Bright squeezed vacuum (BSV) has emerged as a macroscopic nonclassical light source capable of driving strong-field processes. Yet its broad, long-tailed photon-number distribution bears little resemblance to the narrow poissonian distribution of a coherent field, obscuring how the corresponding strong-field responses are connected. We show that field-quadrature space supplies the missing continuous description: coherent, squeezed coherent, and BSV states are Gaussian wave packets distinguished only by their centers and widths. This representation provides a unified framework for tracing the coherent-to-BSV transition at fixed mean photon number and for analyzing both ionization yields and photoelectron spectra. Crucially, BSV is a symmetry-protected endpoint in quadrature space. Near the BSV limit, we identify a simple scaling law of the ionization response associated with a residual coherent component. We show that this scaling arises from parity-induced stationarity with respect to the Gaussian center, together with the accompanying width variation near the BSV limit. The result provides a symmetry-based criterion for approaching the BSV regime and a potential probe of a mode-matched coherent displacement through the strong-field response itself.
Abstract Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. A challenge to this is the fact that different functional causal models can induce the same conditional probability distribution over observed variables while encoding different amounts of causal influence. Motivated by this observation, we study the underlying functional mechanisms, including uncertainty over them, as meaningful objects in their own right and develop a resource-theoretic framework for quantifying causal influence and knowledge of causal influence. We focus on the simplest nontrivial setting--- two variables that are causally ordered, meaning that the first has the potential to influence the second, without hidden confounding. First, we introduce the resource theory that directly quantifies causal influence of a functional dependence in this setting and show that the problem of deciding convertibility of resources and identifying a complete set of monotones has a relatively straightforward solution. Following this, we introduce the resource theory that arises naturally when one has uncertainty about the functional dependence. We describe a linear program for deciding the question of whether one resource (i.e., state of knowledge about the functional dependence) can be converted to another. Then, we focus on the case where the variables are binary. In this case, we identify a triple of monotones that are complete in the sense that they capture the partial order over the set of all resources, and we provide an interpretation of each.
Abstract Quantum batteries have been proposed as locally precharged work sources for superconducting quantum technologies, suggesting a route to reduce continuously supplied microwave drives. Here we ask what a finite bosonic pump must provide to replace the pump tone of a nondegenerate parametric amplifier during a readout window. Quantizing the pump exposes a resource distinction hidden in the classical description: stored energy and the ordinary marginal signal response can survive pump phase twirling, whereas a reproducible phase-locked signal-idler field requires pump coherences in the number sectors coupled by the mixing process. In a closed trilinear model, a coherent pump and its number-matched phase-twirled counterpart generate the same number-like marginal observables, but only the coherent pump produces anomalous two-mode coherence and an EPR-squeezed interference dip. Including leakage, we collect the emitted fields into cascaded temporal modes. At matched collector bandwidth, the coherent pump gives the interference certifier \(I_{\min}^{(f)}=0.553\), whereas the phase-randomized control gives \(I_{\min}^{(f)}\simeq1.94\). A weak seeded-signal analysis shows more sharply that an exact pump phase twirl leaves the collected signal marginal invariant by phase covariance while eliminating the anomalous signal-idler coherence. A finite-cutoff scan also indicates that weak amplitude squeezing can modestly deepen the phase-sensitive dip by reducing pump-number fluctuations while preserving most of the coherent displacement. Thus, for the three-wave-mixing pump families studied here, adjacent-number pump coherence is the resource that establishes a phase-locked joint amplifier field, rather than a prerequisite for energy transfer or ordinary marginal signal response.
We present an analytical framework for the emergence of nonclassical radiation in strongly laser-driven quantum systems, with a focus on high-order harmonic generation (HHG). Starting from a Pauli–Fierz description, we employ a parametric factorization of the coupled light–matter wavefunction that reduces the dynamics to coupled equations for a field-driven electronic state and a quantized light mode. Within this framework, we identify a simple and predictive mechanism for nonclassicality: it originates from the nonlinear dependence of the electronic dipole response on the light-mode coordinate. An approximately constant dipole yields coherent radiation, a linear dependence produces squeezing, and higher-order nonlinearities give rise to Wigner-function negativity. We illustrate this mechanism for atomic and molecular model systems and analyze its scaling in multi-emitter configurations, indicating routes toward high-photon-number nonclassical radiation in HHG. Our results provide a transparent connection between strong-field dynamics and quantum-optical properties of emitted light, offering a basis for engineering nonclassical states in intense laser–matter interactions.
This work introduces a method for quantifying errors in quantum computations using multiple echoes of a target circuit. Our approach addresses a gap in the range of available benchmarking methods: unlike existing approaches that evaluate the average performance of a device, circuit, or gate, our method estimates the error in a target computation using the same initial state and circuit as the computation itself. It therefore captures how noise manifests in the specific computation of interest. We present two variants of the approach. The first estimates incoherent errors through purity loss, while the second estimates the echo infidelity, which captures both incoherent errors and non-invertible coherent errors, such as crosstalk. The purity-loss method applies to low-error circuits, or layers of gates, regardless of system size. The echo-infidelity method applies to circuits of arbitrary size and remains effective even at high error rates. Because our approach does not rely on an explicit noise model, it can complement methods that provide more detailed error information by testing the validity of the sparsity assumptions underlying those models. Finally, we discuss platforms on which our method can be implemented immediately.
