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Reducing the average resource consumption is the central quest in discriminating non-orthogonal quantum states for a fixed admissible error rate $\varepsilon$. The globally optimal fixed local projective measurement (GOFL) for this task is…
In this paper, we propose concurrence classes for an arbitrary multi-qubit state based on orthogonal complement of a positive operator valued measure, or POVM in short, on quantum phase. In particular, we construct concurrence for an…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we…
We present a general scheme to realize the POVMs for the unambiguous discrimination of quantum states. For any set of pure states it enables us to set up a feasible linear optical circuit to perform their optimal discrimination, if they are…
We present adaptive measurement techniques tailored for variational quantum algorithms on near-term small and noisy devices. In particular, we generalise earlier "learning to measure" strategies in two ways. First, by considering a class of…
We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. This structured discrimination problems allow for a novel scheme that provides a certified level of error, that is,…
We address the class of positive operator-valued measures (POVMs) for qubit systems that are obtained by coupling the signal qubit with a probe qubit and then performing a projective measurement on the sole probe system. These POVMs, which…
The gauge invariance of geometric phases for mixed states is analyzed by using the hidden local gauge symmetry which arises from the arbitrariness of the choice of the basis set defining the coordinates in the functional space. This…
We describe a technique for self consistently characterizing both the quantum state of a single qubit system, and the positive-operator-valued measure (POVM) that describes measurements on the system. The method works with only ten…
Qubit-efficient optimization studies how large combinatorial problems can be addressed with quantum circuits whose width is far smaller than the number of logical variables. In quadratic unconstrained binary optimization (QUBO), objective…
We present a theoretical study of minimum error probability discrimination, using quantum- optical probe states, of M optical phase shifts situated symmetrically on the unit circle. We assume ideal lossless conditions and full freedom for…
We present the first experimental demonstration of the maximum confidence measurement strategy for quantum state discrimination. Applying this strategy to an arbitrary set of states assigns to each input state a measurement outcome which,…
The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors,…
The optimal discrimination of non-orthogonal quantum states with minimum error probability is a fundamental task in quantum measurement theory as well as an important primitive in optical communication. In this work, we propose and…
We present graphical representation for genaralized quantum measurements (POVM). We represent POVM elements as Bloch vectors and find the conditions these vectors should satisfy in order to describe realizable physical measurements. We show…
Quantum fidelity is a measure to quantify the closeness of two quantum states. In an operational sense, it is defined as the minimal overlap between the probability distributions of measurement outcomes and the minimum is taken over all…
Identification of nonorthogonal quantum states without error is crucial for various applications in quantum information technology, as well as the foundations of quantum physics. Theoretical studies have proposed measurements that maximize…
The quantum-phase-estimation algorithm (QPEA) is widely used to find estimates of unknown phases. The original algorithm relied on an input state in a uniform superposition of all possible bit strings. However, it is known that other input…
We find optimality conditions for testers in discrimination of quantum channels. These conditions are obtained using semidefinite programming and are similar to optimality conditions for POVMs obtained by Holevo for ensembles of quantum…