Entanglement and symmetrization lead to non-separable states that can modify physical properties. Using the example of atomic absorption we compare both types of effects when they are relevant at once. The presence of multi-particle superpositions largely alters the absorption rates of identical atoms, even inhibiting the dependence on overlapping for fermions. We also identify a set of non-standard excluded states related to multi-fermion superposition that naturally emerge in this context. We propose an arrangement based on the dissociation of molecules to test these ideas.
Two-photon anti-bunching at a beamsplitter is only possible if the photons are entangled in a specific state, anti-symmetric in the spatial modes. Thus, observation of anti-bunching is an indication of entanglement in a degree of freedom which might not be easily accessible in an experiment. We experimentally demonstrate this concept in the case of the interference of two frequency entangled photons with continuous frequency detunings. The principle of anti-symmetrisation of the spatial part of a wavefunction and subsequent detection of hidden entanglement via anti-bunching at a beamsplitter m…
Consider a quantum system with $m$ subsystems with $n$ qubits each, and suppose the state of the system is living in the symmetric subspace. It is known that, in the limit of $m\to\infty$, entanglement between any two subsystems vanishes. In this paper we study asymptotic behavior of the entanglement as $m$ and $n$ grows. Our conjecture is that if $m$ is a polynomially bounded function in $n$, then the entanglement decreases polynomially. The motivation of this study is a study of quantum Merlin-Arthur game. If this conjecture is ture, we can prove that bipartite separable certificate does not…
A recent paper claimed to give an entanglement measure for composite systems, including Bose condensation and superconductivity. It is not an entanglement measure. It does not distinguish entanglement and non-factorization merely due to (anti)symmetrization for identical particles. In fact, the nature of entanglement, beyond the effect of (anti)symmetrization, in important states of many identical particles such as Bose condensation and superconductivity, had already been studied earlier.
Given two arbitrary pure states $ |ϕ>$ and $ |ψ>$ of qubits or higher level states, we provide arguments in favor of states of the form $ \frac{1}{\sqrt{2}}(|ψ> |ϕ> + i |ϕ> |ψ>) $ instead of symmetric or anti-symmetric states, as natural candidates for optimally entangled states constructed from these states. We show that such states firstly have on the average a high value of concurrence, secondly can be constructed by a universal unitary operator independent of the input states. We also show that these states are the only ones which can be produced with perfect fidelity by any quantum operat…
We revisit the problem of absorption by identical atoms with entanglement and symmetrization acting at once. We introduce the recoil of the atoms in the calculations and compare the results with those of distinguishable systems instead of mixtures. These absorption rates have been proposed to test entanglement-induced exclusion. The manifestation of exclusion in this framework is a sharp increase of the absorption rates in its proximity. The control of the superposition coefficients used in this representation is simpler than that of the overlapping degree considered in the initial proposal. A…
When a measurement is carried out on one of the entangled parties, the second party can extract work owing to the reduction in its entropy. Here we inquire the amount of work/energy corresponding to the symmetrization entanglement of identical particles (bosons) in a condensate. One measures the quantum state of a particular boson which can be performed only under some certain conditions. We learn that the extracted work comes out to be the \textit{complete} thermodynamical energy present in the condensate. %We learn that the work extracted by the remaining part of the condensate is equal to t…
Reasonable requirements of (a) physical invariance under particle permutation and (b) physical completeness of state descriptions, enable us to deduce a Symmetric Permutation Rule(SPR): that by taking care with our state descriptions, it is always possible to construct state vectors (or wave functions) that are purely symmetric under pure permutation for all particles, regardless of type distinguishability or spin. The conventional exchange antisymmetry for two identical half-integer spin particles is shown to be due to a subtle interdependence in the individual state descriptions arising from…
Nonlocality without entanglement in exclusion of quantum states
Indian Institute of Technology Bhubaneswar（印度理工学院布巴内斯瓦尔分校）；S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）；Indian Institute of Science Education and Research Thiruvananthapuram（特鲁万纳姆普拉尔印度科学与教育研究所）
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes of incompatible measurements on one physical system, and a second reference system. We provide a more stringent formulation of both the uncertainty principle and the information exclusion principle, with direct applications for, e.g., the security analysis of quantum key distribution, entanglement estimation, and quantum communication. We also highlight a f…
We consider the bipartite spin entanglement between two identical fermions generated in spin-independent scattering. We show how the spatial degrees of freedom act as ancillas for the creation of entanglement to a degree that depends on the scattering angle, $θ$. The number of Slater determinants generated in the process is greater than 1, corresponding to genuine quantum correlations between the identical fermions. The maximal entanglement attainable of 1 ebit is reached at $θ=π/2$. We also analyze a simple $θ$ dependent Bell's inequality, which is violated for $π/4<θ\leqπ/2$. This phenomenon…
