Slow decay of dynamical correlation functions for nonequilibrium quantum states

A property of dynamical correlation functions for nonequilibrium states is discussed. We consider arbitrary dimensional quantum spin systems with local interaction and translationally invariant states with nonvanishing current over them. A correlation function between local charge and local Hamiltonian at different spacetime points is shown to exhibit slow decay.Comment: typos correcte

Stability of quantum states of finite macroscopic systems against classical noises, perturbations from environments, and local measurements

We study the stability of quantum states of macroscopic systems of finite volume V, against weak classical noises (WCNs), weak perturbations from environments (WPEs), and local measurements (LMs). We say that a pure state is `fragile' if its decoherence rate is anomalously great, and `stable against LMs' if the result of a LM is not affected by another LM at a distant point. By making full use of the locality and huge degrees of freedom, we show the following: (i) If square fluctuation of every additive operator is O(V) or less for a pure state, then it is not fragile in any WCNs or WPEs. (ii) If square fluctuations of some additive operators are O(V^2) for a pure state, then it is fragile in some WCNs or WPEs. (iii) If a state (pure or mixed) has the `cluster property,' then it is stable against LMs, and vice versa. These results have many applications, among which we discuss the mechanism of symmetry breaking in finite systems.Comment: 6 pages, no figure.Proof of the theorem is described in the revised manuscrip

Strongly Incompatible Quantum Devices

The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement devices, and we call this relation compatibility. Two devices are incompatible if they cannot be implemented as parts of a single measurement setup. We introduce also a more stringent notion of incompatibility, strong incompatibility. Both incompatibility and strong incompatibility are rigorously characterized and their difference is demonstrated by examples.Comment: 27 pages (AMSart), 6 figure

Noise-Disturbance Relation and the Galois Connection of Quantum Measurements

The relation between noise and disturbance is investigated within the general framework of Galois connections. Within this framework, we introduce the notion of leak of information, mathematically defined as one of the two closure maps arising from the observable-channel compatibility relation. We provide a physical interpretation for it, and we give a comparison with the analogous closure maps associated with joint measurability and simulability for quantum observables

Witnessing incompatibility of quantum channels

We introduce the notion of incompatibility witness for quantum channels, defined as an affine functional that is non-negative on all pairs of compatible channels and strictly negative on some incompatible pair. This notion extends the recent definition of incompatibility witnesses for quantum measurements. We utilize the general framework of channels acting on arbitrary finite-dimensional von Neumann algebras, thus allowing us to investigate incompatibility witnesses on measurement-measurement, measurement-channel, and channel-channel pairs. We prove that any incompatibility witness can be implemented as a state discrimination task in which some intermediate classical information is obtained before completing the task. This implies that any incompatible pair of channels gives an advantage over compatible pairs in some such state discrimination task

Energies and collapse times of symmetric and symmetry-breaking states of finite systems with a U(1) symmetry

We study quantum systems of volume V, which will exhibit the breaking of a U(1) symmetry in the limit of V \to \infty, when V is large but finite. We estimate the energy difference between the `symmetric ground state' (SGS), which is the lowest-energy state that does not breaks the symmetry, and a `pure phase vacuum' (PPV), which approaches a symmetry-breaking vacuum as V \to \infty. Under some natural postulates on the energy of the SGS, it is shown that PPVs always have a higher energy than the SGS, and we derive a lower bound of the excess energy. We argue that the lower bound is O(V^0), which becomes much larger than the excitation energies of low-lying excited states for a large V. We also discuss the collapse time of PPVs for interacting many bosons. It is shown that the wave function collapses in a microscopic time scale, because PPVs are not energy eigenstates. We show, however, that for PPVs the expectation value of any observable, which is a finite polynomial of boson operators and their derivatives, does not collapse for a macroscopic time scale. In this sense, the collapse time of PPVs is macroscopically long.Comment: In the revised manuscript, Eq. (22), Ref. [8], and Notes [13], [15] and [17] have been adde