The controlled generation and identification of quantum correlations, usually encoded in either qubits or continuous degrees of freedom, builds the foundation of quantum information science. Recently, more sophisticated approaches, involving a combination of two distinct degrees of freedom, have been proposed to improve on the traditional strategies. Hyperentanglement describes simultaneous entanglement in more than one distinct degree of freedom, whereas hybrid entanglement refers to entanglement shared between a discrete and a continuous degree of freedom. In this work we propose a scheme that allows us to combine the two approaches, and to extend them to the strongest form of quantum correlations. Specifically, we show how two identical, initially separated particles can be manipulated to produce Bell nonlocality among their spins, among their momenta, as well as across their spins and momenta. We discuss possible experimental realizations with atomic and photonic systems.
The controlled generation and identification of quantum correlations, usually encoded in either qubits or continuous degrees of freedom, builds the foundation of quantum information science. Recently, more sophisticated approaches, involving a combination of two distinct degrees of freedom, have been proposed to improve on the traditional strategies. Hyperentanglement describes simultaneous entanglement in more than one distinct degree of freedom, whereas hybrid entanglement refers to entanglement shared between a discrete and a continuous degree of freedom. In this work we propose a scheme that allows us to combine the two approaches, and to extend them to the strongest form of quantum correlations. Specifically, we show how two identical, initially separated particles can be manipulated to produce Bell nonlocality among their spins, among their momenta, as well as across their spins and momenta. We discuss possible experimental realizations with atomic and photonic systems.
"The field of quantum information science promises incredible enhancements in computing, metrology, simulation, and communication, but the challenge of creating, manipulating, and measuring the large quantum states has limited current implementations of such techniques. Such limitations affect photonic quantum information in particular, because photons lack the strong nonlinear interactions required for building up many-particle entangled states and performing multi-photon gates; nevertheless, because photons are currently the only ""flying qubit"", i.e., qubits that are mobile, they are a required resource for quantum communication protocols. One strategy to partially mitigate this limitation is to encode multiple entangled qubits on the different degrees of freedom of a single pair of photons. Such ""hyperentangled"" quantum states may be created with enough qubits to enable a whole new class of quantum information experiments. Furthermore, while nonlinear interactions are required to implement multi-qubit gates between qubits encoded on different particles, such gates can be implemented between qubits encoded on the same particle using only linear elements, enabling a much broader class of measurements. We use hyperentangled states to implement various quantum communication and quantum metrology protocols. Specifically, we demonstrate that hyperentangled photons can be used to increase the classical channel capacity of a quantum channel, transport quantum information between two remote parties efficiently and deterministically, and efficiently characterize quantum channels. We will discuss how to produce, manipulate, and measure hyperentangled states and discuss how entanglement in multiple degrees of freedom enables each technique. Finally, we discuss the limitations of each of these techniques and how they might be improved as technology advances."
Entanglement is a key resource for fundamental tests of physics and emerging quantum technologies. In quantum optics, two perspectives on entanglement coexist. In the continuous-variable framework, entanglement is understood as holding between optical modes. In contrast, discrete-variable quantum optics focuses on quantum correlations in degrees of freedom such as polarization that label fixed numbers of photons. In this paper, we show that entanglement can transcend this separation. Spontaneous parametric down-conversion inherently generates correlations in optical phase space, photon number, and labelling degrees of freedom simultaneously. In polarization, this structure is traditionally described by macroscopic Bell states. Existing witnesses, however, fail to detect the genuine hybrid entanglement of these states, which goes beyond the continuous-discrete-variable categorization. Here, we lay the groundwork for a general framework unifying continuous- and discrete-variable notions of entanglement. In particular, we derive an operational witness providing a sufficient criterion for genuine hybrid number-polarization entanglement and outline its experimental implementation. Finally, we discuss exemplary states which, together with our results on macroscopic Bell states, motivate a broader classification of genuine hybrid quantum correlations.
Hybrid entangled states generated, e.g., in a trapped-ion or atom-cavity system, have exactly one ebit of entanglement, but are not maximally entangled. We demonstrate this by showing that they violate, but, in general, not maximally, Bell's inequality due to Clauser, Horne, Shimony, and Holt [Phys. Rev. Lett. 23, 880 (1969)]. These states are interesting in that they exhibit the entanglement between two distinct degrees of freedom (one is discrete and another is continuous). We then demonstrate these entangled states as a valuable resource in quantum-information processing including quantum teleportation, entanglement swapping and quantum computation with ``parity qubits.'' Our work establishes an interesting link between quantum-information protocols of discrete and continuous variables.
