Measuring<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Tr</mml:mi><mml:msup><mml:mi>ρ</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:math>on Single Copies of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi></mml:math>Using Random Measurements

Enk, S. J. van; Beenakker, C. W. J.

doi:10.1103/physrevlett.108.110503

Cited by 158 publications

(130 citation statements)

References 17 publications

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“…Only a single instance of a quantum state is required in a third class of protocols [16,17,28,30], utilizing statistical correlations of randomized measurements, which we discuss in the remainder of this paper.…”

Section: State Preparationmentioning

confidence: 99%

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Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states

et al. 2019

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We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models. In particular, we discuss the theoretical details underlying the recent measurement of the second Rényi entropy of highly mixed quantum states consisting of up to 10 qubits in a trapped-ion quantum simulator [Brydges et al., Science 364, 260 (2019)]. We generalize the protocol to access the overlap of quantum states, prepared sequentially in one experiment. Furthermore, we discuss proposals for quantum state tomography based on randomized measurements within our framework and the respective scaling of statistical errors with system size.

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Section: State Preparationmentioning

confidence: 99%

“…The expression in the second line has first been given in Ref. [28]. If independent local random unitaries on individual qudits are used [case (ii)], the purity is estimated from…”

Section: A Second Rényi Entropy From Statistical Correlations Of Ranmentioning

confidence: 99%

Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states

et al. 2019

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“…These order parameters satisfy the following properties: (i) are quantized to 0 or log 2 depending on the phase being topologically trivial or not-trivial, and are thus able to detect the single entanglement bit -an ebit 1 One simple example is the equivalence between the entanglement spectra of the ground state of finite Ising and Kitaev chains. 2 random measurement methods [26].…”

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confidence: 99%

Entanglement topological invariants for one-dimensional topological superconductors

et al. 2020

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Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors. These order parameters quantitatively capture the entanglement that is possible to distill from the ground state manifold, and are thus quantized to 0 or log 2. Their quantization property is inferred from the underlying lattice gauge theory description of topological superconductors, and is corroborated via exact solutions and numerical simulations. Transitions between topologically trivial and non-trivial phases are accompanied by scaling behavior, a hallmark of genuine order parameters, captured by entanglement critical exponents. These order parameters are experimentally measurable utilizing state-of-the-art techniques. Panel b): quadripartite von Neumann entropy S D as a function of µ/t, U/t, at fixed ∆ = 1 and LA = LB = 12. Black lines as from Ref. [22]. The colour plot is obtained via interpolation on a 6 x 8 grid.-that can be distilled from the ground state manifold; (ii) display scaling behavior when approaching quantum phase transitions, and thus allow for the definition of entanglement critical exponents that describe the build-up of non-local quantum correlations across such transitions; (iii) are experimentally measurable in-and out-of-equilibrium utilizing recently introduced [14,15] and demonstrated [25] techniques based on arXiv:1909.04035v1 [cond-mat.supr-con]

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“…(2)(3)(4) of the main text can be seen by just considering the simple 2-qubit case. See the following figure, where the rectangles represent π pulses about x (or y) axis:…”

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confidence: 99%

Experimental Implementation of Efficient Quantum Pseudorandomness on a 12-Spin System

Luo

Xin

et al. 2019

Phys. Rev. Lett.

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Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing these objects in realistic physical systems can be a challenging task. In this work, we study quantum pseudorandomness generation on a 12-spin nuclear magnetic resonance system. The experimental process is based on the recently proposed design Hamiltonian approach, which has the merit of being significantly more efficient than previous protocols. By applying random refocusing sequences to the experimental system we create a design Hamiltonian the dynamics of which quickly forms unitary designs. We then use multiple-quantum techniques to measure spreading of quantum coherences over system's degrees of freedom, and so to probe the growth of quantum pseudorandomness. The measured multiple-quantum coherence spectra indicate that substantial quantum pseudorandomness have been achieved.

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MeasuringTrρnon Single Copies ofρUsing Random Measurements

Cited by 158 publications

References 17 publications

Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states

Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states

Entanglement topological invariants for one-dimensional topological superconductors

Experimental Implementation of Efficient Quantum Pseudorandomness on a 12-Spin System

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