Related papers: Quantum State Detection Via Elimination
One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed…
Most measurements are designed to tell you which of several alternatives have occurred, but it is also possible to make measurements that eliminate possibilities and tell you an alternative that did not occur. Measurements of this type have…
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…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
Quantum information technologies provide promising applications in communication and computation, while machine learning has become a powerful technique for extracting meaningful structures in 'big data'. A crossover between quantum…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
In this paper, we mainly investigate the detection of quantum states containing fewer than $k$ unentangled particles in multipartite quantum systems. Based on calculations about operators, we derive two practical criteria for judging…
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 present a polynomial time exact quantum algorithm for the hidden subgroup problem in $Z_{m^k}^n$. The algorithm uses the quantum Fourier transform modulo m and does not require factorization of m. For smooth m, i.e., when the prime…
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…
The measurement of quantum states is one of the most important problems in quantum mechanics. We introduce a quantum state tomography technique in which the state of a qubit is reconstructed, while the qubit remains undetected. The key…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
Anomaly detection is used for identifying data that deviate from `normal' data patterns. Its usage on classical data finds diverse applications in many important areas like fraud detection, medical diagnoses, data cleaning and surveillance.…
It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly…
An algorithm is presented allowing the construction of fast Fourier transforms for any solvable group on a classical computer. The special structure of the recursion formula being the core of this algorithm makes it a good starting point to…
In quantum information and computation, the generation of entanglement through unitary gates remains a significant and active area of research. However, there are states termed as absolutely separable, from which entanglement cannot be…
Quantum computers can solve specific complex tasks for which no reasonable-time classical algorithm is known. Quantum computers do however also offer inherent security of data, as measurements destroy quantum states. Using shared entangled…
Quantum data hiding is the existence of pairs of bipartite quantum states that are (almost) perfectly distinguishable with global measurements, yet close to indistinguishable when only measurements implementable with local operations and…
We explore the sense in which the state of a physical system may or may not be regarded (an) observable in quantum mechanics. Simple and general arguments from various lines of approach are reviewed which demonstrate the following no-go…
We consider a protocol to perform the optimal quantum state discrimination of $N$ linearly independent non-orthogonal pure quantum states and present a computational code. Through the extension of the original Hilbert space, it is possible…