Entanglement in multiple degrees of freedom has many benefits over entanglement in a single one. The former enables quantum communication with higher channel capacity and more efficient quantum information processing and is compatible with diverse quantum networks. Establishing multi-degree-of-freedom entangled memories is not only vital for high-capacity quantum communication and computing, but also promising for enhanced violations of nonlocality in quantum systems. However, there have been yet no reports of the experimental realization of multi-degree-of-freedom entangled memories. Here we experimentally established hyper- and hybrid entanglement in multiple degrees of freedom, including path (K-vector) and orbital angular momentum, between two separated atomic ensembles by using quantum storage. The results are promising for achieving quantum communication and computing with many degrees of freedom.
In the case of mixed states ρAB of the composite system A ⊗ B, the previous relation generalizes to ρAB = ∑ k pkρ A k ⊗ρk , where pk are probabilities and ρk ’s (ρk ’s) are generic density matrix of the system A (B). The entanglement derives from “subtle” nonlocal correlations between the parts of a quantum system and combines three basic structural elements of quantum theory: the superposition principle, the quantum non-separability property and the exponential scaling of the state space with the number of partitions. This unique resource can be used to perform computational and cryptographic tasks otherwise impossible with classical systems. An entangled state shared by two or more separated parties is a valuable resource for fundamental quantum protocols, such as quantum teleportation [2], quantum computing [3] and quantum cryptography. By using entangled states we can deeply investigate the nonlocal properties of the quantum world. In fact, an entangled system exhibits correlations between two (or more) parties, which cannot be reproduced by a classical theory or, in general, by a Local Hidden Variables Theory (LHVT). Quantum optics represents an excellent experimental test bench for various novel concepts introduced within the framework of quantum information theory. Quantum states of photons, generally produced by a probabilistic process, namely spontaneous parametric down conversion (SPDC), may be easily and accurately manipulated using linear and nonlinear optical devices and measured by efficient single-photon detectors. Photonic qubits represent the typical carrier of quantum information and can be distributed over long distances, either in free-space or in low-loss optical fibers. Two-particle experiments correspond to operate with qubits belonging to a (2 × 2) Hilbert space. Many quantum information tasks and fundamental tests of quantum mechanics, such as the simulation of properties of quantum systems, the realization of quantum algorithms of increasing complexity and the investigation of the quantum world at a mesoscopic level, deal with a large number of qubits. In order to take full advantage of the possibilities offered by quantum mechanics, more qubits must be added to a quantum state. Two approaches may be followed to increase the number of qubits. The first one consists of increasing the number of entangled particles. In this way, multi-qubit entangled states are created by distributing the qubits between the particles so that each particle carries one qubit. A second strategy consists of encoding more than one qubit in each particle, by exploiting different degrees of freedom (DOFs) of the photon such as the polarization, the path, the emission time, the orbital angular momentum. This has been used to create two-photon fourand six-qubit states and up to five-photon ten-qubit graph states. The entanglement of two particles in different DOFs corresponds to socalled hyperentanglement. It is worth noting that multi-qubit hyperentanglement allows to achieve higher
Photon system is a promising candidate for quantum information processing, and it can be used to achieve some important tasks with the interaction between a photon and an atom (or a artificial atom), such as the transmission of secret information, the storage of quantum states, and parallel quantum computing. Several degrees of freedom (DOFs) of a photon system can be used to carry information in the realization of quantum information processing, such as the polarization, spatial-mode, orbit-angular-momentum, time-bin, and frequency DOFs. A hyperparallel quantum computer can implement the quantum operations on several DOFs of a quantum system simultaneously, which reduces the operation time and the resources consumed in quantum information processing. The hyperparallel quantum operations are more robust against the photonic dissipation noise than the quantum computing in one DOF of a photon system. Hyperentanglement, defined as the entanglement in several DOFs of a quantum system, can improve the channel capacity and the security of long-distance quantum communication, and it can also be conductive to completing some important tasks in quantum communication. Hyperentangled Bell-state analysis is used to completely distinguish the 16 hyperentangled Bell states, which is very useful in high-capacity quantum communication protocols and quantum repeaters. In order to depress the effect of noises in quantum channel, hyperentanglement concentration and hyperentanglement purification are required to improve the entanglement of the quantum systems in long-distance quantum communication, which is also very useful in high-capacity quantum repeaters. Hyperentanglement concentration is used to distill several nonlocal photon systems in a maximally hyperentangled state from those in a partially hyperentangled pure state, and hyperentanglement purification is used to distill several nonlocal photon systems in a high-fidelity hyperentangled state from those in a mixed hyperentangled state with less entanglement. In this reviewing article, we review some new applications of photon systems with multiple DOFs in quantum information processing, including hyperparallel photonic quantum computation, hyperentangled-Bell-state analysis, hyperentanglement concentration, and hyperentanglement purification.