Only with the simultaneous estimation of multiple parameters are the quantum aspects of metrology fully revealed. This is due to the incompatibility of observables. The fundamental bound for multiparameter quantum estimation is the Holevo Cramér-Rao bound (HCRB) whose evaluation has so far remained elusive. For finite-dimensional systems we recast its evaluation as a semidefinite program, with reduced size for rank-deficient states. We show that it also satisfies strong duality. We use this result to study phase and loss estimation in optical interferometry and three-dimensional magnetometry with noisy multiqubit systems. For the former, we show that, in some regimes, it is possible to attain the HCRB with the optimal (single-copy) measurement for phase estimation. For the latter, we show a nontrivial interplay between the HCRB and incompatibility and provide numerical evidence that projective single-copy measurements attain the HCRB in the noiseless 2-qubit case.
We implement an experiment on a photonic quantum processor establishing efficacy of the elementary quantum system in classical information storage. The advantage is established by considering a class of simple bipartite games played with the communication resource qubit and classical bit (c bit), respectively. Conventional wisdom, supported by the no-go theorems of Holevo and Frenkel-Weiner, suggests that such a quantum advantage is unattainable when the sender and receiver share randomness or classical correlations.
This paper discusses the foundation of security theory for the Quantum stream cipher based on the Holevo-Yuen theory, which allows the use of "optical amplifiers". This type of cipher is a technology that provides information-theoretic security (ITS) to optical data transmission by randomizing ultrafast optical communication signals with quantum noise. In general, the quantitative security of ITS is evaluated in terms of the unicity distance in Shannon theory.
Holevo introduced a fidelity between quantum states that is symmetric and as effective as the trace distance in evaluating their similarity. This fidelity is bounded by a function of the trace distance, a relationship to which we will refer as Holevo's inequality. More broadly, Holevo's fidelity is part of a one-parameter family of symmetric Petz-Rényi relative entropies, which in turn satisfy a Pinsker's-like inequality with respect to the trace distance.
Sensing a classical signal using a linear quantum device is a pervasive application of quantum-enhanced measurement. The fundamental precision limits of linear waveform estimation, however, are not fully understood. In certain cases, there is an unexplained gap between the known waveform-estimation quantum Cramér-Rao bound and the optimal sensitivity from quadrature measurement of the outgoing mode from the device.
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; and Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5.
We show that the second law of thermodynamics poses a restriction on how well we can discriminate between quantum states. By examining an ideal gas with a quantum internal degree of freedom undergoing a cycle based on a proposal by Peres, we establish a nontrivial upper bound on the attainable accuracy of quantum state discrimination. This thermodynamic bound, which relies solely on the linearity of quantum mechanics and the constraint of no work extraction, matches Holevo's bound on accessible information, but is looser than the Holevo-Helstrom bound.
