Master equations govern the time evolution of a quantum system interacting with an environment, and may be written in variety forms. Time-independent or memoryless master equations, particular, can cast well-known Lindblad form. Any time-local equation, Markovian non-Markovian, fact also Lindblad-like A diagonalization procedure results unique, this sense canonical, representation which used to fully characterize non-Markovianity evolution. Recently, several different measures have been...

The derivation of Bell inequalities requires an assumption measurement independence, related to the amount free will experimenters have in choosing settings. Violation these by singlet state correlations brings this into question. A simple measure degree independence is defined for correlation models, and it shown that all spin a can be modeled via giving up just 14% independence. underlying model deterministic no signaling. It may thus favorably compared with other models state, which...

Various measures have been suggested recently for quantifying the coherence of a quantum state with respect to given basis. We first use two these, ${l}_{1}$-norm and relative entropy measures, investigate tradeoffs between coherences mutually unbiased bases. Results include relations coherence, uncertainty, purity; tight general bounds restricting bases; an exact complementarity relation qubit coherences. further define average state. For measure this is related natural ``coherence radius''...

The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must individually or jointly relaxed in any model necessary degrees relaxation are quantified here, via natural distance information-theoretic measures. This allows quantitative comparisons between different models terms the resources, number bits, randomness, communication, and/or...

We introduce information-theoretic definitions for noise and disturbance in quantum measurements prove a state-independent noise-disturbance tradeoff relation that these quantities have to satisfy any conceivable setup. Contrary previous approaches, the we define are invariant under relabelling of outcomes allow possibility using or classical operations "correct" disturbance. also show how our bound implies strong relations mean square deviations.

The question of which two-qubit states are steerable (i.e.permit a demonstration EPR-steering) remains open.Here, strong necessary condition is obtained for the steerability having maximally-mixed reduced states, via construction local hidden state models.It conjectured that this in fact sufficient.Two provably sufficient conditions also obtained, asymmetric EPR-steering inequalities.Our work uses ideas from quantum steering ellipsoid formalism, and explicitly evaluates integral n/(n An) 2...

We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is huge, but finite, number classical 'worlds', and effects arise solely from universal interaction between these worlds, without reference to any wave function. Here `world' means an entire universe with well-defined properties, determined by configuration its particles fields. In our approach each world evolves deterministically; probabilities due ignorance given observer...

It is shown that a unique measure of volume associated with any statistical ensemble, which directly quantifies the inherent spread or localization ensemble. applicable whether ensemble classical quantum, continuous discrete, and may be derived from small number theory-independent geometric postulates. Remarkably, this proportional to exponential entropy, hence provides an interesting characterization latter quantity. Applications include unified volume-based derivations results in quantum...

The principle of complementarity is quantified in two ways: by a universal uncertainty relation valid for arbitrary joint estimates any observables from given measurement setup and general the optimal same when state system prior to known. A formula estimate observable, based on data information about system, which generalizes provides more robust interpretation previous formulas ``local expectations'' ``weak values'' quantum observables. As an example, canonical position $X$ momentum $P$...

Various protocols exist by which a referee can be convinced that two observers share an entangled resource. Such typically specify the types of communication allowed, and degrees trust required, between each observer. Here it is shown need for any degree completely removed via using classical quantum channels appropriately. In particular, trust-free verification Bell nonlocality, Einstein-Podolsky-Rosen steering, entanglement, respectively, requires channels, one channel, channels. These...

Complementarity restricts the accuracy with which incompatible quantum observables can be jointly measured. Despite popular conception, Heisenberg uncertainty relation does not quantify this principle. We report experimental verification of universally valid complementarity relations, including an improved derived here. exploit Einstein-Poldolsky-Rosen correlations between two photonic qubits to measure one. The product our measurement inaccuracies is low enough violate widely used, but...

