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Register a new userThe best approximation of an objective state with a given set of quantum states
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Approximating a quantum state by the convex mixing of some given states has strong experimental significance and provides potential applications in quantum resource theory. Here we find a closed form of the minimal distance in the sense of l_2 norm between a given d-dimensional objective quantum state and the state convexly mixed by those restricted in any given (mixed-) state set. In particular, we present the minimal number of the states in the given set to achieve the optimal distance. The validity of our closed solution is further verified numerically by several randomly generated quantum states.
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The structural study of entanglement in multipartite systems is hindered by the lack of necessary and sufficient operational criteria able to discriminate among the various entanglement properties of a given mixed state. Here, we pursue a different route to the study of multipartite entanglement based on the closeness of a multipartite state to the set of separable ones. In particular, we analyze multipartite diagonal symmetric N qubit states and provide the analytical expression for their Best Separable Approximation (BSA [Phys. Rev. Lett. 80, 2261 (1998)]), that is, their unique convex decomposition into a separable part and an entangled one with maximal weight of the separable one.
In Variational Quantum Simulations, the construction of a suitable parametric quantum circuit is subject to two counteracting effects. The number of parameters should be small for the device noise to be manageable, but also large enough for the circuit to be able to represent the solution. Dimensional expressivity analysis can optimize a candidate circuit considering both aspects. In this article, we will first discuss an inductive construction for such candidate circuits. Furthermore, it is sometimes necessary to choose a circuit with fewer parameters than necessary to represent all relevant states. To characterize such circuits, we estimate the best-approximation error using Voronoi diagrams. Moreover, we discuss a hybrid quantum-classical algorithm to estimate the worst-case best-approximation error, its complexity, and its scaling in state space dimensionality. This allows us to identify some obstacles for variational quantum simulations with local optimizers and underparametrized circuits, and we discuss possible remedies.
Precisely characterizing and controlling realistic open quantum systems is one of the most challenging and exciting frontiers in quantum sciences and technologies. In this Letter, we present methods of approximately computing reachable sets for coherently controlled dissipative systems, which is very useful for assessing control performances. We apply this to a two-qubit nuclear magnetic resonance spin system and implement some tasks of quantum control in open systems at a near optimal performance in view of purity: e.g., increasing polarization and preparing pseudo-pure states. Our work shows interesting and promising applications of environment-assisted quantum dynamics.
It is shown that the nature of quantum states that emerge from decoherence is such that one can {em measure} the expectation value of any observable of the system in a single measurement. This can be done even when such pointer states are a priori unknown. The possibility of measuring the expectation value of any observable, without any prior knowledge of the state, points to the objective existence of such states.
We study efficient quantum certification algorithms for quantum state set and unitary quantum channel. We present an algorithm that uses $O(varepsilon^{-4}ln |mathcal{P}|)$ copies of an unknown state to distinguish whether the unknown state is contained in or $varepsilon$-far from a finite set $mathcal{P}$ of known states with respect to the trace distance. This algorithm is more sample-efficient in some settings. Previous study showed that one can distinguish whether an unknown unitary $U$ is equal to or $varepsilon$-far from a known or unknown unitary $V$ in fixed dimension with $O(varepsilon^{-2})$ uses of the unitary, in which the Choi state is used and thus an ancilla system is needed. We give an algorithm that distinguishes the two cases with $O(varepsilon^{-1})$ uses of the unitary, using much fewer or no ancilla compared with previous results.
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