Related papers: Proper Versus Improper Mixtures: Towards a Quatern…
We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a…
Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from,…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
Contrary to previous claims, it is shown that, for an ensemble of either single-particle systems or multi-particle systems, the realistic interpretation of a superposition state that mathematically describes the ensemble does not imply that…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
We describe a technique for self consistently characterizing both the quantum state of a single qubit system, and the positive-operator-valued measure (POVM) that describes measurements on the system. The method works with only ten…
The development of quantum information theory has renewed interest in the idea that the state vector does not represent the state of a quantum system, but rather the knowledge or information that we may have on the system. I argue that this…
A fundamental task in quantum information science is to measure nonlinear functionals of quantum states, such as $\mathrm{Tr}(\rho^k O)$. Intuitively, one expects that computing a $k$-th order quantity generally requires $O(k)$ copies of…
Projective measurement is a commonly used assumption in quantum mechanics. However, advances in quantum measurement techniques allow for partial measurements, which accurately estimate state information while keeping the wavefunction…
We consider highly inaccurate measurements made on classical stochastic and quantum systems. In the quantum case such a \e{weak} measurement preserves coherence between the system's alternatives. We demonstrate that in both cases the…
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets.…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
The persistence of sub-Planck structure in phase space with loss of coherence is demonstrated in a mixed state, which comprises two terms in the density matrix. Its utility in carrying out Heisenberg-limited measurement and quantum…
It is argued that recent claims by A. Hobson that standard quantum theory has no measurement problem cannot be sustained. Moreover, it is pointed out that taking the reduced density operator of a component system as an epistemic…
Quantum mechanics, devoid of any additional assumption, does not give any theoretical constraint on the projection basis to be used for the measurement process. It is shown in this paper that it does neither allow any physical means for an…
The probability operator is derived from first principles for an equilibrium quantum system. It is also shown that the superposition states collapse into a mixture of states giving the conventional von Neumann trace form for the quantum…
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient…
We define a quantum entropy conditioned on post-selection which has the von Neumann entropy of pure states as a special case. This conditional entropy can take negative values which is consistent with part of a quantum system containing…
Decoherence is the phenomenon of non-unitary dynamics that arises as a consequence of coupling between a system and its environment. It has important harmful implications for quantum information processing, and various solutions to the…
The convex set of quantum states of a composite $K \times K$ system with positive partial transpose is analysed. A version of the hit and run algorithm is used to generate a sequence of random points covering this set uniformly and an…