We discuss a self-contained spin-boson model for a measurement-driven engine, in which a demon generates work from thermal excitations of a quantum spin via measurement and feedback control. Instead of granting it full direct access to the spin state and to Landauer's erasure strokes for optimal performance, we restrict this demon's action to pointer measurements, i.e. random or continuous interrogations of a damped mechanical oscillator that assumes macroscopically distinct positions depending on the spin state. The engine can reach simultaneously the power and efficiency benchmarks and operate in temperature regimes where quantum Otto engines would fail.
The exact conditions on valid pointer states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any pointer state with vanishing probability current density. This condition is found both for weak measurements of noncommuting observables and for $c$-number observables. In addition, the interaction between pointer and object must be sufficiently weak. There is no restriction on the purity of the pointer state. For example, a thermal pointer state is fully valid.
We study the emergence and dynamics of pointer states in the motion of a quantum test particle affected by collisional decoherence. These environmentally distinguished states are shown to be exponentially localized solitonic wave functions which evolve according to the classical equations of motion. We explain their formation using the orthogonal unraveling of the master equation, and we demonstrate that the statistical weights of the arising mixture are given by projections of the initial state onto the pointer basis.
We consider the interaction of a quantum system (spin-1/2) with a macroscopic quantum apparatus (harmonic oscillator) which in turn is coupled to a bath of harmonic oscillators. Exact solutions of the Markovian Master equation show that the reduced density matrix of the system-apparatus combine decoheres to a statistical mixture where up and down spins eventually correlate with pointer states of the apparatus. For the zero temperature bath these pointer states turn out to be coherent states of the harmonic oscillator for arbitrary initial states of the apparatus. For a high temperature bath po…
Weak measurements are a unique tool for accessing information about weakly interacting quantum systems with minimal back action. Joint weak measurements of single-particle operators with pointer states characterized by a two-dimensional Gaussian distribution can provide, in turn, key information about quantum correlations which can be of relevance for quantum information applications. Here we demonstrate that by employing two-dimensional pointer states endowed with orbital angular momentum (OAM), it is possible to extract weak values of the higher order moments of single-particle operators, an…
It is well-known that the pointer basis of a quantum system satisfies the condition to diagonalize the interaction Hamiltonian between the subsystems. We show that this condition can be translated into the form $δΛ=0,$ where $Λ$, so-called the action, is the time integrated interaction energy: it is found out naturally in the phase of state vectors due to diagonal interaction. The careful treatment of a two states system demonstrates that the states of the total system branch into the states with different values of the action. Mathematically the pointer states are selected out by the saddle p…
We use the classical correlation between a quantum system being measured and its measurement apparatus to analyze the amount of information being retrieved in a quantum measurement process. Accounting for decoherence of the apparatus, we show that these correlations may have a sudden transition from a decay regime to a constant level. This transition characterizes a non-asymptotic emergence of the pointer basis, while the system-apparatus can still be quantum correlated. We provide a formalization of the concept of emergence of a pointer basis in an apparatus subject to decoherence. This contr…
Observers restricted to the observation of pointer states of apparatus cannot conclusively demonstrate that the pointer of an apparatus A registers the state of a system of interest S without perturbing S. Observers cannot, therefore, conclusively demonstrate that the states of a system S are redundantly encoded by pointer states of multiple independent apparatus without destroying the redundancy of encoding. The redundancy of encoding required by quantum Darwinism must, therefore, be assumed from outside the quantum-mechanical formalism and without the possibility of experimental demonstratio…
We propose the notion of quantum coherence for superpositions over states which are not necessarily mutually orthogonal. This anticipatedly leads to a resource theory of non-orthogonal coherence. We characterize free states and free operations in this theory, and connect the latter with free operations in the resource theory of quantum coherence for orthogonal bases. We show that the concept of non-orthogonal coherence naturally furnishes us with a wave-particle duality in quantum double-slit experiments where the channels beyond the slits are leaky between them. Furthermore, we demonstrate ex…
