Non-separable State Research Articles

Logical rotation of non-separable states via uniformly self-assembled chiral superstructures

The next generation of high-capacity, multi-task optical informatics requires sophisticated manipulation of multiple degrees of freedom (DoFs) of light, especially when they are coupled in a non-separable way. Vector beam, as a typical non-separable state between the spin and orbital angular momentum DoFs, mathematically akin to entangled qubits, has inspired multifarious theories and applications in both quantum and classical regimes. Although qubit rotation is a vital and ubiquitous operation in quantum informatics, its classical analogue is rarely studied. Here, we demonstrate the logical rotation of vectorial non-separable states via the uniform self-assembled chiral superstructures, with favorable controllability, high compactness and exemption from formidable alignment. Photonic band engineering of such 1D chiral photonic crystal renders the incident-angle-dependent evolution of the spatially-variant polarizations. The logical rotation angle of a non-separable state can be tuned in a wide range over 4π by this single homogeneous device, flexibly providing a set of distinguished logic gates. Potential applications, including angular motion tracking and proof-of-principle logic network, are demonstrated by specific configuration. This work brings important insight into soft matter photonics and present an elegant strategy to harness high-dimensional photonic states.

Generating arbitrary non-separable states with polarization and orbital angular momentum of light

We demonstrate an experimental method to generate arbitrary non-separable states of light in two degrees of freedom i.e., polarization and orbital angular momentum (OAM). We observe the intensity distribution corresponding to OAM modes of the light beam by projecting the non-separable state into different polarization states. We further verify the presence of non-separability by measuring the degree of polarization and linear entropy. This classical non-separability can be easily transferred to the quantum domain using spontaneous parametric down-conversion for applications in quantum communication and quantum sensing.

Pseudo-spin-orbit-coupling-based manipulation of vector beams using electromagnetically induced transparency.

Based on the electromagnetically induced transparency (EIT) model and the higher-order Poincaré sphere (HOPS) framework, we establish a general paradigm to investigate the paraxial evolution of a vector beam in a tripod EIT system. By quantum-optical analogy, we introduce a formalism with a generalized Pauli-like equation under rotational invariance, in which the pseudo-spin-orbit coupling (PSOC) and the spin-orbit nonseparability of light can coexist. More importantly, we find that both the PSOC-based real and imaginary potentials play a key role in controlling and modulating the nonseparable state of the vector beam to traverse the entire HOPS, where the orientation and ellipticity of the transmitted polarization can be modified by varying the PSOC coefficients. Therefore, an all-optical scheme can be proposed to improve the flexibility for tailoring the space-variant polarization of light in coherent media, where the tunable spatial-polarization multiplexing may be useful in conventional and quantum information processing.

Comparing entanglement and identity effects in tunnelling

The probability of simultaneous tunnelling of two particles is modified when the system is in a non-separable state, either entangled or symmetrised. We compare both effects in the rectangular potential barrier by evaluating the transmission rates in superposition states. For large momenta, their simultaneous presence greatly changes the form of the transmission rates. The joint effects are much larger than the superposition ones. Moreover, there are significant differences between bosons and fermions. We present an unified view of the combined effects as a quantum interference phenomenon. The analysis also illustrates a novel aspect of exclusion in entangled systems, the existence of superposition states one of whose terms is forbidden by Pauli's principle.

Evaluating the Atmospheric Loss of H2 by NO3 Radicals: A Theoretical Study

Molecular hydrogen (H2) is now considered among the most prominent substitute for fossil fuels. The environmental impacts of a hydrogen economy have received more attention in the last years, but still, the knowledge is relatively poor. In this work, the reaction of H2 with NO3 radical (the dominant night-time detergent of the atmosphere) is studied for the first time using high-level composite G3B3 and modification of high accuracy extrapolated ab initio thermochemistry (mHEAT) methods in combination with statistical kinetics analysis using non-separable semi-classical transition state theory (SCTST). The reaction mechanism is characterized, and it is found to proceed as a direct H-abstraction process to yield HNO3 plus H atom. The reaction enthalpy is calculated to be 12.8 kJ mol−1, in excellent agreement with a benchmark active thermochemical tables (ATcT) value of 12.2 ± 0.3 kJ mol−1. The energy barrier of the title reaction was calculated to be 74.6 and 76.7 kJ mol−1 with G3B3 and mHEAT methods, respectively. The kinetics calculations with the non-separable SCTST theory give a modified-Arrhenius expression of k(T) = 10−15 × T0.7 × exp(−6120/T) (cm3 s−1) for T = 200–400 K and provide an upper limit value of 10−22 cm3 s−1 at 298 K for the reaction rate coefficient. Therefore, as compared to the main consumption pathway of H2 by OH radicals, the title reaction plays an unimportant role in H2 loss in the Earth’s atmosphere and is a negligible source of HNO3.

