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arXiv:quant-ph/0303117

Accessible Information and Quantum operations

Qing-yu Cai

Published Mar 19, 2003• 3 citations
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Abstract

The accessible information decreases under quantum operations. We analyzed the connection between quantum operations and accessible information. We show that a general quantum process cannot be operated accurately. Futhermore, an unknown state of a closed quantum system can not be operated arbitrarily by a unitary quantum operation.
DOI
10.48550/arxiv.quant-ph/0303117

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The amount of extractable work from a physical system is fundamentally connected to the information available about its state, as illustrated by Maxwell's demon and the Gibbs paradox. In standard thermodynamic protocols involving system--bath interactions, the maximum work is given by the free-energy difference between the initial state and the corresponding Gibbs state at the bath temperature. This motivates a natural question: does information also limit work extraction in closed quantum systems that do not involve a heat bath and where work is obtained through unitary operations generated by a time-dependent Hamiltonian? While ergotropy quantifies the maximum work extractable via unitary operations, it assumes complete knowledge of the quantum state, typically requiring full state tomography. In realistic scenarios, however, only partial information is accessible. In this case, the relevant figure of merit is observational ergotropy, which depends explicitly on the measurement used to probe the system. We show that observational ergotropy decreases under classical post-processing of measurement outcomes, implying that fine-grained measurements allow greater work extraction than coarse-grained ones. Moreover, maximizing observational ergotropy over all possible measurements recovers standard ergotropy, which decomposes into incoherent (classical) and coherent (quantum) contributions. Our results demonstrate that coherence in the measurement projectors constitutes the key resource, enabling work extraction beyond the incoherent limit and establishing coherence as the origin of quantum advantage in observational ergotropy extraction.
We introduce a quantum measurement process that is capable of characterizing an unknown state of a system almost without disturbing or collapsing it. The underlying idea is to extract information of a system from the thermodynamic quantities like work(s) and heat in a process, thereby uncovering a fundamental correspondence between information and thermodynamics. We establish an improved notion of information isolation and show that a process is isolated if it respects the first law of quantum thermodynamics for a given set of conserved quantities or charges. The measurement process involves a global unitary evolution of the system, an apparatus, and a battery which supplies work(s). The global unitary respects the first law. The full information about the system is accessed by counting the charge-wise work costs to implement the reduced evolution on the system and the apparatus. After the work costs are determined, the process is undone where a state of the system is retrieved arbitrarily close to the original initial state. The measurement process is also capable of characterizing an unknown quantum operation. Fundamentally, our findings make an important step towards resolving the paradoxes arising from the quantum measurement problem, such as the Wigner's friend paradox, and the issue related to the objective reality of quantum states. We discuss the technological implications of the almost collapse-free measurement process.
Although the interpretation of the concept of information is not clear, even in the classical framework, new interpretive problems have arisen with the advent of the so-called quantum information, which combine the difficulties in understanding the concept of information with the well-known foundational puzzles derived from quantum mechanics itself. The aim of this paper is to consider some arguments traditionally put forward to support the idea that quantum information is qualitatively different from classical information. The final conclusion is that there are no reasons to admit the existence of quantum information as qualitatively different from classical information: there is only one kind of information, physically neutral, which can be encoded by means of classical or quantum states.
The accurate identification of faulty hardware is a fundamental requirement for reliable quantum information processing. We address this problem in a quantum setting, where a series of nnn devices is intended to apply the same unitary operation, but kkk malfunctioning devices among them apply a different, unknown unitary action. Under the assumption of complete ignorance regarding the specific unitary transformation applied, we model our hypotheses using representation-theoretic tools and study the zero-error protocol for identifying these faulty devices. We derive the optimal success probability for the single- and two-anomaly scenarios, demonstrating that it is independent of the total number of devices in the series. Furthermore, we present a simple protocol that makes use of ancillary systems that achieves this optimal limit. Notably, this protocol offers significant operational advantages, such as allowing us to test each device independently. Finally, we extend our analysis to the general scenario in which both the number of anomalies and the local dimension of the systems are arbitrary, evaluating our protocol's performance and conjecturing its global optimality in the general case.