Quantum coherence quantifies the amount of superposition in a quantum system, and is the reason and resource behind several phenomena and technologies. It depends on the natural basis in which the quantum state of the system is expressed, which in turn hinges on the physical set-up being analyzed and utilized. While quantum coherence has hitherto been conceptualized by employing different categories of complete bases, there do exist interesting physical situations, where the natural basis is an incomplete one, an example being an interferometric set-up with the observer controlling only a cert…
This paper is devoted to the study of behavior of open quantum systems consistently based on the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation which covers evolution in situations when decoherence can be distinguished. We focus on the quantum measurement operation which is determined by final stationary states of an open system - so called pointers. We find pointers by applying the FGKLS equation to asymptotically constant density matrix. In seeking pointers, we have been able to propose a perturbative scheme of calculation, if we take the interaction components with an environ…
It has been shown that a macroscopic system being in a high-temperature thermal coherent state can be, in principle, driven into a non-classical state by coupling to a microscopic system. Therefore, thermal coherent states do not truly represent the classical limit of quantum description. Here, we study the classical limit of quantum state of a more relevant macroscopic system, namely the pointer of a detector, after the phase-preserving linear amplification process. In particular, we examine to what extent it is possible to find the corresponding amplified state in a superposition state, by c…
We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. We consider two typical problems arising in studying decoherence of quantum systems consisting of few coupled spins: (i) determining the pointer states of the system, and (ii) determining the temporal decay of quantum oscillations. As our results demonstrate, for determining the pointer states, the Chebyshev-based scheme is at least a factor of 8 faster than existing algorithms based on the Suzuki-Trotter decomposition. For the problems of second type, th…
Both classical and quantum mechanics assume that physical laws are invariant under changes in the way that the world is labeled. This Principle of Decompositional Equivalence is formalized, and shown to forbid finite experimental demonstrations that given pointer states |p1> and |p2> refer to the same physical system S. It is then shown that any extra-theoretical assumption that given pointer states |p1> and |p2> with indistinguishable coefficients in a Schmidt basis for the universe refer to the same physical system S is stronger than the assumption of classicality. Standard interpretations o…
We present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak-value amplification. The shift in the state of a pointer, in both angular position and the conjugate orbital angular momentum bases, is used to estimate angular rotations. This is done by an amplification of both the real and imaginary parts of the weak-value of a polarization operator that has been coupled to the pointer, which is a spatial mode, via a spin-orbit coupling. Our experiment demonstrates the first realization of weak-value amplification in the azimuthal deg…
In a close form without referring the time-dependent Hamiltonian to the total system, a consistent approach for quantum measurement is proposed based on Zurek's triple model of quantum decoherence [W.Zurek, Phys. Rev. D 24, 1516 (1981)]. An exactly-solvable model based on the intracavity system is dealt with in details to demonstrate the central idea in our approach: by peeling off one collective variable of the measuring apparatus from its many degrees of freedom, as the pointer of the apparatus, the collective variable de-couples with the internal environment formed by the effective internal…
We investigate a weak measurement described by a von Neumann type interaction $\hat{A}\otimes \hat{p}^2$, where $\hat{A}$ is a system observable and $\hat{p}^2$ is a measurement pointer observable. We consider the weak measurement in terms of thermodynamics by adopting a mixed Gaussian state as a quantum state of the measurement pointer. We show that Maxwell's demon appears as a measure who carries out post-selections. It is found that, even if the demon only knows the weak value, a difference in the von Neumann entropy between the initial and final system can be the QC mutual information cont…
The notion of weak measurement in quantum mechanics has gained a significant and wide interest in realizing apparently counterintuitive quantum effects. In recent times, several theoretical and experimental works have been reported for demonstrating the joint weak value of two observables where the coupling strength is restricted to the second order. In this paper, we extend such a formulation by providing a complete treatment of joint weak measurement scenario for all-order-coupling for the observable satisfying $A^2=\mathbb{I}$ and $A^2=A$, which allows us to reveal several hitherto unexplor…