Quantum channel correction with twisted light using compressive sensing

Compressive sensing is used to perform high-dimensional quantum channel estimation with classical light. As an example, we perform a numerical simulation for the case of a three-dimensional classically non-separable state that is propagated through atmospheric turbulence. Using singular value thresholding algorithm based compressive sensing, we determine the channel matrix, which we subsequently use to correct for the atmospheric turbulence induced distortions. As a measure of the success of the procedure, we calculate the fidelity and the trace distance of the corrected density matrix with respect to the input state, and compare the results with those of the density matrix for the uncorrected state. Furthermore, we quantify the amount of classical non-separability in the density matrix of the corrected state by calculating its negativity. The results show that compressive sensing could contribute in the development and implementation of free-space quantum and optical communication systems.

Experimental demonstration of generating arbitrary total angular momentum states

We experimentally demonstrated an approach to generate arbitrary total angular momentum (TAM) states by using two liquid crystal devices. Photons’ TAM, the sum of spin and orbital angular momenta (SAM and OAM) under paraxial approximation, has found many applications in optics and attracted increasing attention in recent years. Our approach is based on the orthogonality of two eigen SAM components, that arbitrary TAM states will be produced through encoding different holograms in one system. The comparison with theoretical predications yields an excellent agreement, including both the separable state and the non-separable state. The proposed scheme takes a step forward for generating complex structured fields and broadens its application to various fields like laser processing and large capacity data transmission.

Classical simulation of high-dimensional entanglement by non-separable angular-radial modes.

An analogous model system for high-dimensional quantum entanglement is proposed, based on the angular and radial degrees of freedom of the improved Laguerre Gaussian mode. Experimentally, we observed strong violations of the Bell-CGLMP inequality for maximally non-separable states of dimension 2 through 10. The results for violations in classical non-separable state are in very good agreement with quantum instance, which illustrates that our scheme can be a useful platform to simulate high-dimensional non-local entanglement. Additionally, we found that the Bell measurements provide sufficient criteria for identifying mode separability in a high-dimensional space. Similar to the two-dimensional spin-orbit non-separable state, the proposed high-dimensional angular-radial non-separable state may provide promising applications for classical and quantum information processing.

Entanglement distribution statistic in Andreev billiards

We investigate statistical aspects of the entanglement production for open chaotic mesoscopic billiards in contact with superconducting parts, known as Andreev billiards. The complete distributions of concurrence and entanglement of formation are obtained by using the Altland–Zirnbauer symmetry classes of circular ensembles of scattering matrices, which complements previous studies in chaotic universal billiards belonging to other classes of random matrix theory. Our results show a unique and very peculiar behavior: the realization of entanglement in a Andreev billiard always results in non-separable state, regardless of the time reversal symmetry. The analytical calculations are supported by a numerical Monte Carlo simulation.

Entanglement classification in the noninteracting Fermi gas

In this paper, entanglement classification shared among the spins of localized fermions in the noninteracting Fermi gas is studied. It is proven that the Fermi gas density matrix is block diagonal on the basis of the projection operators to the irreducible representations of symmetric group [Formula: see text]. Every block of density matrix is in the form of the direct product of a matrix and identity matrix. Then it is useful to study entanglement in every block of density matrix separately. The basis of corresponding Hilbert space are identified from the Schur–Weyl duality theorem. Also, it can be shown that the symmetric part of the density matrix is fully separable. Then it has been shown that the entanglement measure which is introduced in Eltschka et al. [New J. Phys. 10, 043104 (2008)] and Guhne et al. [New J. Phys. 7, 229 (2005)], is zero for the even [Formula: see text] qubit Fermi gas density matrix. Then by focusing on three spin reduced density matrix, the entanglement classes have been investigated. In three qubit states there is an entanglement measure which is called 3-tangle. It can be shown that 3-tangle is zero for three qubit density matrix, but the density matrix is not biseparable for all possible values of its parameters and its eigenvectors are in the form of W-states. Then an entanglement witness for detecting non-separable state and an entanglement witness for detecting nonbiseparable states, have been introduced for three qubit density matrix by using convex optimization problem. Finally, the four spin reduced density matrix has been investigated by restricting the density matrix to the irreducible representations of [Formula: see text]. The restricted density matrix to the subspaces of the irreducible representations: [Formula: see text], [Formula: see text] and [Formula: see text] are denoted by [Formula: see text], [Formula: see text] and [Formula: see text], respectively. It has been shown that some highly entangled classes (by using the results of Miyake [Phys. Rev. A 67, 012108 (2003)] for entanglement classification) do not exist in the blocks of density matrix [Formula: see text] and [Formula: see text], so these classes do not exist in the total Fermi gas density matrix.

