Diagnosing time-directional asymmetry in open quantum systems requires a metric robust to basis choice, because basis-dependent diagnostics yield contradictory answers to whether an asymmetry exists. We employ the trace distance O(g) = 1/2 tr|rho+ - rho-| - the maximal probability advantage for distinguishing forward from backward steady states - and establish it as a basis-free order parameter for steady-state time asymmetry in two analytically solvable minimal models of open two-qubit systems: a driven model, in which a unitary U-symmetry rigorously enforces that the asymmetry is stored entirely in quantum coherences (robust by symmetry), and a bath model, in which coherence-only storage is a dynamical coincidence (robust by tuning). In both models the asymmetry exhibits an interior peak in coupling strength, a classical jump-counting detector is provably blind to it, and pure dephasing destroys it while leaving the population sector untouched. In the driven model the energy and activity observables are exactly U-even while the order parameter is U-odd, so information and energy are carried by orthogonal symmetry sectors - a structural, not numerical, separation. We then derive the first closed-form solution O(lambda,kappa) = lambda/(lambda^2 + 1/2 + 2 kappa) for a single driven qubit with dissipation and pure dephasing, give the optimal drive ratio lambda* = sqrt(1/2 + 2 kappa), and provide a ready-to-run superconducting-transmon measurement protocol with a 2.7% error budget that turns the predicted asymmetry into a directly falsifiable experiment. A multi-qubit generalization yields the exact even-odd staircase O_(2k-1) = O_(2k) with asymptotic enhancement sqrt(2N/pi) - a parameter-free test of permutation-symmetric preparation.
Diagnosing time-directional asymmetry in open quantum systems requires a metric robust to basis choice, because basis-dependent diagnostics yield contradictory answers to whether an asymmetry exists. We employ the trace distance O(g) = 1/2 tr|rho+ - rho-| - the maximal probability advantage for distinguishing forward from backward steady states - and establish it as a basis-free order parameter for steady-state time asymmetry in two analytically solvable minimal models of open two-qubit systems: a driven model, in which a unitary U-symmetry rigorously enforces that the asymmetry is stored entirely in quantum coherences (robust by symmetry), and a bath model, in which coherence-only storage is a dynamical coincidence (robust by tuning). In both models the asymmetry exhibits an interior peak in coupling strength, a classical jump-counting detector is provably blind to it, and pure dephasing destroys it while leaving the population sector untouched. In the driven model the energy and activity observables are exactly U-even while the order parameter is U-odd, so information and energy are carried by orthogonal symmetry sectors - a structural, not numerical, separation. We then derive the first closed-form solution O(lambda,kappa) = lambda/(lambda^2 + 1/2 + 2 kappa) for a single driven qubit with dissipation and pure dephasing, give the optimal drive ratio lambda* = sqrt(1/2 + 2 kappa), and provide a ready-to-run superconducting-transmon measurement protocol with a 2.7% error budget that turns the predicted asymmetry into a directly falsifiable experiment. A multi-qubit generalization yields the exact even-odd staircase O_(2k-1) = O_(2k) with asymptotic enhancement sqrt(2N/pi) - a parameter-free test of permutation-symmetric preparation.
Abstract Strong symmetries in open quantum systems lead to broken ergodicity and the emergence of multiple degenerate steady states. From a quantum jump (trajectory) perspective, the appearance of multiple steady states is related to underlying dynamical phase transitions (DPTs) at the fluctuating level, leading to a dynamical coexistence of different transport channels classified by symmetry. In this paper we investigate how strong symmetries affect both the transport properties and the activity patterns of a particular class of Markovian open quantum system, a three-qubit model under the action of a magnetic field and in contact with a thermal bath. We find a pair of twin DPTs in exciton current statistics, induced by the strong symmetry and related by time reversibility, where a zero-current exchange-antisymmetric phase coexists with a symmetric phase of negative exciton current. On the other hand, the activity statistics exhibits a single DPT where the symmetric and antisymmetric phases of different but nonzero activities dynamically coexists. Interestingly, the maximum current and maximum activity phases do not coincide for this three-qubits system. We also investigate how symmetries are reflected in the joint large deviation statistics of the activity and the current, a central issue in the characterization of the complex quantum jump dynamics. The presence of a strong symmetry under nonequilibrium conditions implies non-analyticities in the dynamical free energy in the dual activity-current plane (or equivalently in the joint activity-current large deviation function), including an activity-driven current lockdown phase for activities below some critical threshold. Remarkably, the DPT predicted around the steady state and its Gallavotti–Cohen twin dual are extended into lines of first-order DPTs in the current-activity plane, with a nontrivial structure which depends on the transport and activity properties of each of the symmetry phases. Finally, we also study the effect of a symmetry-breaking, ergodicity-restoring dephasing channel on the coupled activity-current statistics for this model. Interestingly, we observe that while this dephasing noise destroys the symmetry-induced DPTs, the underlying topological symmetry leaves a dynamical fingerprint in the form of an intermittent, bursty on/off dynamics between the different symmetry sectors.
We present a concise review and perspective on noise-induced synchronization and coherence protection in open quantum systems, with emphasis on recent work involving coupled spins, oscillators, and anyons. When local environments exhibit internal correlations, the structure of the noise determines which collective modes become decoherence-protected. This leads to steady-state entanglement, phase locking, and exceptional points (EPs) in the Liouvillian spectrum, signaling a collapse of the mode basis and the emergence of non-dissipative stabilized dynamics. Using a Lindblad framework, we show that symmetry in the noise correlations acts as a control parameter, protecting symmetric or antisymmetric modes depending on the sign of the correlation. In the pure-dephasing limit, coherence decay mirrors the Anderson-Kubo model, where the effective fluctuation strength scales as σ2(1±ξ), and the dynamical regime (Gaussian vs. Lorentzian) is set by the ratio σ/γ. Thus, the environment not only drives decoherence but can also selectively suppress it through symmetry filtering. We also revisit historical and conceptual origins of this idea, beginning with Huygens synchronized pendulum clocks and culminating in modern non-Hermitian dynamics. Correlated noise-though classically stochastic-can organize quantum dynamics and protect coherence without direct control over the system. These insights offer a unifying view of synchronization in classical and quantum regimes, with implications for quantum sensing, engineered decoherence, and long-lived coherence in complex environments such as biological light-harvesting complexes or avian magnetoreception.
