Related papers: Optimal estimation of SU(d) using exact and approx…
We consider the Unambiguous State Discrimination (USD) of two mixed quantum states. We study the rank and the spectrum of the elements of an optimal USD measurement. This naturally leads to a partial fourth reduction theorem. This theorem…
There have been some major advances in the theory of optimal designs for interference models. However, the majority of them focus on one-dimensional layout of the block and the study for two-dimensional interference model is quite limited…
We present optimal measuring strategies for the estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general…
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…
Approximate circuit design has gained significance in recent years targeting error tolerant applications. In this paper, we first demonstrate that the commonly used assumption that the inputs to the adder are uniformly distributed results…
When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the…
We study discrimination of m quantum measurements in the scenario when the unknown measurement with n outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple…
Using a specially constructed set of hard 2-SAT problems with four satisfying assignments, we study the scaling and sampling performance of numerical simulation of quantum annealing as well as that of the physical quantum annealers offered…
We study the minimum mean-squared error for 2-means clustering when the outcomes of the vector-valued random variable to be clustered are on two touching spheres of unit radius in $n$-dimensional Euclidean space and the underlying…
We consider the problem of designing experiments for the estimation of a target in regression analysis if there is uncertainty about the parametric form of the regression function. A new optimality criterion is proposed, which minimizes the…
A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be…
Using quantum systems as sensors or probes has been shown to greatly improve the precision of parameter estimation by exploiting unique quantum features such as entanglement. A major task in quantum sensing is to design the optimal…
Measurement based quantum computation requires the generation of a cluster state (quantum resource) prior to starting a computation. Generation of this entangled state can be difficult with many schemes already proposed. We present an…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications…
We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…
Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…
One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with…
The ability to uniquely identify a quantum state is integral to quantum science, but for non-orthogonal states, quantum mechanics precludes deterministic, error-free discrimination. However, using the non-deterministic protocol of…
We introduce the concept of selective quantum state tomography or SQST, a tomographic scheme that enables a user to estimate arbitrary elements of an unknown quantum state using a fixed measurement record. We demonstrate how this may be…