Related papers: Extending Hudson's theorem to mixed quantum states
Gaussian states are widely regarded as one of the most relevant classes of continuous-variable (CV) quantum states, as they naturally arise in physical systems and play a key role in quantum technologies. This motivates a fundamental…
We provide a scheme for efficient simulation of a broad class of quantum optics experiments. Our efficient simulation extends the continuous variable Gottesman-Knill theorem to a large class of non-Gaussian mixed states, thereby identifying…
We discuss the case of a Markovian master equation for an open system, as it is frequently found from environmental decoherence. We prove two theorems for the evolution of the quantum state. The first one states that for a generic initial…
Quantum non-Gaussianity is a key resource for quantum advantage in continuous-variable systems. We introduce a general framework to quantify non-Gaussianity based on correlation generation: two copies of a state become correlated at a…
Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are…
We address the joint estimation of changes in the position and linear momentum of a quantum particle or, equivalently, changes in the complex field of a bosonic mode. Although these changes are generated by non-commuting operators, we show…
Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to…
Non-Gaussianity, a distinctive characteristic of bosonic quantum states, is pivotal in advancing quantum networks, fault-tolerant quantum computing, and high-precision metrology. Verifying the quantum nature of a state, particularly its…
Number state filtering in coherent states leads to sub-Poissonian photon statistics. These states are more suitable for phase estimation when compared with the coherent states. Nonclassicality of these states is quantified in terms of the…
Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position…
We address detection of quantum non-Gaussian states, i.e. nonclassical states that cannot be expressed as a convex mixture of Gaussian states, and present a method to derive a new family of criteria based on generic linear functionals. We…
Generation of high fidelity photonic non-Gaussian states is a crucial ingredient for universal quantum computation using continous-variable platforms, yet it remains a challenge to do so efficiently. We present a general framework for a…
Quasiprobability has become an increasingly popular notion for characterising non-classicality in quantum information, thermodynamics, and metrology. Two important distributions with non-positive quasiprobability are the Wigner function and…
We develop a resource theory for continuous-variable systems grounded on operations routinely available within current quantum technologies. In particular, the set of free operations is convex and includes quadratic transformations and…
Randomness is a key feature of quantum physics. Heisenberg's uncertainty principle reveals the existence of an intrinsic noise, usually explored through Gaussian squeezed states. Due to their insufficiency for quantum advantage, the focus…
We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a…
Non-Gaussian quantum states, described by negative valued Wigner functions, are important both for fundamental tests of quantum physics and for emerging quantum information technologies. One of the promising ways of generation of the…
Non-Gaussian states are essential for achieving a quantum advantage in continuous-variable (CV) information processing. Among these, coherent superpositions of squeezed states are a foundational resource. While exact higher-order statistics…
We consider the Wigner function evolution of Fock states $|n\rangle$ linearly coupled to a Markovian bath of oscillators. In the absence of environmental coupling, apparent ``quantumness'' increases with $n$, but the presence of any…
Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed,…