We present a concise review and perspective on noise-induced synchronisation and coherence protection in open quantum systems, with emphasis on recent work involving coupled spins, oscillators, and anyons. When local environments exhibit internal correlations, the structure of the noise determines which collective modes become decoherence-protected. This leads to steady-state entanglement, phase locking, and exceptional points (EPs) in the Liouvillian spectrum, signalling a collapse of the mode basis and the emergence of non-dissipative stabilised dynamics. Using a Lindblad framework, we show that symmetry in the noise correlations acts as a control parameter–protecting symmetric or antisymmetric modes depending on the sign of the correlation. In the pure-dephasing limit, coherence decay mirrors the Anderson–Kubo model, where the effective fluctuation strength scales as σ2(1±ξ), and the dynamical regime (Gaussian vs. Lorentzian) is set by the ratio σ/γ. Thus, the environment not only drives decoherence but can also selectively suppress it through symmetry filtering. We also revisit historical and conceptual origins of this idea, beginning with Huygens' synchronised pendulum clocks and culminating in modern non-Hermitian dynamics. Correlated noise–though classically stochastic–can organise quantum dynamics and protect coherence without direct control over the system. These insights offer a unifying view of synchronisation in classical and quantum regimes, with implications for quantum sensing, engineered decoherence, and long-lived coherence in complex environments such as biological light-harvesting complexes or avian magnetoreception.
Understanding symmetry restoration in isolated quantum many-body systems is an important problem in nonequilibrium many-body quantum physics. Recent studies have shown that the quantum Mpemba effect can be characterized through entanglement asymmetry, where states with stronger initial symmetry breaking restore symmetry faster. However, it remains unclear whether conventional energy-based measures, such as the trace distance, capture the same phenomenon. We investigate this question in closed spin-1/2 quantum systems with different symmetries by analyzing the dynamics of symmetry-breaking initial states. Combining numerical simulations with an analytical decomposition of the trace distance into symmetry-coherence and residual contributions, we identify the conditions under which trace distance tracks entanglement asymmetry and reproduces the Mpemba--like behavior observed in it. For charge symmetry, the residual contribution is negligible, making the trace distance effectively governed by symmetry-sector coherences. In contrast, for permutation symmetry, a significant residual contribution leads to qualitatively different relaxation dynamics. Our results establish when conventional energy-based diagnostics reliably capture symmetry-restoration dynamics and clarify the distinct physical information encoded by entanglement asymmetry and trace distance.
Understanding quantum coherence and proposing protection mechanisms has become one of the fundamental challenges in quantum physics research. We investigate a generic driven open quantum system, i.e., the driven spin-boson model, beyond the rotating-wave approximation. Although steady-state coherence vanishes in Floquet-Markov and Bloch-Redfield approaches, it becomes finite within a time-non-local master equation with a memory kernel. We analytically reveal that the steady-state coherence is associated with the overlap between the spectral densities associated with neighboring Floquet quasifrequencies. Motivated by this, we show that increasing temperature and introducing mixed transverse and longitudinal baths broadens the spectral density, thereby enhancing steady-state coherence. This is described by resonance fluorescence spectra, which exhibit clear spectral broadening and enhanced steady-state values. For a transverse dissipative coupling to the bath, three transition frequencies emerge in the Floquet basis, corresponding to the Mollow triplet. For weak resonant driving, these quasienergies become nearly degenerate, leading to closely spaced peaks in the resonance fluorescence spectrum, and the steady-state quantum coherence asymptotically approaches its maximum. For a longitudinal coupling to the bath, the quantum system exhibits a single transition frequency, thereby resulting in a complete suppression of the steady-state quantum coherence. We systematically investigate the influences of driving strength, frequency, temperature, and various dissipative baths on steady-state quantum coherence. These findings provide a foundational framework for efficiently engineering steady-state quantum coherence in nanoscale open quantum devices under optical field excitation.
For both unitary and open qubit dynamics, we compare asymmetry monotone-based bounds on the minimal time required for an initial qubit state to evolve to a final qubit state from which it is probabilistically distinguishable with fixed minimal error probability (i.e., the minimal error distinguishability time). For the case of unitary dynamics generated by a time-independent Hamiltonian, we derive a necessary and sufficient condition on two asymmetry monotones that guarantees that an arbitrary state of a two-level quantum system or a separable state of N two-level quantum systems will unitarily evolve to another state from which it can be distinguished with a fixed minimal error probability δ∈[0,1/2] . This condition is used to order the set of qubit states based on their distinguishability time, and to derive an optimal release time for driven two-level systems such as those that occur, e.g., in the Landau-Zener problem. For the case of non-unitary dynamics, we compare three lower bounds to the distinguishability time, including a new type of lower bound which is formulated in terms of the asymmetry of the uniformly time-twirled initial system-plus-environment state with respect to the generator HSE of the Stinespring isometry corresponding to the dynamics, specifically, in terms of ‖[HSE,ρav(τ)]‖1 , where ρav(τ):=1τ∫0τdte−iHSEtρ⊗|0⟩E⟨0|EeiHSEt .