David R. M. Arvidsson-Shukur

We uncover features of generalized contextuality by connecting it to the Kirkwood-Dirac (KD) quasiprobability distribution. Quantum states can be represented by KD distributions, which take values in the complex unit disk. Only for “KD-positive” states are the KD distributions joint probability distributions. A KD distribution can be measured by a series of weak and projective measurements. We design such an experiment and show that it is contextual iff the underlying state is not KD positive. We analyze this connection with respect to mixed KD-positive states that cannot be decomposed as convex combinations of pure KD-positive states. Our result is the construction of a noncontextual experiment that enables an experimenter to verify contextuality.

Given two orthonormal bases ( | a i ⟩ ) i and ( | b j ⟩ ) j , one can associate to every quantum state a Kirkwood–Dirac (KD) quasiprobability distribution. KD distributions are like joint classical probabilities except that they can have negative or nonreal values, which are associated to nonclassical features of the state. In the last decade, KD distributions have proven to be versatile tools to investigate and construct quantum advantages and nonclassical phenomena. KD distributions are also used to determine quantum–classical boundaries, for example in the theory of (non)contextuality. Optimal use of the KD distributions relies on useful witnesses of KD nonpositivity. Previous works have established such a witness based on the observation that KD-nonpositive pure states have large support uncertainty with respect to the bases ( | a i ⟩ ) i and ( | b j ⟩ ) j . Here, we extend this witness to mixed states. We introduce two convex roof constructions: the convex roof of the support uncertainty and the convex roof of the KD nonpositivity. These constructions both witness the set of quantum states that cannot be written as a convex combination of KD-positive pure states. Moreover, the first one extends to mixed states the relation between two phenomena: large support uncertainty and the fact that the state belongs to the convex hull of the KD-positive pure states. The convex roof of the KD nonpositivity together with the KD nonpositivity itself give a necessary and sufficient condition for a state to be KD positive but not to belong to the convex hull of the KD-positive pure states.

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 states can reduce certain Bayesian risks of the final estimate. Here, we derive a method to find the risk-minimizing input state for any risk. These states are represented by an eigenvector of a Toeplitz matrix with elements given by the Fourier coefficients of the loss function of interest. We show that, while the true optimal state does not have a closed form for a general loss function, it is well approximated by a state with a cosine form. When the cosine frequency is chosen appropriately, these states outperform the original QPEA and achieve the optimal theoretical quantum-advantage scaling for three common risks. Furthermore, we prove that the uniform input state is suboptimal for any reasonable loss function. Finally, we design methods to mitigate the impact of depolarizing noise on the performance of QPEA.

The Kirkwood–Dirac (KD) quasiprobability distribution can describe any quantum state with respect to the eigenbases of two observables A and B. KD distributions behave similarly to classical joint probability distributions but can assume negative and nonreal values. In recent years, KD distributions have proven instrumental in mapping out nonclassical phenomena and quantum advantages. These quantum features have been connected to nonpositive entries of KD distributions. Consequently, it is important to understand the geometry of the KD-positive and -nonpositive states. Until now, there has been no thorough analysis of the KD positivity of mixed states. Here, we investigate the dependence of the full convex set of states with positive KD distributions on the eigenbases of A and B and on the dimension d of the Hilbert space. In particular, we identify three regimes where convex combinations of the eigenprojectors of A and B constitute the only KD-positive states: (i) any system in dimension 2; (ii) an open and dense probability one set of bases in dimension d = 3; and (iii) the discrete-Fourier-transform bases in prime dimension. Finally, we show that, if for example d = 2m, there exist, for suitable choices of A and B, mixed KD-positive states that cannot be written as convex combinations of pure KD-positive states. We further explicitly construct such states for a spin-1 system.

The goal of quantum metrology is to improve measurements’ sensitivities by harnessing quantum resources. Metrologists often aim to maximize the quantum Fisher information, which bounds the measurement setup’s sensitivity. In studies of fundamental limits on metrology, a paradigmatic setup features a qubit (spin-half system) subject to an unknown rotation. One obtains the maximal quantum Fisher information about the rotation if the spin begins in a state that maximizes the variance of the rotation-inducing operator. If the rotation axis is unknown, however, no optimal single-qubit sensor can be prepared. Inspired by simulations of closed timelike curves, we circumvent this limitation. We obtain the maximum quantum Fisher information about a rotation angle, regardless of the unknown rotation axis. To achieve this result, we initially entangle the probe qubit with an ancilla qubit. Then, we measure the pair in an entangled basis, obtaining more information about the rotation angle than any single-qubit sensor can achieve. We demonstrate this metrological advantage using a two-qubit superconducting quantum processor. Our measurement approach achieves a quantum advantage, outperforming every entanglement-free strategy.

In a recent paper [Das, Modak, and Bera, Phys. Rev. A 107, 042413 (2023)], Das et al. claim that Kirkwood-Dirac negativity is not required to achieve anomalous values of the quantum Fisher information encoded in postselected (filtered) particles. We argue that this claim is wrong. Further, we show that the quantum Fisher information in optimal postselected metrology is directly proportional to the total Kirkwood-Dirac nonclassicality.

Adaptive variational quantum eigensolvers (ADAPT-VQEs) are promising candidates for simulations of strongly correlated systems on near-term quantum hardware. To further improve the noise resilience of these algorithms, recent efforts have been directed towards compactifying, or layering, their Ansatz circuits. Here, we broaden the understanding of the algorithmic layering process in three ways. First, we investigate the noncommutation relations between the different elements that are used to build ADAPT-VQE Ansätze. In doing so, we develop a framework for studying and developing layering algorithms, which produce shallower circuits. Second, based on this framework, we develop a new subroutine that can reduce the number of quantum-processor calls by optimizing the selection procedure with which a variational quantum algorithm appends Ansatz elements. Third, we provide a thorough numerical investigation of the noise-resilience improvement available via layering the circuits of ADAPT-VQE algorithms. We find that layering leads to an improved noise resilience with respect to amplitude-damping and dephasing noise, which, in general, affect idling and nonidling qubits alike. With respect to depolarizing noise, which tends to affect only actively manipulated qubits, we observe no advantage of layering.