Related papers: Characterization of quantum states based on creati…
Recent oracle separations [Kretschmer, TQC'21, Kretschmer et. al., STOC'23] have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if the polynomial hierarchy collapses. We…
We propose a quantum circuit composed of $cNOT$ gates and four single-qubit gates to generate a $W$ state of three qubits. This circuit was then enhanced by integrating two-qubit gates to create a $W$ state of four and five qubits. After a…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
Quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of…
We give a polynomial time algorithm that, given copies of an unknown quantum state $\vert\psi\rangle=U\vert 0^n\rangle$ that is prepared by an unknown constant depth circuit $U$ on a finite-dimensional lattice, learns a constant depth…
We present "Diagrams of States", a way to graphically represent and analyze how quantum information is elaborated during the execution of quantum circuits. This introductory tutorial illustrates the basics, providing useful examples of…
In quantum mechanics, a state is an element of a Hilbert space whose dimension exponentially grows with the increase of the number of particles (or qubits, in quantum computing). The vague question "is this huge Hilbert space really there?"…
The creation of complex entangled states, resources that enable quantum computation, can be achieved via simple 'probabilistic' operations which are individually likely to fail. However, typical proposals exploiting this idea carry a severe…
Probabilistically creating n perfect clones from m copies for one of N priori known quantum states with minimum failure probability is a long-standing problem. We provide a rigorous proof for the geometric approach to this probabilistic…
We present a necessary and sufficient product criterion for bipartite quantum states based on the rank of realignment matrix of density matrix. Then, this approach is generalized to multipartite systems. We first introduce the concept of…
Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic…
We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary…
Cluster states can be used to perform measurement-based quantum computation. The cluster state is a useful resource, because once it has been generated only local operations and measurements are needed to perform universal quantum…
The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can however be lifted when considering sets of quantum states. Here we introduce the concept of set…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
Entanglement is one of the pillars of quantum mechanics and quantum information processing, and as a result the quantumness of nonentangled states has typically been overlooked and unrecognized. We give a robust definition for the…
Cluster states for measurement-based quantum computing can be created with entangling operations of arbitrary low success probability. This will place a lower bound on the minimum lifetime of the qubits used in the implementation. Here, we…
We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number $m$ of electrons occupying a given number $n$ of spin…
Distinguishing different quantum states is a fundamental task having practical applications for information processing. Despite the efforts devoted so far, however, strategies for optimal discrimination are known only for specific examples.…
State preparation is a fundamental routine in quantum computation, for which many algorithms have been proposed. Among them, perhaps the simplest one is the Grover-Rudolph algorithm. In this paper, we analyse the performance of this…