Error-Disturbance Trade-off in Sequential Quantum Measurements

Abstract

We derive a state-dependent error-disturbance trade-off based on a statistical distance in the sequential measurements of a pair of noncommutative observables and experimentally verify the relation with a photonic qubit system. We anticipate that this Letter may further stimulate the study on the quantum uncertainty principle and related applications in quantum measurements.

Quantum Disturbance without State Change: Defense of State-Dependent Error-Disturbance Relations

“…Both accounts ensure that universally valid EDRs [9,[15][16][17] reliably represent a dynamical aspect of Heisenberg's uncertainty principle besides the well-established relation for the indeterminacy in quantum states representing a kinetic aspect of the principle. Thus, the objections to state-dependent formulations of EDRs are unfounded, although those views appear to still prevail in the literature [38,39]. We conclude that the theory [9][10][11][15][16][17][18] and experiments [12-14, 19, 21] for state-dependent formulations of EDRs are reliable and that state-dependent formulations are inevitable to represent Heisenberg's original idea underlying the uncertainty principle.…”

The role of system–meter entanglement in controlling the resolution and decoherence of quantum measurements

“…We achieve this higher level of precision by defining a separate resolution for each pair of eigenstates, which is naturally related to the loss of coherence between these eigenstates. It might be worth noting that this approach is fundamentally different from all of the global measures for resolution and disturbance considered in the [8][9][10][11][12][13][14][15][16][17][18] mentioned in the introduction. It is therefore quite possible that the detailed description of resolution and decoherence given here is the essential key to a more fundamental understanding of the uncertainty trade-off in quantum measurements.…”

“…A widespread impression at the time was that textbook definitions of measurement uncertainties were inadequate. This impression was strengthened by the state-dependent analysis of measurement uncertainties introduced by Ozawa [8], resulting in yet another round of criticisms and controversy [9][10][11][12][13][14]. At the same time, measurement theories attained new relevance in the context of quantum information, where the focus shifted from uncertainties towards quantum state discrimination [15][16][17][18][19].…”

Experimental test of tight state-independent preparation uncertainty relations for qubits

“…A detailed experimental investigation of this issue can be found in [5]. New uncertainty measures and uncertainty relations for error and disturbance have been proposed [6,7], refined [8,9], and experimentally tested in neutronic [10][11][12][13][14][15] and photonic [16][17][18][19][20][21] systems: In Ozawa's operator-based approach [6], or operator formalism, the measurement process is described by an indirect measurement model, introduced in [22]. Here the object system is coupled to a probe system by a unitary operator acting on the composite object-probe system.…”

“…In general it is difficult to avoid state dependence in measurement uncertainties. However, there continues to be some debate as to the appropriate measure of measurement (in)accuracy and of disturbance [6][7][8]10,11,13,16,[18][19][20][21]23,[25][26][27][28][29][30].…”