Related papers: Unambiguous discrimination among oracle operators
We address the problem of unambiguous discrimination among a given set of quantum operations. The necessary and sufficient condition for them to be unambiguously distinguishable is derived in the cases of single use and multiple uses…
The discrimination of quantum operations has long been an intriguing challenge, with theoretical research significantly advancing our understanding of the quantum features in discriminating quantum objects. This challenge is closely related…
Discrimination of unitary operations is fundamental in quantum computation and information. A lot of quantum algorithms including the well-known Deutsch-Jozsa algorithm, Simon's algorithm, and Grover's algorithm can essentially be regarded…
Distinguishability is a fundamental and operational task generally connected to information applications. In quantum information theory, from the postulates of quantum mechanics it often has an intrinsic limitation, which then dictates and…
We prove a new universal identity for umbral operators. This motivates the definition of a subclass satisfying a simplified identity, which we fully characterize. The results are illustrated with common examples of the theory of umbral…
Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary…
We examine how to distinguish between unitary operators, when the exact form of the possible operators is not known. Instead we are supplied with "programs" in the form of unitary transforms, which can be used as references for identifying…
We investigate a discrimination scheme between unitary processes. By introducing a margin for the probability of erroneous guess, this scheme interpolates the two standard discrimination schemes: minimum-error and unambiguous…
We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…
We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one…
The standard oracle operator corresponding to a function f is a unitary operator that computes this function coherently, i.e. it maintains superpositions. This operator acts on a bipartite system, where the subsystems are the input and…
A universal programmable discriminator can perform the discrimination between two unknown states, and the optimal solution can be approached via the discrimination between the two averages over the uniformly distributed unknown input pure…
We show that a unitary operation (quantum circuit) secretely chosen from a finite set of unitary operations can be determined with certainty by sequentially applying only a finite amount of runs of the unknown circuit. No entanglement or…
When are two algorithms the same? How can we be sure a recently proposed algorithm is novel, and not a minor variation on an existing method? In this paper, we present a framework for reasoning about equivalence between a broad class of…
The classification of separable operator spaces and systems is commonly believed to be intractable. We analyze this belief from the point of view of Borel complexity theory. On one hand we confirm that the classification problems for…
We reformulate the notion of uncertainty of pairs of unitary operators within the context of guessing games and derive an entropic uncertainty relation for a pair of such operators. We show how distinguishable operators are compatible while…
The paper studies unambiguous discrimination of Fermionic states through local operations and classical communication (LOCC). In the task of unambiguous discrimination, no error is tolerated but an inconclusive result is allowed. We show…
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…
State discrimination with the aim to minimize the error probability is a well studied problem. Instead, here the binary decision problem for operators with a given prior is investigated. A black box containing the unknown operator is probed…
Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple…