We develop a formalism to describe squeezed light with large spectral-temporal correlations. This description is valid in all regimes, but is especially applicable in the long pulse to continuous-wave limit where the photon density at any particular time is small, although the total number of photons can be quite large. Our method relies on the Whittaker-Shannon interpolation formula applied to the joint temporal amplitude of squeezed light, which allows us to ``deconstruct'' the squeezed state. This provides a local description of the state and its photon statistics, making the underlying physics more transparent than does the use of the Schmidt decomposition. The formalism can easily be extended to more exotic nonclassical states where a Schmidt decomposition is not possible.
We define the deconstruction cost of a tripartite quantum state on systems
ABE as the minimum rate of noise needed to apply to the
AE systems, such that there is negligible disturbance to the marginal state on the
BE systems, while the system
A of the resulting state is locally recoverable from the
E system alone. We refer to such actions as deconstruction operations and protocols implementing them as state deconstruction protocols. State deconstruction generalizes Landauer erasure of a single-party quantum state as well the erasure of correlations of a two-party quantum state. We find that the deconstruction cost of a tripartite quantum state on systems
ABE is equal to its conditional quantum mutual information (CQMI)
I(A;B∣E), thus giving the CQMI an operational interpretation in terms of a state deconstruction protocol. We also define a related task called conditional erasure, in which the goal is to apply noise to systems
AE in order to decouple system
A from systems
BE, while causing negligible disturbance to the marginal state of systems
BE. We find that the optimal rate of noise for conditional erasure is also equal to the CQMI
I(A;B∣E). State deconstruction and conditional erasure lead to operational interpretations of the quantum discord and squashed entanglement, which are quantum correlation measures based on the CQMI. We find that the quantum discord is equal to the cost of simulating einselection, the process by which a quantum system interacts with an environment, resulting in selective loss of information in the system. The squashed entanglement is equal to half the minimum rate of noise needed for deconstruction and/or conditional erasure if Alice has available the best possible system
E to help in the deconstruction and/or conditional erasure task.
A recent construction showed that iteratively gauging symmetries of a quantum field theory can generate an emergent extra spatial dimension. Here we identify the precise mechanism underlying this phenomenon: it is dimensional deconstruction, the procedure by which an extra dimension is encoded in the structure of a quiver gauge theory. We demonstrate this by showing that the standard deconstruction action, upon dualizing the Goldstone fields on the Higgs branch, is exactly equivalent to the action produced by iterative gauging. The dictionary is transparent: quiver nodes correspond to gauge fields, and quiver links correspond to the gauge fields introduced to couple to magnetic symmetries. We further show that starting by gauging the electric rather than the magnetic symmetry produces the deconstructed theory written in the dual variables, with all coupling constants inverted.