Pancharatnam phase in non-separable states of light

We generate the non-separable state of polarization and orbital angular momentum using a laser beam. The generated state undergoes a cyclic polarization evolution which introduces a Pancharatnam geometric phase to the polarization state and, in turn, a relative phase in the non-separable state. We experimentally study the violation of the Bell-like inequality for different Pancharatnam phases introduced by various cyclic polarization evolutions with linear and circular states as measurement bases. While measuring in linear bases, the Bell-CHSH parameter oscillates with a Pancharatnam phase. One can overcome this dependence by introducing a relative phase in one of the projecting states. However, for measurements in circular bases, the Pancharatnam phase does not affect the Bell-like inequality violation.

Recovering the vorticity of a light beam after scattering

We generate optical vortices and scatter them through a rough surface. However, the scattered light passing through a lens shows the same vorticity when probed at the Fourier plane. The vorticity is measured using a nonseparable state of polarization and orbital angular momentum of light as it cannot be confirmed by the standard interferometric technique. The observed vorticity is found to be independent of the amount of scattered light collected. Therefore, vortices can be used as information carriers even in the presence of scattering media. The experimental results are well supported by the theoretical results.

Real-time imaging of photonic quantum teleportation

The science fiction depiction of teleportation refers to the transfer of matter between two spatially separated spaces without the transfer of information. This largely differs from the concept of quantum teleportation, one of the most exciting concepts in modern quantum theory, though often misunderstood.1 The key difference between the sci-fi portrayal and quantum teleportation is that information is transferred between two spatially separated parties, rather than a direct transfer of matter. Applications may include quantum key distribution and quantum cryptography. At the heart of such teleportation is the phenomenon of quantum entanglement, in which the quantum state corresponding to non-local particles cannot be described independently. Sender (Alice) and receiver (Bob) share a pair of particles that are entangled. Alice performs a set of measurements (known as the Bell states analysis) on the state of her particle and that of a third particle (Charlie)—the particle whose state should be teleported to Bob. Based on the outcome of her measurements, Alice sends a signal to Bob. Bob applies a set of unitary transformations, without knowing the state, to the state of his particle. After these transformations, the state of Bob’s particle is identical to Charlie’s. Note that, during this process, Alice and Bob have no information about the state of Charlie’s particle. This process is probabilistic when implemented with entangled photons and linear optics,2 and means that sometimes Alice’s measurement outcome—that of two particles’ Bell states analysis—is not determined. Thus, Bob does not receive any classical signal, and the teleportation fails. Nevertheless, when Bob receives the signal from Alice, the state is the correct one, and teleportation has succeeded with a 100% fidelity. We can use a single particle possessing two different quantum properties to present a non-separable state, where Figure 1. (a) The setup for remote-hybrid-teleportation of photons from the spin to the orbital-angular-momentum degree of freedom (OAM DOF). A UV laser pumps a barium borate (BBO) crystal to generate photon pairs that are entangled in their OAM DOF. A polarizing Sagnac interferometer containing a dove prism (PSI-DP), shown in the inset, in combination with the half-wave plate (H), spatial light modulator (SLM), bandpass interference filter (IF) and single mode optical fiber (SMF) perform the single photon spin-OAM non-separable Bell state measurement.4 The photons couple via a fiber coupler (FC) into the SMF for detection by an avalanche photodiode (APD). The APD triggers the intensified charge-coupled camera (ICCD) to record the spatial distribution of photon B. During the preparation and measurement of photon A, photon B propagates in the delay line (D), compensating for electronic delay. (b) First and second columns show the polarization (SAM) state of C and the OAM state of the teleported photon to B. jLi, jH i, and jV i: left, horizontal, and vertical polarization, respectively. M: Mirror. PBS: Polarizing beam splitter. TEM: Transverse electromagnetic mode—this refers to the fundamental transverse mode (beam with a Gaussian profile). Q: Quarter-wave plate.

Thermodynamics ofN-dimensional quantum walks

The entanglement between the position and the coin state of an $N$-dimensional quantum walker is shown to lead to a thermodynamic theory. The entropy, in this thermodynamics, is associated with the reduced density operator for the evolution of chirality, taking a partial trace over positions. From the asymptotic reduced density matrix it is possible to define thermodynamic quantities, such as the asymptotic entanglement entropy, temperature, and Helmholz free energy. We study in detail the case of a two-dimensional quantum walk, in the case of two initial conditions: a nonseparable coin-position initial state and a separable one. The resulting entanglement temperature is presented as a function of the parameters of the system and those of the initial conditions.

