TY - JOUR

T1 - Noisy frequency estimation with noisy probes

AU - Górecka, Agnieszka

AU - Pollock, Felix A.

AU - Liuzzo-Scorpo, Pietro

AU - Nichols, Rosanna

AU - Adesso, Gerardo

AU - Modi, Kavan

PY - 2018/8/1

Y1 - 2018/8/1

N2 - We consider frequency estimation in a noisy environment with noisy probes. This builds on previous studies, most of which assume that the initial probe state is pure, while the encoding process is noisy, or that the initial probe state is mixed, while the encoding process is noiseless. Our work is more representative of reality, where noise is unavoidable in both the initial state of the probe and the estimation process itself. We prepare the probe in a GHZ diagonal state, starting from n + 1 qubits in an arbitrary uncorrelated mixed state, and subject it to parameter encoding under dephasing noise. For this scheme, we derive a simple formula for the (quantum and classical) Fisher information, and show that quantum enhancements do not depend on the initial mixedness of the qubits. That is, we show that the so-called 'Zeno' scaling is attainable when the noise present in the encoding process is time inhomogeneous. This scaling does not depend on the mixedness of the initial probe state, and it is retained even for highly mixed states that can never be entangled. We then show that the sensitivity of the probe in our protocol is invariant under permutations of qubits, and monotonic in purity of the initial state of the probe. Finally, we discuss two limiting cases, where purity is either distributed evenly among the probes or concentrated in a single probe.

AB - We consider frequency estimation in a noisy environment with noisy probes. This builds on previous studies, most of which assume that the initial probe state is pure, while the encoding process is noisy, or that the initial probe state is mixed, while the encoding process is noiseless. Our work is more representative of reality, where noise is unavoidable in both the initial state of the probe and the estimation process itself. We prepare the probe in a GHZ diagonal state, starting from n + 1 qubits in an arbitrary uncorrelated mixed state, and subject it to parameter encoding under dephasing noise. For this scheme, we derive a simple formula for the (quantum and classical) Fisher information, and show that quantum enhancements do not depend on the initial mixedness of the qubits. That is, we show that the so-called 'Zeno' scaling is attainable when the noise present in the encoding process is time inhomogeneous. This scaling does not depend on the mixedness of the initial probe state, and it is retained even for highly mixed states that can never be entangled. We then show that the sensitivity of the probe in our protocol is invariant under permutations of qubits, and monotonic in purity of the initial state of the probe. Finally, we discuss two limiting cases, where purity is either distributed evenly among the probes or concentrated in a single probe.

KW - Frequency estimation

KW - Mixed states

KW - Open quantum systems

KW - Quantum metrology

UR - http://www.scopus.com/inward/record.url?scp=85053134664&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/aad4e5

DO - 10.1088/1367-2630/aad4e5

M3 - Article

AN - SCOPUS:85053134664

VL - 20

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 8

M1 - 083008

ER -