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In the usual entanglement detection scenario the possible measurements and the corresponding data are assumed to be fully characterized. We consider the situation where the measurements are known, but the data is scrambled, meaning the…
The complexity of simulating quantum many-body dynamics, or quantum computations, in the Heisenberg picture is governed by the scrambling of initially simple operators into superpositions of exponentially many Pauli strings. The…
We present a new technique to reduce the expected number of measurements to declare an unknown quantum state as entangled. Our method is based on the geometric criterion and so requires only local Pauli measurements. Using concentration of…
We present a classical algorithm based on Pauli propagation for estimating expectation values of arbitrary observables on random unstructured quantum circuits across all circuit architectures and depths, including those with all-to-all…
Quantum illumination (QI) is an entanglement-based protocol for improving lidar/radar detection of unresolved targets beyond what a classical lidar/radar of the same average transmitted energy can do. Originally proposed by Lloyd as a…
Motivated by the limited qubit capacity of current quantum systems, we study the quantum sample complexity of $k$-qubit quantum operators, i.e., operations applicable on only $k$ out of $d$ qubits. The problem is studied according to the…
Quantum entanglement is an essential resource for quantum science and technology. However, entanglement detection and quantification, via typical entanglement measures such as linear entanglement entropy or negativity, can be a very…
Quantum nonlocality offers a secure way to produce random numbers: their unpredictability is intrinsic and can be certified just by observing the statistic of the measurement outcomes, without assumptions on how they are produced. To do…
We propose a resource-efficient shadow-tomography scheme using equatorial-stabilizer measurements generated from subsets of Clifford unitaries. For $n$-qubit systems, equatorial-stabilizer-based shadow-tomography schemes can estimate $M$…
We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system. First we consider sparse quantum circuits such that each qubit…
A general method for the study of the entanglement evolution of graph states under the action of Pauli was recently proposed in [Cavalcanti, et al., Phys. Rev. Lett. 103, 030502 (2009)]. This method is based on lower and upper bounds on the…
Using polarization-entangled photons from spontaneous parametric downconversion, we have implemented Ekert's quantum cryptography protocol. The near-perfect correlations of the photons allow the sharing of a secret key between two parties.…
Quantum learning encounters fundamental challenges when estimating non-linear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal…
Classical entanglement is a powerful tool which provides a neat numerical estimate for the study of classical correlations. Its experimental investigation, however, has been limited to special cases. Here, we demonstrate that the…
The one-shot success probability of a noisy classical channel for transmitting one classical bit is the optimal probability with which the bit can be sent via a single use of the channel. Prevedel et al. (PRL 106, 110505 (2011)) recently…
Entangled two-photon spectroscopy is expected to provide advantages compared with classical protocols. It is achieved by coherently controlling the spectral properties of energy-entangled photons. We present here an experimental setup that…
We introduce an approach for estimating the expectation values of arbitrary $n$-qubit matrices $M \in \mathbb{C}^{2^n\times 2^n}$ on a quantum computer. In contrast to conventional methods like the Pauli decomposition that utilize $4^n$…
Large weak values have been used to amplify the sensitivity of a linear response signal for detecting changes in a small parameter, which has also enabled a simple method for precise parameter estimation. However, producing a large weak…
We present a formal quantum mechanical analysis of the communication protocol of Prevedel {\it et al.}\ [Phys. Rev. Lett. \textbf{106}, 110505 (2011)], in which entanglement shared by sender and receiver is used to enhance, beyond that…
Bell sampling is a simple yet powerful tool based on measuring two copies of a quantum state in the Bell basis, and has found applications in a plethora of problems related to stabiliser states and measures of magic. However, it was not…