Realizing quantum speed limit in open system with a PT -symmetric trapped-ion qubit

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 paritytime (PT ) symmetric Hamiltonian. Here we study the QSLs with both PT and anti-PT 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.

Non-Hermitian CHSH* Game with a Single Trapped-Ion Qubit

“…Relevant experimental work has been observed in Ref. [10], where this uneven evolution in a dissipative qubit is experimentally confirmed. In the non-Hermitian CHSH * game, the winning probability is obtained by adding the probability of occurrence of four operations.…”

“…The interest for exploring the CHSH * game in non-Hermitian systems is that, in conventional quantum mechanics, Hermiticity is regarded as a fundamental assumption to guarantee some conventional quantum principles, such as entanglement monotonicity, [6,7] the no-signaling principle, [8,9] quantum speed limit, [10] and quantum indistinguishability between quantum states. [11] These principles obey Hermitian quantum mechanics unquestionably, but the violations of some principles were verified in non-Hermitian systems, particularly in 𝒫𝒯 -symmetric quantum systems, [8][9][10][12][13][14] which is proposed by Bender and colleagues in 1998. [15] Recently, 𝒫𝒯 symmetry has been constructed in quantum systems including single photons, [16] cold atoms, [17] and trapped ions, [18,19] etc.…”

“…Experimental studies on 𝒫𝒯 symmetry can be found in the earlier works of our research group. [10,17,19] The experimental scheme is shown in Fig. 1(c).…”

“…Instead, it can be accurately ascertained by implementing an additional Rabi 𝜋 flip before detection to exchange the populations of |0⟩ and |1⟩, given that the total probability across all four ground states (|0⟩, |1⟩, and |𝑎⟩) remains equal to 1. [10] Laser Microwave Results and Discussion. The player's winning probability is theoretically determined by the coupling rate 𝐽 and the dissipation rate 𝛾 as described in Eq.…”