Related papers: A three state invariant
We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the…
We investigate the problem of optimally approximating a desired state by the convex mixing of a set of available states. The problem is recasted as finding the optimal state with the minimum distance from target state in a convex set of…
We consider a single copy of a mixed state of two qubits and show how its fidelity or maximal singlet fraction is related to the entanglement measures concurrence and negativity. We characterize the extreme points of the convex set of…
We present a review on the notion of pure states and mixtures as mathematical concepts that apply for both classical and quantum physical theories, as well as for any other theory depending on statistical description. Here, states will be…
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…
Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more…
In a system of n quantum particles, we define a measure of the degree of irreducible n-way correlation, by which we mean the correlation that cannot be accounted for by looking at the states of (n-1) particles. In the case of almost all…
The distinction between pure states and mixed states is a kernel ingredient of what is considered to be the standard formulation of quantum mechanics and plays today a kernel role in foundational debates about the meaning of quantum…
Entanglement is a purely quantum mechanical phenomenon and thus it has no classical analog. On the other hand, coherence is a well-known phenomenon in classical optics and in quantum mechanics. Recent research shows that quantum coherence…
We establish a sharp quantum advantage in determining the parity (even/odd) of an unknown permutation applied to any number $n \ge 3$ of particles. Classically, this is impossible with fewer than $n$ labels, being that the success is…
Various parameterizations for the orbits under local unitary transformations of three-qubit pure states are analyzed. The interconvertibility, symmetry properties, parameter ranges, calculability and behavior under measurement are looked…
In this paper we analyze the canonical forms into which any pure three-qubit state can be cast. The minimal forms, i.e. the ones with the minimal number of product states built from local bases, are also presented and lead to a complete…
It is shown that the fidelity, a basic notion of quantum information science, may be used to characterize quantum phase transitions, regardless of what type of internal order is present in quantum many-body states. If the fidelity of two…
We study quantum states for which the PPT criterion is both sufficient and necessary for separability. We present a class of 3x3 bipartite mixed states and show that these states are separable if and only if they are PPT.
Recent cosmological measurements tend to confirm that the fine structure constant {\alpha} is not immutable and has undergone a tiny variation since the Big Bang. Choosing adequate units, this could also reflect a variation of Planck's…
We show that pure states of multipartite quantum systems are multiseparable (i.e. give separable density matrices on tracing any party) if and only if they have a generalized Schmidt decomposition. Implications of this result for the…
An extension to computational mechanics complexity measure is proposed in order to tackle quantum states complexity quantification. The method is applicable to any $n-$partite state of qudits through some simple modifications. A Werner…
For pure symmetric 3-qubit states there are only three algebraically independent entanglement measures; one choice is the pairwise concurrence $\mathcal C$, the 3-tangle $\tau$, and the Kempe invariant $\kappa$. Using a canonical form for…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
We consider quantum enhanced measurements with initially mixed states. We show very generally that for any linear propagation of the initial state that depends smoothly on the parameter to be estimated, the sensitivity is bound by the…