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We present a theoretical investigation of the properties of quantum correlation functions in a multimode system. We define a total $m$th order equal-time correlation function, summed over all modes, which is shown to be conserved if the Hamiltonian possesses U(1) symmetry. It is also conserved in the presence of dissipation, provided the loss rate is the same for all modes of the system. As examples, we demonstrate this conservation using numerical simulations of a coupled cavity system and the Jaynes-Cummings model.

The uncertainty principle is one of the central concepts in quantum theory. Different forms of this principle have been discussed in various foundational and information theoretic topics. Whereas in the discrete input-output scenario the limited nonlocal behavior of quantum theory has been explained by the fine-grained uncertainty relation, in the continuous-variable paradigm the Robertson-Schrödinger (RS) uncertainty relation has been used to detect multimode entanglement. Here we show that the RS uncertainty relation plays an important role in discriminating between quantum and postquantum nonlocal correlations in the multimode continuous outcome scenario. We provide a class of $m$-mode postquantum nonlocal correlations with a continuous outcome spectrum. While nonlocality of the introduced class of correlations is established through the Calvalcanti-Foster-Reid-Drummond class of Bell inequalities, the RS uncertainty relation detects their postquantum nature. Our result suggests a wider role of the uncertainty principle in the study of nonlocality in continuous-variable multimode systems.

We examine, in correlated mixed states of qudit-qubit systems, the set of all conditional qubit states that can be reached after local measurements at the qudit based on rank-1 projectors. While for a similar measurement at the qubit the conditional postmeasurement qudit states lie on the surface of an ellipsoid, for a measurement at the qudit we show that the set of postmeasurement qubit states can form more complex solid regions. In particular, we show the emergence, for some classes of mixed states, of sets which are the convex hull of solid ellipsoids and which may lead to conelike and trianglelike shapes in limit cases. We also analyze the associated measurement-dependent conditional entropy, providing a full analytic determination of its minimum and of the minimizing local measurement at the qudit for the previous states. Separable rank-2 mixtures are also discussed.

Transmission efficiency (TE) of remote state preparation (RSP) with a shared quantum state and one bit of classical communication is considered. Following Dakić et al. [Nat. Phys. 8, 666 (2012)], the encoding and decoding operators of the protocol are restricted to the physically relevant classes of projective measurements and unitary operators, respectively. It is shown that contrary to the previous arguments, the quadratic fidelity as well as the linear fidelity could be a valid figure of merit to quantify the TE of RSP. Then, the TE of the protocol in terms of both linear and quadratic fidelities is evaluated in a fully optimized scenario which includes the maximization over the encoding parameters as well as a meaningful maximization over the decoding parameters. The results show that, in this scenario, the TE scales with the sum of the two largest eigenvalues of the squared correlation matrix of the resource state that is zero only for product states. This approach successfully quantifies the performance of the protocol in terms of the resource state parameters and provides a means to compare the usefulness of any two resource states for RSP.

In a no-signaling world, the outputs of a nonlocal box cannot be completely predetermined, a feature that is exploited in many quantum information protocols exploiting nonlocality, such as device-independent randomness generation and quantum key distribution. This relation between nonlocality and randomness can be formally quantified through the min-entropy, a measure of the unpredictability of the outputs that holds conditioned on the knowledge of any adversary that is limited only by the no-signaling principle. This quantity can easily be computed for the noisy Popescu-Rohrlich (PR) box, the paradigmatic example of nonlocality. In this paper, we consider the min-entropy associated to several copies of noisy PR boxes. In the case where $n$ noisy PR boxes are implemented using $n$ noncommunicating pairs of devices, it is known that each PR box behaves as an independent biased coin: the min-entropy per PR box is constant with the number of copies. We show that this does not hold in more general scenarios where several noisy PR boxes are implemented from a single pair of devices, either used sequentially $n$ times or producing $n$ outcome bits in a single run. In this case, the min-entropy per PR box is smaller than the min-entropy of a single PR box, and it decreases as the number of copies increases.

We revisit a continuous-variable version of the Clauser-Horne-Shimony-Holt inequality with sign binning, first proposed by Bell [J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 1st ed. (Cambridge University, New York, 1987); Ann. N.Y. Acad. Sci. 480, 263 (1986)]. To explore Bell nonlocality, we use a biphoton effective wave function resulting from a type-I spontaneous parametric down-conversion process. After reviewing the approximations involved in the production and time evolution of such biphotons, we judiciously choose a series expansion for the sinc function part of the biphoton wave function in order to integrate the Wigner function. We conclude that we can qualitatively achieve Bell nonlocality within a regime in which the twin photons are described.

The author of the Comment [Phys. Rev. A 104, 016401 (2021)] pointed out the missing part in the proof of Theorem 20 in our work [L. Qian et al., Phys. Rev. A 99, 032312 (2019)], and presented a sufficient and necessary condition for the separability of completely symmetric (CS) states in the two-qutrit system. While being technically correct, the proposed example is still a separable CS state according to Ha's sufficient and necessary condition. We provide another proof to show that every bipartite CS state of rank five is separable. This result bridges the gap appearing in our previous proof. It turns out that every two-qutrit CS state is separable, and thus making our conclusion (Theorem 20 of our work) still valid.

