verification of energy-time uncertainty. ## 2. Background The ML bound states that a quantum system requires at least $ t_{\text{QSL}} \geq \hbar / (2\Delta E) $, where $ \Delta E $ is the energy spread. The MT bound $ t_{\text{QSL}} \geq \hbar / (2E) $, with $
Abstract We present a new quantum speed limit (QSL) for open quantum systems governed by Markovian dynamics. Our approach is based on analyzing the time derivative of the Bures angle between the initial pure state and its time-evolved state, leading to an analytically computable upper bound on the evolution speed. This bound naturally decomposes into three distinct physical contributions: a unitary term, a dissipative deformation term, and a fluctuation term. Building on this structure, we establish a general inequality that connects the QSL to the quantum Fisher information (QFI) in the short-time regime. This reveals a fundamental trade-off between evolution speed and estimation precision, and clarifies how decoherence can both accelerate and constrain information acquisition in open quantum systems.
Quantum speed limits set the maximal pace of state evolution. Two well-known limits exist for a unitary time-independent Hamiltonian: the Mandelstam-Tamm and Margolus-Levitin bounds. The former restricts the rate according to the state energy uncertainty, while the latter depends on the mean energy relative to the ground state. Here we report on an additional bound that exists for states with a bounded energy spectrum. This bound is dual to the Margolus-Levitin one in the sense that it depends on the difference between the state's mean energy and the energy of the highest occupied eigenstate. Each of the three bounds can become the most restrictive one, depending on the spread and mean of the energy, forming three dynamical regimes which are accessible in a multilevel system. The new bound is relevant for quantum information applications, since in most of them, information is stored and manipulated in a Hilbert space with a bounded energy spectrum.