Quantum parameter estimation on coherently superposed noisy channels

Abstract

A generic qubit unitary operator affected by quantum noise is duplicated and inserted in a coherently superposed channel, superposing two paths offered to a probe qubit across the noisy unitary, and driven by a control qubit. A characterization is performed of the transformation realized by the superposed channel on the joint state of the probe-control qubit pair. The superposed channel is then specifically analyzed for the fundamental metrological task of phase estimation on the noisy unitary, with the performance assessed by the Fisher information, classical or quantum. A comparison is made with conventional estimation techniques and also with a quantum switched channel with indefinite causal order recently investigated for a similar task of phase estimation. In the analysis here, a first important observation is that the control qubit of the superposed channel, although it never directly interacts with the unitary being estimated, can nevertheless be measured alone for effective estimation, while discarding the probe qubit that interacts with the unitary. This property is also present with the switched channel but is inaccessible with conventional techniques. The optimal measurement of the control qubit here is characterized in general conditions. A second important observation is that the noise plays an essential role in coupling the control qubit to the unitary, and that the control qubit remains operative for phase estimation at very strong noise, even with a fully depolarizing noise, whereas conventional estimation and the switched channel become inoperative in these conditions. The results extend the analysis of the capabilities of coherently controlled channels which represent novel devices exploitable for quantum signal and information processing.

Indefinite causal order for quantum metrology with quantum thermal noise

“…Such a constructive role of the thermal noise here, which may benefit to the efficiency of the control qubit for estimation, was similarly observed with the depolarizing noise in the coherently superposed channels of [17,39]. Such a constructive role of noise can be related to a phenomenon of stochastic resonance, a general effect taking place in diverse information processing operations, classical [40,41,42,43] or quantum [44,45,46,47,48], and where maximum efficacy is observed at a non-vanishing optimal amount of noise.…”

Quantum Switch as a Thermodynamic Resource in the Context of Passive States

“…It implements the controlled superposition of orders in which two (or more) unitaries (or, more generally, quantum channels) are applied to a target system. Among other aspects, it has been shown that with the help of QS one can gain computational advantages [2,[6][7][8], communication advantages [9][10][11] or even the super Heisenberg limit in metrology [12][13][14][15][16]. For example, it has been predicted [10] that completely depolarizing quantum channels (which have zero capacity, i.e., they do not transmit any information), if superposed with the help of the QS, can be used for information transmition.…”

“…We note that in this case the Weyl commutation relation between position and momentum unitary displacement operators is crucial; therefore, it is not just a bare resourcefulness of the quantum switch playing the role. The topic of metrology using indefinite causal order has further been investigated in a comprehensive way [13,15,21,22].…”

Breaking the limits of purification: postselection enhances heat-bath algorithmic cooling

“…ICO has been demonstrated in a number of groundbreaking experiments [49][50][51][52][53][54][55][56][57], many of which rely on a device known as a quantum switch to enable superpositions of the order in which unitary operations are applied to a system. Perhaps even more importantly, ICO provides a new approach to thinking about old problems and can inspire simpler solutions with definite causal order that take advantage of coherent superpositions of operations to achieve the same goals [58][59][60]. This is a powerful new tool that is only beginning to be understood so, while it is remarkable to find yet another important application for coherent superpositions of unitaries, it would not be surprising to discover that coherent-superposition protocols have many more varied applications that we are only beginning to fathom.…”