Bell non-locality between distant quantum systems—that is, joint correlations which violate a inequality—can be verified without trusting the measurement devices used, nor those performing measurements. This leads to unconditionally secure protocols for information tasks such as cryptographic key distribution. However, complete verification of requires high detection efficiencies, and is not robust typical transmission losses over long distances. In contrast, or Einstein–Podolsky–Rosen...

With the advent of quantum information, violation a Bell inequality is used to witness absence an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. One assumptions Bell's theorem existence experimental "free will," meaning that measurement settings can be chosen at random independently by each party. The relaxation this assumption potentially shifts balance power towards eavesdropper. We consider no-signaling model with reduced will" bound adversary’s...

We propose quantum versions of the Bell-Ziv-Zakai lower bounds for error in multiparameter estimation. As an application, we consider measurement a time-varying optical phase signal with stationary Gaussian prior statistics and power-law spectrum ∼1/|ω|p, p>1. With no other assumptions, show that mean-square has bound scaling as 1/N2(p−1)/(p+1), where N is time-averaged mean photon flux. Moreover, this achievable by sampling interpolation, any This thus rigorous generalization Heisenberg...

Two very similar proposals have been made recently for witnessing nonclassical features of gravity, by Bose et al. and Marletto Vedral. However, while these are asserted to be general, they in fact based on a strong claim: that quantum systems cannot become entangled via classical intermediary. We point out the support provided this claim is only applicable limited class quantum-classical interaction models, corresponding Koopman-type dynamics. show also valid mean-field but it contradicted...

The authors demonstrate that, under mild measurement assumptions, two qubits cannot both be recycled to generate Bell nonlocality between multiple independent observers on each side. also derive corresponding ``one-sided monogamy relations'' that rule out two-sided recycling for a wide range of parameters and propose possible experimental test.

The Fisher information of a quantum observable is shown to be proportional both (i) the difference and classical variance, thus providing measure nonclassicality; (ii) rate entropy increase under Gaussian diffusion, robustness. joint nonclassicality position momentum observables complementary their robustness in an exact sense.

For any master equation which is local in time, whether Markovian, non-Markovian, of Lindblad form or not, a general procedure given for constructing the corresponding linear map from initial state to at time t, including its Kraus-type representations. Formally, this equivalent solving equation. an N-dimensional Hilbert space it requires (i) first order N 2×N 2 matrix evolution (to obtain completely positive map), and (ii) diagonalizing related representation). Conversely, time-dependent...

The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as $1/\ensuremath{\langle}N\ensuremath{\rangle}$, where $\ensuremath{\langle}N\ensuremath{\rangle}$ is mean number of photons in probe. However, this has loopholes which potentially might be exploited to achieve measurements with even greater accuracy. Here we close these by proving completely rigorous form for average error over all shifts, applicable any estimate unknown shift. Our result gives...

The quantum steering ellipsoid can be used to visualize 2-qubit states, and thus provides a generalization of the Bloch picture for single qubit. Recently, monogamy relation volumes ellipsoids has been derived pure 3-qubit states shown stronger than celebrated Coffman-Kundu-Wootters inequality. We first demonstrate close connection between this volume classification under stochastic local operations classical communication. then show that does not hold general mixed derive weaker such...

There is currently much interest in the recycling of entangled systems, for use quantum information protocols by sequential observers. In this work, we study generation Bell nonlocality via one or both components two-qubit states. We first give a description two-valued qubit measurements terms measurement bias, strength, and reversibility, derive useful tradeoff relations between them. Then, one-sided monogamy unbiased observables that strengthen recent conjecture Cheng et al. [Phys. Rev. A...

This paper is primarily concerned with the development and application of quantum bounds on mutual information, although some methods developed can be applied to any figure merit indicating degree correlation, such as coincidence rate. Three basic techniques for obtaining are described: mappings between joint-measurement communication correlation contexts; a duality relation ensembles measurements; an information exclusion principle [M. J. W. Hall, Phys. Rev. Lett. 74, 3307 (1995)]. Results...

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of strength which determined by and scales inversely with in position, leads from equations motion Schrödinger equation.