Multiparameter squeezing for optimal quantum enhancements in sensor networks

Abstract

Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous-and discrete-variable settings and technological applications. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. The development of multiparameter quantum metrology is yet hindered by the intrinsic difficulty in finding saturable sensitivity bounds and feasible estimation strategies. Here, we derive the general operational concept of multiparameter squeezing, identifying metrologically useful states and optimal estimation strategies. When applied to spin-or continuousvariable systems, our results generalize widely-used spin-or quadrature-squeezing parameters. Multiparameter squeezing provides a practical and versatile concept that paves the way to the development of quantum-enhanced estimation of multiple phases, gradients, and fields, and for the efficient characterization of multimode quantum states in atomic and optical sensor networks.

Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox

“…Bob’s estimation of the phase is assisted by steering from Alice who picks different measurement settings X i as a function of the acting Hamiltonian H i and includes details of H i in her communication to Bob. Achieving high sensitivity for multiple generators is relevant for multiparameter quantum metrology 36 – 41 , but the identification of a single measurement observable that is suitable for all parameters 42 , 43 provides an additional complication that is not considered in our scenario.…”

Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields

“…Hence, the implementation of ample cavities would be necessary due to the electron's free propagation. These operations are usually implemented via ion traps [6][7][8][9] or optical devices 10,11 , and receive special attention in a variety of applications where the unbounded motion shall be guided in a particular way, e.g. particle accelerators.…”

“…To this aim, first note that the diagonal elements of h(t) satisfy dh 11 dt = dh 22 dt = h 21 − h 12 β(t) , but according to the initial condition h 11 = h 22 = 1 at t = 0 , allowing to write consistently, it follows that det(h(t)) = ( 1 2 dθ(t) dt ) 2 − h 21 θ(t) = 1 , therefore: substituting into (27) and rearranging terms, yields h 12 β(t) = h 21 − dh 11 dt . Even more, since θ(t) = h 12 it directly means dh 11 dt = 1 2…”

Quantum enhanced multiple-phase estimation with multi-mode N00N states

“…Various strategies have been thus proposed to enhance the sensitivity by optimizing either the probe states or the measurement scheme 14 – 22 . For example, quantum strategies exploiting various quantum probe states such as Greenberger–Horne–Zeilinger states 23 , single-photon Fock states 24 , squeezed states 12 , 25 – 28 , Holland-Bernett states 29 – 31 , and N 00 N states 14 , 32 , 33 have been extensively studied.…”