Quantum entanglement and nonlocality are inequivalent notions: There exist entangled states that nevertheless admit local-realistic interpretations. This paper studies a special class of local-hidden-variable theories, in which the linear structure of quantum measurement operators is preserved. It has been proven that a quantum state has such linear hidden-variable representations if, and only if, it is not entangled. Separable states are known to admit nonclassical correlations as well, which are captured by quantum discord and related measures. In the unified framework presented in this paper, zero-discordant states are characterized as the only states that admit fully consistent classical probability representations. Possible generalization of this framework to the quasiprobability representation of multipartite quantum states is also discussed.

Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g., via quasiprobabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are noncontextual and are consistent with all constraints expected from a quantum probability. We study two noncommuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts with theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two noncommuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not excluded anymore, but they are still constrained by imprecise probabilities.

In the field of continuous-variable systems a fundamental role is played by Gaussian unitaries, that is, operators that preserve the Gaussian character of the states. The paper deals with the implementation of an arbitrary multimode Gaussian unitary by means of primitive components, namely, single-mode operators and simple two-mode operators (beam splitters). A partial solution to this problem is provided by the Bloch-Messiah reduction, which gives an architecture consisting of a multimode displacement, a diagonal squeezer, and two rotation operators. In this architecture displacement and squeezing are already formed by primitive components, so that it remains to find the implementation of the rotation operators. To this end, a suitable factorization of unitary matrices allows one to complete the desired implementation with primitive components. The theory is illustrated with an example of application to a four-mode Gaussian unitary.

Nonlocal correlations between a fully characterized quantum system and an untrusted black box device are described by an assemblage of conditional quantum states. These assemblages form a convex set, whose extremal points are relevant in many operational contexts. We give necessary and sufficient conditions for an assemblage to be extremal using linear independence conditions and an algorithm to decompose a generic assemblage into extremal points. A matlab implementation of this algorithm is also provided.

We observe experimentally the fractional topological phase (FTP) robustness to the dephasing noise in two-qudit photonic systems. We use a source of photon pairs generated by spontaneous parametric down-conversion, hyperentangled in the polarization and photon path degrees of freedom. The dephasing noise is described theoretically via Kraus maps and experimentally implemented via the spatial light modulator. The FTP is a great candidate to explore in the implementation of quantum processing and communication due to its robustness to dephasing noise.

In the following paper, we discuss a possible detection of nonlocality in two-mode light states in the Bell protocol, where the local observables are constructed using displacement operators, implemented by Mach-Zehnder interferometers fed by strong coherent states. We report numerical results showing that maximizing the Braunstein-Caves chained Bell inequalities requires equal phases of displacements. On the other hand, we prove that nonlocality cannot be detected if the phases of displacements are unknown. Hence, the Bell experiment has to be equipped with a synchronization mechanism. We discuss such a mechanism and its consequences.

We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions. In particular, we examine the eigenstates, spectrum, and entanglement entropy (EE) of the density matrix for various ground and excited states, with or without mass anisotropy. We focus on an important class of regions that contain sharp corners or cusps, leading to a geometric angle-dependent contribution to the EE. We unravel surprising relations by comparing this corner term at different fillings. We further find that the corner term, when properly normalized, has nearly the same angle dependence as numerous conformal field theories (CFTs) in two spatial dimensions, which hints at a broader structure. In fact, the Hall corner term is found to obey bounds that were previously obtained for CFTs. In addition, the low-lying entanglement spectrum and the corresponding eigenfunctions reveal “excitations” localized near corners. Finally, we present an outlook for fractional quantum Hall states.

Wave-particle duality is a bizarre feature at the heart of quantum mechanics which refers to the mutually exclusive dual attributes of quantum objects as the wave and the particle. Quantum eraser presents a counterintuitive aspect of the wave-particle duality. In this paper, we show that quantum eraser can be quantitatively understood in terms of the recently developed duality-entanglement relation. In other words, we show that wave-particle-entanglement triality captures all the physics of the quantum erasure. We find that a controllable partial erasure of the which-path information is attainable, enabling the partial recovery of the quantum interference and extending the scope of the conventional quantum eraser protocols.

Producing contextual correlations in sequences of measurements on single quantum systems faces two major problems. One is the experimental difficulty of performing sequences of ideal measurements on high-dimensional quantum systems, a problem that also affects other forms of quantum temporal correlations. The other is the simulability with classical light of existing contextuality experiments with photons. Here, we introduce a scheme that solves both problems. We show that, by encoding quantum information in $n\ge 2$ indistinguishable bosons in $m\ge 2$ modes, targeting observables exploiting the bunching-antibunching of bosons, and performing ideal measurements by dispersively coupling these systems with auxiliary qubits, it is possible to realize sequential quantum measurements on high-dimensional quantum systems and produce contextuality which cannot be simulated by classical light, as it relies on indistinguishability and higher-order interference.

We analyze the structure of the space of temporal correlations generated by quantum systems. We show that the temporal correlation space under dimension constraints can be nonconvex. For the general case, we provide the necessary and sufficient dimension of a quantum system needed to generate a convex correlation space for a given scenario. We further prove that this dimension coincides with the dimension necessary to generate any point in the temporal correlation polytope. As an application of our results, we derive nonlinear inequalities to witness the nonconvexity for qubits and qutrits in the simplest scenario, and present an algorithm which can help to find the minimum for a certain type of nonlinear expressions under dimension constraints.