Quantum fidelity measures for mixed states

Liang, Yeong-Cherng; Yeh, Yu-Hao; Mendonça, Paulo E. M. F.; Teh, R. Y.; Reid, M. D.; Drummond, P. D.

doi:10.1088/1361-6633/ab1ca4

Cited by 129 publications

(79 citation statements)

References 165 publications

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“…This is in agreement with the known metric properties of the trace distance (see, e.g., Ref. [47,48]); it also confirms some observations done for excited states of CFTs [49,50], as well as out of equilibrium [51].…”

Section: Trace Distance and Its Propertiessupporting

confidence: 92%

Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

et al. 2020

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We carry out a comprehensive comparison between the exact modular Hamiltonian and the lattice version of the Bisognano-Wichmann (BW) one in one-dimensional critical quantum spin chains. As a warm-up, we first illustrate how the trace distance provides a more informative mean of comparison between reduced density matrices when compared to any other Schatten nn-distance, normalized or not. In particular, as noticed in earlier works, it provides a way to bound other correlation functions in a precise manner, i.e., providing both lower and upper bounds. Additionally, we show that two close reduced density matrices, i.e. with zero trace distance for large sizes, can have very different modular Hamiltonians. This means that, in terms of describing how two states are close to each other, it is more informative to compare their reduced density matrices rather than the corresponding modular Hamiltonians. After setting this framework, we consider the ground states for infinite and periodic XX spin chain and critical Ising chain. We provide robust numerical evidence that the trace distance between the lattice BW reduced density matrix and the exact one goes to zero as \ell^{-2}ℓ−2 for large length of the interval \ellℓ. This provides strong constraints on the difference between the corresponding entanglement entropies and correlation functions. Our results indicate that discretized BW reduced density matrices reproduce exact entanglement entropies and correlation functions of local operators in the limit of large subsystem sizes. Finally, we show that the BW reduced density matrices fall short of reproducing the exact behavior of the logarithmic emptiness formation probability in the ground state of the XX spin chain.

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Section: Trace Distance and Its Propertiessupporting

confidence: 92%

Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

et al. 2020

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“…In practice, experimental state preparation is nontrivial. Conditional state preparation is often necessary when high fidelities are required [75]. Thus, there are quantum states where preparation on demand is far from easy, and this requires discussion, given the approach to reality described here.…”

Section: B Boundary Conditionsmentioning

confidence: 99%

Retrocausal model of reality for quantum fields

Drummond

Reid

2020

Phys. Rev. Research

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We show that one may interpret physical reality as random fields in space-time. These have a probability given by the expectation of a coherent state projection operator, called the Q-function. The resulting dynamical evolution includes retrocausal effects. This suggests that a physical universe exists without requiring observers, but with a well-defined probability for its field configuration. By including the meter dynamics, we show that field trajectories have quantum measurement properties without wave-function collapse, including sharp measured eigenvalues. We treat continuous and discrete measurements and show that this model predicts Bell inequality violations for measurements on correlated spins. A discussion is give of a number of well-known quantum paradoxes, showing how these can be treated in a realistic model of measurement. Our theory resolves a number of practical and philosophical issues in quantum measurement, and we compare it with earlier theories.

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“…As for the real-time true state ρ k which is in the free-evolution and evolves to the maximum mixed state gradually. The performance of the estimated stateρ k is evaluated by the fidelity based on Schatten's 2-norm, defined as [24]…”

Section: Numerical Simulation Experimentsmentioning

confidence: 99%

An online optimization algorithm for the real-time quantum state tomography

Zhang

Cong

et al. 2020

Quantum Inf Process

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Considering the presence of measurement noise in the continuous weak measurement process, the optimization problem of online quantum state tomography (QST) with corresponding constraints is formulated. Based on the online alternating direction multiplier method (OADM) and the continuous weak measurement (CWM), an online QST algorithm (QST-OADM) is designed and derived. Specifically, the online QST problem is divided into two subproblems about the quantum state and the measurement noise. The proposed algorithm adopts adaptive learning rate and reduces the computational complexity to O(d 3 ), which provides a more efficient mechanism for real-time quantum state tomography. Compared with most existing algorithms of online QST based on CWM which require time-consuming iterations in each estimation, the proposed QST-OADM can exactly solve two subproblems at each sampling. The merits of the proposed algorithm are demonstrated in the numerical experiments of online QST for 1, 2, 3, and 4-qubit systems.

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Quantum fidelity measures for mixed states

Cited by 129 publications

References 165 publications

Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

Retrocausal model of reality for quantum fields

An online optimization algorithm for the real-time quantum state tomography

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