1,721,004 research outputs found
State discrimination with postmeasurement information and incompatibility of quantum measurements
Full text linkWe discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later time. Two different scenarios then arise: either Bob is allowed to arrange his measurement setup after Alice has announced him the chosen ensemble, or he is forced to perform the measurement before Alice's announcement. In the latter case, he can only postprocess his measurement outcome when Alice's extra information becomes available. We compare the optimal guessing probabilities in the two scenarios, and we prove that they are the same if and only if there exist compatible (i.e., jointly measurable) optimal measurements for all of Alice's state ensembles. When this is the case, postprocessing any of the corresponding joint measurements is Bob's optimal strategy in the postmeasurement information scenario. Furthermore, we establish a connection between discrimination with postmeasurement information and the standard state discrimination. By means of this connection and exploiting the presence of symmetries, we are able to compute the various guessing probabilities in many concrete examples
Quantum Incompatibility Witnesses
Full text linkWe demonstrate that quantum incompatibility can always be detected by means of a state discrimination task with partial intermediate information. This is done by showing that only incompatible measurements allow for an efficient use of premeasurement information in order to improve the probability of guessing the correct state. Thus, the gap between the guessing probabilities with pre- and postmeasurement information is a witness of the incompatibility of a given collection of measurements. We prove that all linear incompatibility witnesses can be implemented as some state discrimination protocol according to this scheme. As an application, we characterize the joint measurability region of two noisy mutually unbiased bases
Learning sets with separating kernels
Full text linkWe consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of reproducing kernel, that we call separating kernel, plays a crucial role in our study and is analyzed in detail. We prove a new analytic characterization of the support of a distribution, that naturally leads to a family of regularized learning algorithms which are provably universally consistent and stable with respect to random sampling. Numerical experiments show that the proposed approach is competitive, and often better, than other state of the art techniques
Covariant mutually unbiased bases
Full text linkThe connection between maximal sets of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space and finite phase-space geometries is well known. In this article, we classify MUBs according to their degree of covariance with respect to the natural symmetries of a finite phase-space, which are the group of its affine symplectic transformations. We prove that there exist maximal sets of MUBs that are covariant with respect to the full group only in odd prime-power dimensional spaces, and in this case, their equivalence class is actually unique. Despite this limitation, we show that in dimension covariance can still be achieved by restricting to proper subgroups of the symplectic group, that constitute the finite analogues of the oscillator group. For these subgroups, we explicitly construct the unitary operators yielding the covariance
Unitary representations of super groups and Mackey theory
No full textWe outline some basic facts in the theory of unitary representations of super Lie groups along the lines of [C. Carmeli, G. Cassinelli, A. Toigo, and V.S. Varadarajan. "Unitary representations of super lie groups and applications to the classification and multiplet structure of super particles", Comm. Math. Phys. 263 (2006) 217-258]. We define the concept of representation induced from a special sub super group. We give a version of Mackey theory for groups containing a special normal abelian connected sub super group
Verifying the Quantumness of Bipartite Correlations
Full text linkEntanglement is at the heart of most quantum information tasks, and therefore considerable effort has been made to find methods of deciding the entanglement content of a given bipartite quantum state. Here, we prove a fundamental limitation to deciding if an unknown state is entangled or not: we show that any quantum measurement which can answer this question for an arbitrary state necessarily gives enough information to identify the state completely. We also extend our treatment to other classes of correlated states by considering the problem of deciding if a state has negative partial transpose, is discordant, or is fully classically correlated. Remarkably, only the question related to quantum discord can be answered without resorting to full state tomography
Why unsharp observables?
No full textWe discuss why projection valued measures are not sufficient in the description of position and momentum of a one dimensional particle. A satisfactory solution is offered using positive operator measures. We also argue why the relevant positive operator measures, but not all, may be called unsharp observables
Maximally incompatible quantum observables
Full text linkThe existence of maximally incompatible quantum observables in the sense of a minimal joint measurability region is investigated. Employing the universal quantum cloning device it is argued that only infinite dimensional quantum systems can accommodate maximal incompatibility. It is then shown that two of the most common pairs of complementary observables (position and momentum; number and phase) are maximally incompatible
On the coexistence of position and momentum observables
No full textWe investigate the problem of coexistence of position and momentum observables. We characterize those pairs of position and momentum observables which have a joint observable
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