Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity 0.9946 without post selection. As an application, we achieve the highest tomographic efficiency in qubit state tomography to date. Our work offers an effective recipe for beating the precision limit of local measurements in quantum state tomography and metrology. In addition, our study opens an avenue for harvesting the power of collective measurements in quantum information processing and for exploring the intriguing physics behind this power.
We show that a special type of measurements, called symmetric informationally complete positive operator-valued measures (SIC POVMs), provide a stronger entanglement detection criterion than the computable cross-norm or realignment criterion based on local orthogonal observables. As an illustration, we demonstrate the enhanced entanglement detection power in simple systems of qubit and qutrit pairs. This observation highlights the significance of SIC POVMs for entanglement detection.
We introduce and study the entanglement breaking rank of an entanglement breaking channel. We show that the problem of computing the entanglement breaking rank of the channel \beginalign* \mathfrak Z(X) = \frac1d+1(X+\textTr(X)\mathbb I_d) \endalign* is equivalent to the existence problem of symmetric informationally-complete POVMs.
The entanglement detection via local measurements can be experimentally implemented. Based on mutually unbiased measurements and general symmetric informationally complete positive-operator-valued measures, we present separability criteria for bipartite quantum states, which, by theoretical analysis, are stronger than the related existing criteria via these measurements. Two detailed examples are supplemented to show the efficiency of the presented separability criteria.
We study general physical systems with a notion of sequential measurement that satisfies a few simple and intuitive conditions. We show that, apart from two exceptional cases, the systems satisfying these conditions are exactly the real, complex or quaternionic quantum systems. Moreover, only the complex quantum systems remain if systems must be allowed to be composed together in a locally tomographic manner. In other words, quantum theory is the unique locally tomographic theory allowing sequential measurement.
In three very recent papers, (an initial paper by Morishima and Futamase, and two subsequent papers by Morishima, Futamase, and Shimizu), it has been argued that the observed experimental anomaly in the anomalous magnetic moment of the muon might be explained using general relativity. It is my melancholy duty to report that these articles are fundamentally flawed in that they fail to correctly implement the Einstein equivalence principle of general relativity. Insofar as one accepts the underlying logic behind these calculations (and so rejects general relativity) the claimed effect due to the Earth's gravity will be swamped by the effect due to Sun (by a factor of fifteen), and by the effect due to the Galaxy (by a factor of two thousand). In contrast, insofar as one accepts general relativity, then the claimed effect will be suppressed by an extra factor of [(size of laboratory)/(radius of Earth)]^2. Either way, the claimed effect is not compatible with explaining the observed experimental anomaly in the anomalous magnetic moment of the muon.
Identifying the property of the world that enforces the Born rule is a longstanding problem in physics. We prove that in any physical theory that assigns probabilities to the outcomes of ideal measurements, the maximal set of probability assignments for each graph of exclusivity is the one that satisfies the Born rule. Therefore, the agreement between quantum theory and experiments follows from a one-to-one correspondence between the logical possibilities and the physical possibilities and, in particular, implies that the outcomes of quantum measurements are not constrained by any physical reason.
There is an ongoing search for intuitive postulates of quantum theory from which its Hilbert space structure can be derived. The main contribution of this paper is the introduction of two postulates inspired by categorical logical notions from effectus theory, a framework in some ways similar to generalised probabilistic theories, but eschewing the familiar notions of real numbers and probabilities, which allows the description of more general theories. The postulates state the existence of certain physical filters that associate to each effect the subspace where it holds true. We show that when considering an operational probabilistic setting these relatively weak postulates lead to a spectral theorem and a duality between pure states and effects: each effect can be written as a probabilistic combination of perfectly distinguishable sharp effects in a unique way. In such a weak theory it is therefore already possible to define thermodynamic quantities like entropy. For these results we don't need any assumptions on the existence of pure states, or of sufficiently many reversible dynamics or even the existence of an invariant state. We finish the reconstruction of quantum theory by requiring three additional postulates: continuous symmetry, preservation of purity, and observability of energy.
Permutational Quantum Computing (PQC) [\emphQuantum~Info.~Comput., \textbf10, 470--497, (2010)] is a natural quantum computational model conjectured to capture non-classical aspects of quantum computation. An argument backing this conjecture was the observation that there was no efficient classical algorithm for estimation of matrix elements of the $S_n$ irreducible representation matrices in the Young's orthogonal form, which correspond to transition amplitudes of a broad class of PQC circuits. This problem can be solved with a PQC machine in polynomial time, but no efficient classical algorithm for the problem was previously known. Here we give a classical algorithm that efficiently approximates the transition amplitudes up to polynomial additive precision and hence solves this problem. We further extend our discussion to show that transition amplitudes of a broader class of quantum circuits -- the Quantum Schur Sampling circuits -- can be also efficiently estimated classically.
Most works on adversarial examples for deep-learning based image classifiers use noise that, while small, covers the entire image. We explore the case where the noise is allowed to be visible but confined to a small, localized patch of the image, without covering any of the main object(s) in the image. We show that it is possible to generate localized adversarial noises that cover only 2% of the pixels in the image, none of them over the main object, and that are transferable across images and locations, and successfully fool a state-of-the-art Inception v3 model with very high success rates.