In 1985 Deutsch designed a quantum algorithm which evaluates whether the two outputs of a Boolean function are the same or not using only one function evaluation [1]. Deutsch and Jozsa generalized this algorithm for a more general case such as whether a given Boolean function is constant or balanced. This algorithm demonstrated an exponential speed-up on a quantum machine compared to the best performance on classical machines [2]. The most important contribution in this field was achieved when Shor discovered a polynomial-time quantum algorithm for factoring and computing discrete logarithms — yielding an exponentially faster algorithm than the best known classical ones [3]. After this breakthrough many researchers started to find various applications, especially in cryptanalysis. On the other hand, Grover discovered the quantum (virtual) database search algorithm which yields a quadratic speed-up compared to classical database searches [4]. Since the database search algorithm is one of the most widely used algorithms in computer applications, the scientific impact is huge and many researchers have been interested in various applications of the quantum database search algorithm. The work presented here is concerned with a variation of the Grover search algorithm. Recently, several researchers have investigated a partial search where instead of seeking the exact location of a unique target solution, they are interested in finding which ‘target block’ the solution sits in [5, 6]. Indeed, because only a partial search is being performed an improvement in speed over the full search is expected. Indeed, recently proposed algorithms achieve meaningful performance improvements over full search [7]. Meanwhile, until now these works have considered only optimizing the performance at the expense of finding the target block with unit probability. One might hope that partial search could become an important component or subroutine of larger quantum algorithms if a sure success (unit probability) formulation could be found. The idea would be to perform the search on successively smaller block sizes with each partial search successively revealing more information about the location of the target. Indeed, in Ref. 6 the idea for a sure success partial search has been mentioned. In order to achieve this goal we utilized the scheme for partial search as described in Ref. 8 which reduces the problem to one essentially involving rotations in a three-dimensional Hilbert space. In this way we find that a simple modification, involving introducing additional phases in the final step, allows us to construct a sure success partial search algorithm. This paper is organized as follows. Firstly, we review an optimal version of the partial search algorithm, known as GRK algorithm [7]. Secondly, we propose a modification to the phases for the final step to guarantee sure success of the partial search algorithm. We derive a phase condition that must be satisfied for this modification to yield sure success and finally we show numerically that this condition may easily be solved. We conclude with a consideration of other problems that might be extensions suitable for further study.

In this article we outline a method for generating linear optics circuits that encode quantum-error-correcting codes. Using this method we produce a single-error-correcting code encoding one wave packet over five which can be implemented using linear optics and feed-forward correction. This code improves on the capacity of the best known code that can be implemented using linear optics and saturates the lower bound for the number of carriers needed for a single-error-correcting code. Our code can correct arbitrary single errors that occur randomly on each wave packet corresponding to a non-Gaussian error model, thus circumventing the so-called no-go theorem for Gaussian quantum-error correction.

Quantum error-correcting codes can protect multipartite quantum states from errors on some limited number of their subsystems (usually qubits). We construct a family of Bell inequalities which inherit this property from the underlying code and exhibit the violation of local realism, without any quantum information processing (except for the creation of an entangled state). This family shows no reduction in the size of the violation of local realism for arbitrary errors on a limited number of qubits. Our minimal construction requires preparing an 11-qubit entangled state.

Partial search has been proposed recently for finding the target block containing a target element with fewer queries than the full Grover search algorithm which can locate the target precisely. Since such partial searches will likely be used as subroutines for larger algorithms their success rate is important. We propose a partial search algorithm which achieves success with unit probability.

We quantify the resolution with which any probability distribution may be distinguished from a displaced copy of itself in terms of a characteristic width. This width, which we call the resolution, is well defined for any normalizable probability distribution. We use this concept to study the broadcasting of classical probability distributions. Ideal classical broadcasting creates two (or more) output random variables each of which has the same distribution as the input random variable. We show that the universal broadcasting of probability distributions may be achieved with arbitrarily high fidelities for any finite resolution. By restricting probability distributions to any finite resolution we have therefore shown that the classical limit of quantum broadcasting is consistent with the actual classical case.