Abstract We prove sharp universal upper bounds on the number of linearly independent steady and asymptotic states of discrete- and continuous-time Markovian evolutions of open quantum systems. We ...show that the bounds depend only on the dimension of the system and not on the details of the dynamics. A comparison with similar bounds deriving from a recent spectral conjecture for Markovian evolutions is also provided.
Bounds on the ultimate precision attainable in the estimation of a parameter in Gaussian quantum metrology are obtained when the average number of bosonic probes is fixed. We identify the optimal ...input probe state among generic (mixed in general) Gaussian states with a fixed average number of probe photons for the estimation of a parameter contained in a generic multimode interferometric optical circuit, namely, a passive linear circuit preserving the total number of photons. The optimal Gaussian input state is essentially a single-mode squeezed vacuum, and the ultimate precision is achieved by a homodyne measurement on the single mode. We also reveal the best strategy for the estimation when we are given L identical target circuits and are allowed to apply passive linear controls in between with an arbitrary number of ancilla modes introduced.
We show that every finite-dimensional quantum system with Markovian (i.e. GKLS-generated) time evolution has an autonomous unitary dilation which can be dynamically decoupled. Since there is also ...always an autonomous unitary dilation which cannot be dynamically decoupled, this highlights the role of dilations in the control of quantum noise. We construct our dilation via a time-dependent version of Stinespring in combination with Howland’s clock Hamiltonian and certain point-localised states, which may be regarded as a C*-algebraic analogue of improper bra-ket position eigenstates and which are hence of independent mathematical and physical interest.
In the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant ...matrix ensembles for which a two-dimensional Coulomb gas analogy is available. We present a critical revision of the Coulomb gas method in random matrix theory (RMT) borrowing language and tools from large deviations theory. This allows us to formalize an equivalent, but more effective and quicker route toward RMT free energy calculations. Moreover, we argue that this more modern viewpoint is likely to shed further light on the interesting issues of weak phase transitions and evaporation phenomena recently observed in RMT.
The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: Indeed, the decay is ...initially quadratic, while at very large times it follows a power law, with superimposed oscillations. The latter regime is particularly elusive and difficult to observe. Here we employ arrays of single-mode optical waveguides, fabricated by femtosecond laser direct inscription, to implement quantum systems where a discrete state is coupled and can decay into a continuum. The optical modes correspond to distinct quantum states of the photon, and the temporal evolution of the quantum system is mapped into the spatial propagation coordinate. By injecting coherent light states in the fabricated photonic structures and by measuring a small scattered fraction of such light with an unprecedented dynamic range, we are able to experimentally observe not only the exponential decay regime, but also the quadratic Zeno region and the power-law decay at long evolution times.
We derive a universal nonperturbative bound on the distance between unitary evolutions generated by time-dependent Hamiltonians in terms of the difference of their integral actions. We apply our ...result to provide explicit error bounds for the rotating-wave approximation and generalize it beyond the qubit case. We discuss the error of the rotating-wave approximation over long time and in the presence of time-dependent amplitude modulation. We also show how our universal bound can be used to derive and to generalize other known theorems such as the strong-coupling limit, the adiabatic theorem, and product formulas, which are relevant to quantum-control strategies including the Zeno control and the dynamical decoupling. Finally, we prove generalized versions of the Trotter product formula, extending its validity beyond the standard scaling assumption.
We explore the features of an equally-spaced array of two-level quantum emitters, that can be either natural atoms (or molecules) or artificial atoms, coupled to a field with a single continuous ...degree of freedom (such as an electromagnetic mode propagating in a waveguide). We investigate the existence and characteristics of bound states, in which a single excitation is shared among the emitters and the field. We focus on bound states in the continuum, occurring in correspondence of excitation energies in which a single excited emitter would decay. We characterize such bound states for an arbitrary number of emitters, and obtain two main results, both ascribable to the presence of evanescent fields. First, the excitation profile of the emitter states is a sinusoidal wave. Second, we discuss the emergence of multimers, consisting in subsets of emitters separated by two lattice spacings in which the electromagnetic field is approximately vanishing.
Abstract
We consider the estimation of an arbitrary parameter
φ
, such as the temperature or a magnetic field, affecting in a distributed manner the components of an arbitrary linear optical passive ...network, such as an integrated chip. We demonstrate that Heisenberg scaling precision (i.e. of the order of 1/
N
, where
N
is the number of probe photons) can be achieved without any iterative adaptation of the interferometer hardware and by using only a simple, single, squeezed light source and well-established homodyne measurements techniques. Furthermore, no constraint on the possible values of the parameter is needed but only a preliminary shot-noise estimation (i.e. with a precision of
N
) easily achievable without any quantum resources. Indeed, such a classical knowledge of the parameter is enough to prepare a single, suitable optical stage either at the input or the output of the network to monitor with Heisenberg-limited precision any variation of the parameter to the order of
1
/
N
without the need to iteratively modify such a stage.
The free energy at zero temperature of Coulomb gas systems in generic dimension is considered as a function of a volume constraint. The transition between the 'pulled' and the 'pushed' phases is ...characterised as a third-order phase transition, in all dimensions and for a rather large class of isotropic potentials. This suggests that the critical behaviour of the free energy at the 'pulled-to-pushed' transition may be universal, i.e. to some extent independent of the dimension and the details of the pairwise interaction.
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