Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system-a Lindbladian-a unitary symmetry can be imposed in a "weak" or a "strong" way. We characterize the possible Z_{n} symmetry-breaking transitions for both cases. In the case of Z_{2}, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correction.
Abstract This article presents a detailed study of symmetry breaking quantum error correction (QEC) with a focus on the role of single-photon and two-photon losses in continuous-variable quantum systems. By employing a model that includes two-photon driving and several dissipation mechanisms, we explore its phase transitions and error-correction capabilities in different symmetry scenarios. A scheme for estimating the impact of single-photon loss under the symmetry breaking QEC framework is proposed, based on which we further utilize numerical simulations to demonstrate how the system’s parameters affect the fidelity of QEC and the stability of quantum states against the interaction with environments. We expect that the evaluation method shown here can act as an applicable tool for assessing the influence of single-photon loss and therefore guide future experiments to design more robust passive quantum error-correcting codes that operate under realistic conditions.
We investigate the fate of dissipative phase transitions in quantum many-body systems when the individual constituents are qudits (
d-level systems) instead of qubits. As an example system, we employ a permutation-invariant
XY model of
N infinite-range interacting
d-level spins undergoing individual and collective dissipation. In the mean-field limit, we identify a dissipative phase transition, whose critical point is independent of
d after a suitable rescaling of parameters. When the decay rates between all adjacent levels are identical and $d\ensuremath{\ge}4$, the critical point expands, in terms of the ratio between dissipation and interaction strengths, to a critical region in which two phases coexist and which increases as
d grows. In addition, a larger
d leads to a more pronounced change in spin expectation values at the critical point. Numerical investigations for finite
N reveal symmetry-breaking signatures in the Liouvillian spectrum at the phase transition. The phase transition is furthermore marked by maximum entanglement negativity and a significant purity change of the steady state, which become more pronounced as
d increases. Considering qudits instead of qubits thus opens new perspectives on accessing rich phase diagrams in open many-body systems.
We investigate the fate of dissipative phase transitions in quantum many-body systems when the individual constituents are qudits (d-level systems) instead of qubits. As an example system, we employ a permutation- invariant XY model of N infinite-range interacting d-level spins (Lipkin-Meshkov-Glick model) undergoing individual and collective dissipation. In the mean-field limit, we identify a dissipative phase transition, whose critical point is independent of d after a suitable rescaling of parameters. When the decay rates between all adjacent levels are identical and d ≥ 4, the critical point expands, in terms of the ratio between dissipation and interaction strengths, to a critical region in which two phases coexist and which increases as d grows. In addition, a larger d leads to a more pronounced change in spin expectation values at the critical point. Numerical investigations for finite N reveal symmetry breaking signatures in the Liouvillian spectrum at the phase transition. The phase transition is furthermore marked by maximum entanglement negativity and a significant purity change of the steady state, which become more pronounced as d increases. Considering qudits instead of qubits thus opens new perspectives on accessing rich phase diagrams in open many-body systems.
An interesting problem in the field of quantum error correction involves finding a physical system that hosts a "passively protected quantum memory," defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is known only in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model, the photonic-Ising model, which appears to passively correct against both bit-flip and phase-flip errors in two dimensions: a square lattice composed of photonic "cat qubits" coupled via dissipative terms which tend to fix errors locally. Inspired by the presence of two distinct Z_{2}-symmetry-broken phases, our scheme relies on Ising-like dissipators to protect against bit flips and on a driven-dissipative photonic environment to protect against phase flips. We also discuss possible ways to realize the photonic-Ising model.
Symmetry constraints provide a powerful means to control the dynamics of open quantum systems. However, the set of accessible control parameters is often limited. Here, we show that a tunable phase in the collective light-matter coupling of a cavity QED system induces a phase-dependent strong symmetry of the Liouvillian, enabling dynamical control of the open quantum system evolution. We demonstrate that tuning this phase substantially reduces the critical driving strength for dissipative phase transitions between stationary and non-stationary phases. We illustrate this mechanism in two experimentally relevant cavity QED settings: a two-species ensemble of two-level atoms and a single-species ensemble of three-level atoms. Our results establish phase control as a versatile tool for engineering dissipative phase transitions, with implications for quantum state preparation.