We investigate the resources needed for secure teleportation of coherent states. We extend continuous variable teleportation to include quantum teleamplification protocols that allow nonunity classical gains and a preamplification or postattenuation of the coherent state. We show that, for arbitrary Gaussian protocols and a significant class of Gaussian resources, two-way steering is required to achieve a teleportation fidelity beyond the no-cloning threshold. This provides an operational connection between Gaussian steerability and secure teleportation. We present practical recipes suggesting that heralded noiseless preamplification may enable high-fidelity heralded teleportation, using minimally entangled yet steerable resources.

We consider two systems $A$ and $B$ that share Einstein–Podolsky–Rosen (EPR) steering correlations and study how these correlations will decay when each of the systems is independently coupled to a reservoir. EPR steering is a directional form of entanglement, and the measure of steering can change depending on whether system $A$ is steered by $B$, or vice versa. First, we examine the decay of the steering correlations of the two-mode squeezed state. We find that if system $B$ is coupled to a reservoir, then the decoherence of the steering of $A$ by $B$ is particularly marked, to the extent that there is a sudden death of steering after a finite time. We find a different directional effect if the reservoirs are thermally excited. Second, we study the decoherence of the steering of a Schrödinger cat state, modeled as the entangled state of a spin and harmonic oscillator, when the macroscopic system (the cat) is coupled to a reservoir.

We examine how to signify and quantify the mesoscopic quantum coherence of approximate two-mode NOON states and spin-squeezed two-mode Bose-Einstein condensates (BEC). We identify two criteria that verify a nonzero quantum coherence between states with quantum number different by $n$. These criteria negate certain mixtures of quantum states, thereby signifying a generalized $n$-scopic Schrödinger cat-type paradox. The first criterion is the correlation $\langle {\widehat{a}}^{†n}{\widehat{b}}^n\rangle \ne 0$ (here $\widehat{a}$ and $\widehat{b}$ are the boson operators for each mode). The correlation manifests as interference fringes in $n$-particle detection probabilities and is also measurable via quadrature phase amplitude and spin-squeezing measurements. Measurement of $\langle {\widehat{a}}^{†n}{\widehat{b}}^n\rangle$ enables a quantification of the overall $n\text{th}$ order quantum coherence, thus providing an avenue for high efficiency verification of high-fidelity photonic NOON states. The second criterion is based on a quantification of the measurable spin-squeezing parameter ${\xi }_N$. We apply the criteria to theoretical models of NOON states in lossy interferometers and double-well trapped BECs. By analyzing existing BEC experiments, we demonstrate generalized atomic “kitten” states and atomic quantum coherence with $n⪆10$ atoms.

Quantum simulations of Bell inequality violations are numerically obtained using probabilistic phase-space methods, namely, the positive-$P$ representation. In this approach the moments of quantum observables are evaluated as moments of variables that have values outside the normal eigenvalue range. There is thus a parallel with quantum weak measurements and weak values. Nevertheless, the representation is exactly equivalent to quantum mechanics. A number of states violating Bell inequalities are sampled, demonstrating that these quantum paradoxes can be treated with probabilistic methods. We treat quantum dynamics by simulating the time evolution of the Bell state formed via parametric down-conversion and discuss multimode generalizations.

We construct Einstein-Podolsky-Rosen (EPR) steering signatures for the nonlocality of the entangled superposition state described by $\frac{1}{\sqrt{2}}\left\{\right|N\rangle |0\rangle +|0\rangle |N\rangle \}$, called the two-mode NOON state. The signatures are a violation of an EPR steering inequality based on an uncertainty relation. The violation confirms an EPR steering between the two modes and involves certification of an intermode correlation for number, as well as quadrature phase amplitude measurements. We also explain how the signatures certify an $N\mathrm{th}$ order quantum coherence, so the system (for larger $N$) can be signified to be in a superposition of states distinct by a mesoscopic value of quantum number in each mode. Finally, we examine the limitations imposed for lossy scenarios, discussing how experimental realizations may be possible for $N=2,3$.

We show how one may test macroscopic local realism where, differently from conventional Bell tests, all relevant measurements that lead to a violation of a Bell inequality need only distinguish between two macroscopically distinct states of the system being measured. Here, measurements give macroscopically distinct outcomes for some property of the system and do not resolve microscopically (of order $\hslash$). To obtain a quantifiable test, we define $N$-scopic local realism where the outcomes are separated by an amount $\sim N$. We show for $N$ up to 20 that violations of $N$-scopic local realism are predicted for entangled systems of $N$ bosons at each of two sites. We further demonstrate for arbitrarily large $\alpha$ the violation of $\alpha$-scopic local realism, for entangled superpositions of coherent states with amplitudes $\sim \alpha$, infinitely separated in phase space, as $\alpha \to \infty$. To achieve the Bell violations, the two separated subsystems evolve dynamically according to a local nonlinear unitary interaction. The tests may be understood in two ways. First, they are macroscopic Bell tests involving spacelike separated measurement events, where the choice of measurement setting at each site corresponds to a choice between two different times of local interaction. The interaction may be seen as the unitary stage of a local measurement process. Second, the proposal is a strong version of a Leggett-Garg test of "macrorealism" that uses two trajectories, where the usual assumption of noninvasive measurability as applied to measurements at one site is replaced by that of macroscopic locality. For $N=1$, tests are feasible and give a way to demonstrate “no classical trajectories” without the assumption of noninvasive measurability, using instead that of locality.