In a recent paper, Żukowski and Markiewicz showed that Wigner's Friend (and, by extension, Schrödinger's Cat) can be eliminated as physical possibilities on purely logical grounds. I validate this result and demonstrate the source of the contradiction in a simple experiment in which a scientist S attempts to measure the position of object $|O\rangle = |A\rangle_S + |B\rangle_S$ by using measuring device M chosen so that $|A\rangle_M \approx |A\rangle_S$ and $|B\rangle_M \approx |B\rangle_S$. I assume that the measurement occurs by quantum amplification without collapse, in which M can entangle…
Direct weak or strong measurement of quantum wave function has been demonstrated based on the post-selection; however, the efficiency of the measurement is greatly limited by the success probability of the post-selection. Here we propose a modified scheme to directly measure photon's wave function by simply inserting a liquid crystal plate after the coupling between the pointer and wave function. Our modified method can significantly increase the efficiency of the post selection. Numerical simulations demonstrate that our proposal can have a greater efficiency in higher resolution and higher f…
We study numerically the damping of quantum oscillations and the increase of entropy with time in model spin systems decohered by a spin bath. In some experimentally relevant cases, the oscillations of considerable amplitude can persist long after the entropy has saturated near its maximum, i.e. when the system has been decohered almost completely. Therefore, the pointer states of the system demonstrate non-trivial dynamics. The oscillations exhibit slow power-law decay, rather than exponential or Gaussian, and may be observable in experiments.
We propose how to engineer the longitudinal coupling to accelerate the measurement of a qubit longitudinally coupled to a cavity, motivated by the concept of shortcuts to adiabaticity. Different modulations are inversely designed from two methods of inverse engineering and counter-diabatic driving, for achieving larger values of the signal-to-noise ratio (SNR) at nanosecond scale. By comparison, we demonstrate that our protocols outperform the usual periodic modulations on the pointer state separation and SNR. Finally, we show a possible implementation considering state-of-the-art circuit quan…
We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when and how a set of consecutive weak measurements converges to a strong measurement. Second, we show that for a small set of consecutive weak measurements, long before their convergence, one can separate close states without causing their collapse. We thus demonstrate a tradeoff between the success probability and the bias of the original vector towards collapse…
The fact that not all quantum observables are jointly measurable is one of the major differences between quantum and classical theory. In the former, non-commuting observables can only be simultaneously measured with limited precision. We report on an experimental implementation of such a simultaneous measurement of two non-commuting observables based on the framework of weak von Neumann measurements. We use a photonic setup where the polarisation degree of freedom acts as the system and the two components of the transversal position correspond to the pointers of the measurement apparatuses. I…
Unlike classical systems, a measurement performed on a quantum system always alters its state. In this work, the impacts of two diagnostic schemes to determine the performance of quantum Otto heat engines are compared: In one scheme, the energy of the engine's working substance is measured after each stroke (repeated measurements), and in the other one, the energies after each stroke are recorded in one or two pointer states and measured only after the completion of a prescribed number of cycles (repeated contacts). A single pointer state suffices if one is only interested in either work or he…
We show that in wavepacket tunnelling localisation of the transmitted particle amounts to a quantum measurement of the delay it experiences in the barrier. With no external degree of freedom involved, the envelope of the wavepacket plays the role of the initial pointer state. Under tunnelling conditions such 'self measurement' is necessarily weak, and the Hartman effect just reflects the general tendency of weak values to diverge, as post-selection in the final state becomes improbable. We also demonstrate that it is a good precision, or 'not really weak' quantum measurement: no matter how wid…
Quantum measurement remains a puzzle through its stormy history from the birth of quantum mechanics to state-of-the-art quantum technologies. Two complementary measurement schemes have been widely investigated in a variety of quantum systems: von Neumann's projective 'strong' measurement and Aharonov's weak measurement. Here, we report the observation of a weak-to-strong measurement transition in a single trapped $40Ca^+$ ion system. The transition is realized by tuning the interaction strength between the ion's internal electronic state and its vibrational motion, which play the roles of the …
