Related papers: Unambiguous discrimination among oracle operators
We construct a single observable measurement of which mean value on four copies of an {\it unknown} two-qubit state is sufficient for unambiguous decision whether the state is separable or entangled. In other words, there exists a universal…
Given a unitary operator $U$ acting on a composite quantum system what is the entangling capacity of $U$? This question is investigated using a geometric approach. The entangling capacity, defined via metrics on the unitary groups, leads to…
A unital $C^*$-algebra is called $N$-subhomogeneous if its irreducible representations are finite dimensional with dimension at most $N$. We extend this notion to operator systems, replacing irreducible representations by boundary…
Grover search algorithm drives a quantum system from an initial state to a desired final state by using selective phase inversions of these two states. In (1), we studied a generalization of Grover algorithm which relaxes the assumption of…
To effectively utilize quantum incompatibility as a resource in quantum information processing, it is crucial to evaluate how incompatible a set of devices is. In this study, we propose an ordering to compare incompatibility and reveal its…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
Many statistical estimation procedures lead to nonconvex optimization problems. Algorithms to solve these are often guaranteed to output a stationary point of the optimization problem. Oracle inequalities are an important theoretical…
We study how the choices made when designing an oracle affect the complexity of quantum property testing problems defined relative to this oracle. We encode a regular graph of even degree as an invertible function $f$, and present $f$ in…
A long standing problem of Gian-Carlo Rota for associative algebras is the classification of all linear operators that can be defined on them. In the 1970s, there were only a few known operators, for example, the derivative operator, the…
Let $A$ be a unital operator algebra. Let us assume that every {\it bounded\/} unital homomorphism $u\colon \ A\to B(H)$ is similar to a {\it contractive\/} one. Let $\text{\rm Sim}(u) = \inf\{\|S\|\, \|S^{-1}\|\}$ where the infimum runs…
The problem behind this paper is, if the number of queries to unitary operations is fixed, say $k$, then when do local operations and classical communication (LOCC) suffice for optimally distinguishing bipartite unitary operations? We…
Emerging applications of sensor networks for detection sometimes suggest that classical problems ought be revisited under new assumptions. This is the case of binary hypothesis testing with independent - but not necessarily identically…
Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.
We discuss the problem of designing unambiguous programmable discriminators for any $n$ unknown quantum states in an $m$-dimensional Hilbert space. The discriminator is a fixed measurement which has two kinds of input registers: the program…
We show that quantum oracles provide an advantage over classical oracles for answering classical counterfactual questions in causal models, or equivalently, for identifying unknown causal parameters such as distributions over functional…
We study unitarily equivalent bilateral weighted shifts with operator weights. We establish a general characterization of unitary equivalence of such shifts under the assumption that the weights are quasi-invertible. We prove that under…
Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic…
A desirable property of interpretable models is small size, so that they are easily understandable by humans. This leads to the following challenges: (a) small sizes typically imply diminished accuracy, and (b) bespoke levers provided by…
It is well known that there are entire functions whose orbit approximates any other entire function under the action of a sequence of translation operators . This result also holds for an uncountable family of sequences of translation…
We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…