Emilio Bagan

Quantum Chernoff bound as a measure of distinguishability between density matrices: Application to qubit and Gaussian states

Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses given a large number of observations. Recently the combined work of Audenaert et al. Phys. Rev. Lett. 98, 160501 2007 and Nussbaum and Szkola e-print arXiv:quant-ph/0607216 has proved the quantum analog of this bound, which applies when the hypotheses correspond to two quantum states. Based on this quantum Chernoff bound, we define a physically meaningful distinguishability measure and its corresponding metric in the space of states; the latter is shown to coincide with the Wigner-Yanase metric. Along the same lines, we define a second, more easily implementable, distinguishability measure based on the error probability of discrimination when the same local measurement is performed on every copy. We study some general properties of these measures, including the probability distribution of density matrices, defined via the volume element induced by the metric. It is shown that the Bures and the local-measurement based metrics are always proportional. Finally, we illustrate their use in the paradigmatic cases of qubits and Gaussian infinite-dimensional states. DOI: 10.1103/PhysRevA.77.032311

Multiple-copy two-state discrimination with individual measurements

We address the problem of nonorthogonal two-state discrimination when multiple copies of the unknown state are available. We give the optimal strategy when only fixed individual measurements are allowed and show that its error probability saturates the collective slowerd bound asymptotically. We also give the optimal strategy when adaptivity of individual von Neumann measurements is allowed swhich requires classical communicationd and show that the corresponding error probability is exactly equal to the collective one for any number of copies. We show that this strategy can be regarded as Bayesian updating.

Quantum-limited metrology with product states

We study the performance of initial product states of n-body systems in generalized quantum metrology protocols that involve estimating an unknown coupling constant in a nonlinear k-body (kn) Hamiltonian. We obtain the theoretical lower bound on the uncertainty in the estimate of the parameter. For arbitrary initial states, the lower bound scales as 1/nk, and for initial product states, it scales as 1/nk−1/2. We show that the latter scaling can be achieved using simple, separable measurements. We analyze in detail the case of a quadratic Hamiltonian (k=2), implementable with Bose-Einstein condensates. We formulate a simple model, based on the evolution of angular-momentum coherent states, which explains the O(n−3/2) scaling for k=2; the model shows that the entanglement generated by the quadratic Hamiltonian does not play a role in the enhanced sensitivity scaling. We show that phase decoherence does not affect the O(n−3/2) sensitivity scaling for initial product states.

Phase variance of squeezed vacuum states

We consider the problem of estimating the phase of squeezed vacuum states within a Bayesian framework. We derive bounds on the average Holevo variance for an arbitrary number

Recycling of qubits

N

The quantum change point

of uncorrelated copies. We find that it scales with the mean photon number,

Coherence-path duality relations for N paths

n

Optimized probabilistic quantum processors: A unified geometric approach

, as dictated by the Heisenberg limit, i.e., as

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n^{-2}

kerning1

, only for