Novel States of Classical Light and Noncontextuality

A new criterion, based on noncontextuality, is derived to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. An experiment is proposed to test the violation of noncontextuality by a nonseparable state. Such states have only recently begun to be explored. The significance of their nonseparability or entanglement as well as their similarities with and differences from entangled quantum states are discussed.

Decoherence and the Copenhagen cut

While it is widely agreed that decoherence will not solve the measurement problem, decoherence has been used to explain the “emergence of classicality” and to eliminate the need for a Copenhagen edict that some systems simply have to be treated as classical via a quantum-classical “cut”. I argue that decoherence still relies on such a cut. Decoherence accounts derive classicality only in virtue of their incompleteness, by omission of part of the entangled system of which the classical-appearing subsystem is a part. I argue that this omission is only justified by implicit classical assumptions that objectify a subsystem and are employed via either a traditional Copenhagen cut or a functionally equivalent imposition of separability on a system in a non-separable state. I argue that decoherence cannot derive classicality without assuming it in some other form, and I provide an analysis of when it is appropriate to make these otherwise implicit classical assumptions by adopting a minimalistic Copenhagen-style approach to measurement. Finally, I argue that, ironically, the conditions for making these assumptions may be better satisfied in standard measurement situations than in cases of environmental monitoring.

Dual squeezed states in an atom-photon cluster and their manifestations

The general kinetic equation for an isolated two-level atom and a high-Q cavity mode in a heat bath exhibiting quantum correlations (entangled bath) is applied to the analysis of the squeezed states of the collective system. Two types of collective operators are introduced for the analysis: one is based on bosonic commutation relations, and the other, on the commutation relations of the algebra obtained by a polynomial deformation of the angular momentum algebra. On the basis of these relations, formulas for observables are constructed that identify squeezed states in the system. It is shown that, under certain conditions, the collective system exhibits dual squeezing within the relations for boson operators, as well as for the operators constructed from the angular momentum algebra. Such squeezing is demonstrated under a projective measurement of an atom and for an entanglement swapping protocol. In the latter case, when measuring two initially independent atomic systems, depending on the type of measurement, two cavity modes collapse into a nonseparable state, which is described either by a nonseparability relation based on boson operators or by a relation based on the operators of the algebra of the quasimomentum of the collective system consisting of these two modes.

Threshold bounds for noisy bipartite states

For a nonseparable bipartite quantum state violating the Clauser–Horne–Shimony–Holt (CHSH) inequality, we evaluate amounts of noise breaking the quantum character of its statistical correlations under any generalized quantum measurements of Alice and Bob. Expressed in terms of the reduced states, these new threshold bounds can be easily calculated for any concrete bipartite state. A noisy bipartite state, satisfying the extended CHSH inequality and the perfect correlation form of the original Bell inequality for any quantum observables, neither necessarily admits a local hidden variable model nor exhibits the perfect correlation of outcomes whenever the same quantum observable is measured on both 'sides'.

Rate constants from the reaction path Hamiltonian. II. Nonseparable semiclassical transition state theory.

For proton transfer reactions, the tunneling contributions to the rates are often much larger than thermally activated rates at temperatures of interest. A number of separable tunneling corrections have been proposed that capture the dependence of tunneling rates on barrier height and imaginary frequency size. However, the effects of reaction pathway curvature and barrier anharmonicity are more difficult to quantify. The nonseparable semiclassical transition state theory (TST) of Hernandez and Miller [Chem. Phys. Lett. 214, 129 (1993)] accounts for curvature and barrier anharmonicity, but it requires prohibitively expensive cubic and quartic derivatives of the potential energy surface at the transition state. This paper shows how the reaction path Hamiltonian can be used to approximate the cubic and quartic derivatives used in nonseparable semiclassical transition state theory. This enables tunneling corrections that include curvature and barrier anharmonicity effects with just three frequency calculations as required by a conventional harmonic transition state theory calculation. The tunneling correction developed here is nonseparable, but can be expressed as a thermal average to enable efficient Monte Carlo calculations. For the proton exchange reaction NH2 + CH4 <==> NH3 + CH3, the nonseparable rates are very accurate at temperatures from 300 K up to about 1000 K where the TST rate itself begins to diverge from the experimental results.

Quantum interference effects for nonseparable two-electron systems.

We consider a quantum interference experiment in which two incident electrons, moving in complementary regions of space, give rise to a nonseparable two-electron state. Multielectron interference experiments have been considered previously, but it is shown here that a two-electron interference experiment is within the reach of existing laboratory techniques. It is also shown that an electromagnetic action exerted on one of the electrons can result in observable effects involving both electrons, although the conditions of the experiment are chosen such that during or after the exertion of this action on one of the electrons there is no exchange of energy, momentum, or angular momentum between the two electrons