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Register a new userCharacterizing correlation within multipartite quantum systems via local randomized measurements
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Given a quantum system on many qubits split into a few different parties, how much total correlations are there between these parties? Such a quantity -- aimed to measure the deviation of the global quantum state from an uncorrelated state with the same local statistics -- plays an important role in understanding multi-partite correlations within complex networks of quantum states. Yet, the experimental access of this quantity remains challenging as it tends to be non-linear, and hence often requires tomography which becomes quickly intractable as dimensions of relevant quantum systems scale. Here, we introduce a much more experimentally accessible quantifier of total correlations, which can be estimated using only single-qubit measurements. It requires far fewer measurements than state tomography, and obviates the need to coherently interfere multiple copies of a given state. Thus we provide a tool for proving multi-partite correlations that can be applied to near-term quantum devices.
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We provide a method of designing protocols for implementing multipartite quantum measurements when the parties are restricted to local operations and classical communication (LOCC). For each finite integer number of rounds, $r$, the method succeeds in every case for which an $r$-round protocol exists for the measurement under consideration, and failure of the method has the immediate implication that the measurement under consideration cannot be implemented by LOCC no matter how many rounds of communication are allowed, including when the number of rounds is allowed to be infinite. It turns out that this method shows---often with relative ease---the impossibility by LOCC for a number of examples, including cases where this was not previously known, as well as the example that first demonstrated what has famously become known as nonlocality without entanglement.
Local quantum uncertainty captures purely quantum correlations excluding their classical counterpart. This measure is quantum discord type, however with the advantage that there is no need to carry out the complicated optimization procedure over measurements. This measure is initially defined for bipartite quantum systems and a closed formula exists only for $2 otimes d$ systems. We extend the idea of local quantum uncertainty to multi-qubit systems and provide the similar closed formula to compute this measure. We explicitly calculate local quantum uncertainty for various quantum states of three and four qubits, like GHZ state, W state, Dicke state, Cluster state, Singlet state, and Chi state all mixed with white noise. We compute this measure for some other well known three qubit quantum states as well. We show that for all such symmetric states, it is sufficient to apply measurements on any single qubit to compute this measure, whereas in general one has to apply measurements on all parties as local quantum uncertainties for each bipartition can be different for an arbitrary quantum state.
We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in Lu et al. [X. M. Lu, S. Luo, and C. H. Oh, Phys Rev. A 86, 022342 (2012)], we show that the presence of quantum correlation can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord for pure quantum states.
We obtain a formal characterization of the compatibility or otherwise of a set of positive-operator-valued measures (POVMs) via their Naimark extensions. We show that a set of POVMs is jointly measurable if and only if there exists a single Naimark extension, specified by a fixed ancilla state on the same ancilla Hilbert space, that maps them to a set of commuting projective measurements (PVMs). We use our result to obtain an easily checkable sufficient condition for the compatibility of a pair of dichotomic observables in any dimension. This in turn leads to a characterization of the compatibility regions for some important classes of observables including a pair of unsharp qubit observables. Finally, we also outline as to how our result provides an alternate approach to quantifying the incompatibility of a general set of quantum measurements.
Entanglement is the key feature of many-body quantum systems, and the development of new tools to probe it in the laboratory is an outstanding challenge. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a new protocol for measuring entropy, based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts - both in the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, applicable to arbitrary quantum states of up to several tens of qubits.
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