Matrix Product States for Quantum Metrology

Jarzyna, Marcin; Demkowicz-Dobrzański, Rafał

doi:10.1103/physrevlett.110.240405

Cited by 41 publications

(37 citation statements)

References 44 publications

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“…In case channels L x are noisy, the QFI at the output for optimally entangled input probes generically scales linearly with k and the quantum enhancement amount to a constant factor improvement [38]. Moreover, as argued in [62,64] one can achieve almost optimal performance utilizing states where k probes are divided into groups of g particles where entanglement is present only among the particles belonging to the same group. In such a scenario, one can approximate the input state as a product state of large number of groups, number of which will tend to infinity while their size will remain constant when  ¥ k .…”

Section: Strong Estimation Regimementioning

confidence: 99%

Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective

2017

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We point out a contrasting role the entanglement plays in communication and estimation scenarios. In the first case it brings noticeable benefits at the measurement stage (output super-additivity), whereas in the latter it is the entanglement of the input probes that enables significant performance enhancement (input super-additivity). We identify a weak estimation regime where a strong connection between concepts crucial to the two fields is demonstrated; the accessible information and the Holevo quantity on one side and the quantum Fisher information related quantities on the other. This allows us to shed new light on the problem of super-additivity in communication using the concepts of quantum estimation theory. of merit used in estimation and communication approaches are usually different [14]. The central problem of quantum communication and estimation theories is to identify the potential benefits coming from exploiting entanglement in the input states as well as at the measurement stage of the protocols. Interestingly, unlike in the communication problem, there is a great number of examples demonstrating significant gains coming from the use of entangled input probes in quantum estimation protocols, with applications ranging from optical and atomic interferometry, via magnetometry to spectroscopy and atomic clocks stabilization [17][18][19][20][21][22][23]. At the same time, in a typical estimation protocol utilizing unentangled input probes collective measurements are typically irrelevant. Thus a contrasting picture emerges: when thinking of capacities of quantum channels gains in information processing arising from utilizing entanglement are at the measurement stage whereas it is the input stage where entanglement makes a difference in the estimation scenarios.The goal of this paper is to better understand the connections between the two fields from the point of view of the super-additivity issue, understood here as a general question of utility of entanglement in estimation/ communication protocols. We show that in the weak estimation regime, where the amount of information extractable on the parameter is very small compared to the prior information, i.e. the error of estimation is large compared with the variance of prior distribution, the accessible information as well as the Holevo quantity can be expressed using Fisher information (FI)-like concepts, which allows us to discuss utility of entanglement in communication using the properties of quantities well understood within the field of quantum estimation. We also point out that in a communication problem encoding a large number of independent parameters is favored even at the cost of their limited estimation precision, which makes the estimation strategy of learning a given parameter with highest possible accuracy not likely to be useful for the communication purposes. In order to make the paper self-contained we also recall some of the recent results on applications of rate-distortion theory in quantum estimation, which is another way of connecti...

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Section: Strong Estimation Regimementioning

confidence: 99%

Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective

2017

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“…We overcome the problem of mixed states by considering the combined state of the system and output. This is a pure quantum state-actually a matrix product state (MPS) [13,14,16,17]-which encodes the state of the system as well as the record of emissions for the whole observation time. This allows us to find the best estimation precision using the system-output state as a resource.…”

Section: Introductionmentioning

confidence: 99%

Dynamical phase transitions as a resource for quantum enhanced metrology

et al. 2016

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We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated. We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf. "Heisenberg scaling"). In fact, the QFI is identical to the variance of the dynamical observable that characterizes the phases that coexist at the transition, and enhanced scaling is a consequence of the divergence of the variance of this observable at the transition point. This identification makes it possible to establish the finite time scaling of the QFI. Near the transition the QFI is quadratic in time for times shorter than the correlation time of the dynamics. In the regime of enhanced scaling the optimal measurement whose precision is given by the QFI involves measuring both system and output. As a particular realization of these ideas, we describe a theoretical scheme for quantum enhanced estimation of an optical phase shift using the photons being emitted from a quantum system near the coexistence of dynamical phases with distinct photon emission rates.

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“…In such circumstance, for the asymptotic regime where a large number N of qubits are available, an efficient strategy, as also considered for instance in Ref. [36], would be to group the N qubits into independent blocks of N opt optimally entangled qubits. For such strategy with entanglement, the asymptotic regime of large N would be characterized, in terms of Fisher information, by an efficiency growing linearly with N, yet with a level strictly superior to the efficiency of the strategy using the optimal separable probe (which also grows linearly with N).…”

Section: Optimum At Partial Entanglementmentioning

confidence: 99%

Optimized entanglement for quantum parameter estimation from noisy qubits

Chapeau‐Blondeau

2018

Int. J. Quantum Inform.

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For parameter estimation from an N -component composite quantum system, it is known that a separable preparation leads to a mean-squared estimation error scaling as 1/N while an entangled preparation can in some conditions afford a smaller error with 1/N 2 scaling. This quantum superefficiency is however very fragile to noise or decoherence, and typically disappears with any small amount of random noise asymptotically at large N . To complement this asymptotic characterization, here we characterize how the estimation efficiency evolves as a function of the size N of the entangled system and its degree of entanglement. We address a generic situation of qubit phase estimation, also meaningful for frequency estimation. Decoherence is represented by the broad class of noises commuting with the phase rotation, which includes depolarizing, phase-flip, and thermal quantum noises. In these general conditions, explicit expressions are derived for the quantum Fisher information quantifying the ultimate achievable efficiency for estimation. We confront at any size N the efficiency of the optimal separable preparation to that of an entangled preparation with arbitrary degree of entanglement. We exhibit the 1/N 2 superefficiency with no noise, and prove its asymptotic disappearance at large N for any non-vanishing noise configuration. For maximizing the estimation efficiency, we characterize the existence of an optimum N opt of the size of the entangled system along with an optimal degree of entanglement. For nonunital noises, maximum efficiency is usually obtained at partial entanglement. Grouping the N qubits into independent blocks formed of N opt entangled qubits restores at large N a nonvanishing efficiency that can improve over that of N independent qubits optimally prepared. Also, one inactive qubit included in the entangled probe sometimes stands as the most efficient setting for estimation. The results further attest with new characterizations the subtlety of entanglement for quantum information in the presence of noise, showing that when entanglement is beneficial maximum efficiency is not necessarily obtained by maximum entanglement but instead by a controlled degree and finite optimal amount of it.

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Matrix Product States for Quantum Metrology

Cited by 41 publications

References 44 publications

Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective

Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective

Dynamical phase transitions as a resource for quantum enhanced metrology

Optimized entanglement for quantum parameter estimation from noisy qubits

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