Related papers: A unique quasi-probability for projective yes-no m…
We define a simple rule that allows to describe sequences of projective measurements for a broad class of generalized probabilistic models. This class embraces quantum mechanics and classical probability theory, but, for example, also the…
Quantum information is a common topic of research in many areas of quantum physics, such as quantum communication and quantum computation, as well as quantum thermodynamics. It can be encoded in discrete or continuous variable systems, with…
We consider communication scenarios where one party sends quantum states of known dimensionality $D$, prepared with an untrusted apparatus, to another, distant party, who probes them with uncharacterized measurement devices. We prove that,…
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 introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. This quantity is properly defined only for states that possess a positive Wigner function, which we name…
We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared pulses. The state is represented through the Wigner function, a ``quasi-probability density'' on $\mathbb{R}^{2}$…
A quantitative extension of the Wigner-Araki-Yanase theorem is obtained on the limitation on precise, non-disturbing measurements of observables which do not commute with additive conserved quantities, and applied to obtaining a limitation…
We discuss the abstract structure of sequential weak measurement (WM) of general observables. In all orders, the sequential WM correlations without post-selection yield the corresponding correlations of the Wigner function, offering direct…
A unification of the set of quasiprobability representations using the mathematical theory of frames was recently developed for quantum systems with finite-dimensional Hilbert spaces, in which it was proven that such representations require…
Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…
We present a hitherto unknown fundamental limitation to a basic measurement: that of the position of a quantum object when the total momentum of the object and apparatus is conserved. This result extends the famous Wigner-Araki-Yanase (WAY)…
We show that a Kirkwood-Dirac type quasiprobability distribution is sufficient to reveal any arbitrary quantum resource. This is achieved by demonstrating that it is always possible to identify a set of incompatible measurements that…
For a projective measurement, the Born rule provides the probability for an outcome in terms of the inner product between a projector and a quantum state. If the projector represents a pure entangled state and the state for a composite…
In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…
Protective measurements yield properties of the quantum state of a single quantum system without affecting the quantum state. A protective measurement involves adiabatic coupling to the measuring device together with a procedure to protect…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
In every state of a quantum particle, Wigner's quasidistribution is the unique quasidistribution on the phase space with the correct marginal distributions for position, momentum, and all their linear combinations.
Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…
The task of state discrimination for a set of mutually orthogonal pure states is trivial if one has access to the corresponding sharp (projection-valued) measurement, but what if we are restricted to an unsharp measurement? Given that any…