The first characterization of mixed-state entanglement was achieved for two-qubit states in Werner's seminal work [Phys. Rev. A 40, 4277 (1989)]. A physically important extension of this result concerns mixtures of a pure entangled state (such as the Greenberger-Horne-Zeilinger [GHZ] state) and the completely unpolarized state. These mixed states serve as benchmark for the robustness of entanglement. They share the same symmetries as the GHZ state. We call such states GHZ-symmetric. Despite significant progress their multipartite entanglement properties have remained an open problem. Here we g…
In this work, we report that the Hawking radiation effect on fermions is fundamentally different from the case of scalar particles. Intrinsic properties of fermions (exclusion principle and spin) affect strongly the interaction of fermions with both Hawking radiation and metric of the spacetime. In particular we have found the following: first, while the fermion vacuum state seen by the Rindler observer is an entangled state in which the right and left Rindler wedge states appear in correlated pairs as in the case of the scalar particles, the entanglement disappears in the excited state due to…
For a Bose condensate in a double-well potential or with two Josephson-coupled internal states, the condensate wavefunction is a superposition. Here we consider coupling two such Bose condensates, and suggest the existence of a joint condensate wavefunction, which is in general a superposition of all products of the bases condensate wavefunctions of the two condensates. The corresponding many-body state is a product of such superposed wavefunctions, with appropriate symmetrization. These states may be potentially useful for quantum computation. There may be robustness and stability due to macr…
We study the probability distribution of entanglement in the Quantum Symmetric Simple Exclusion Process, a model of fermions hopping with random Brownian amplitudes between neighboring sites. We consider a protocol where the system is initialized in a pure product state of $M$ particles, and focus on the late-time distribution of Rényi-$q$ entropies for a subsystem of size $\ell$. By means of a Coulomb gas approach from Random Matrix Theory, we compute analytically the large-deviation function of the entropy in the thermodynamic limit. For $q>1$, we show that, depending on the value of the rat…
The hyperlink representation of entanglement and the inclusion-exclusion principle
Universidad Carlos III de Madrid（马德里卡洛斯三世大学）；Indian Institute of Technology (ISM), Dhanbad（印度理工学院（ISM）丹巴德分校）；Instituto de Física Teórica, UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Universidad Nacional de Educación a Distancia (UNED)（西班牙国立远程教育大学）
Some thermodynamical properties of solids, such as heat capacity and magnetic susceptibility, have recently been shown to be linked to the amount of entanglement in a solid. However this entanglement may appear a mere mathematical artifact of the typical symmetrization procedure of many-body wave function in solid state physics. Here we show that this entanglement is physical demonstrating the principles of its extraction from a typical solid state system by scattering two particles off the system. Moreover we show how to simulate this process using present-day optical lattices technology. Thi…
The study of entanglement properties of multi-qubit states that are invariant under permutations of qubits is motivated by potential applications in quantum computing, quantum communication, and quantum metrology. In this work, we generalize the notions of symmetrization, Dicke states, and the Majorana representation to the alternating, cyclic, and dihedral subgroups of the full group of permutations. We use these tools to characterize states that are invariant under these subgroups and analyze their entanglement properties.
We analyse some compositeness effects and their relation with entanglement. We show that the purity of a composite system increases, in the sense of the expectation values of the deviation operators, with large values of the entanglement between the components of the system. We also study the validity of Pauli's principle in composite systems. It is valid within the limits of application of the approach presented here. We also present an example of two identical fermions, one of them entangled with a distinguishable particle, where the exclusion principle cannot be applied. This result can be …
We investigate multipartite entanglement in a non-interacting fermion gas, as a function of fermion separation, starting from the many particle fermion density matrix. We prove that all multiparticle entanglement can be built only out of two-fermion entanglement. Although from the Pauli exclusion principle we would always expect entanglement to decrease with fermion distance, we surprisingly find the opposite effect for certain fermion configurations. The von Neumann entropy is found to be proportional to the volume for a large number of particles even when they are arbitrarily close to each o…
The properties of non-product states, both (anti)symmetrized and entangled, have been extensively studied in the literature. In this paper, by extending previous partial results, we introduce a general framework to describe atomic absorption and emission in these states. Our approach shows the existence of some fundamental differences between entanglement and (anti)symmetrization and between absorption and emission. For instance, modifications of the emission properties with respect to that of uncorrelated systems occur for any (anti)symmetrized state but only for some very specific entangled …
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…
We analyze the dynamical phases of the current-biased 1D and multi-lane open asymmetric simple exclusion processes (ASEP), using matrix product states and the density matrix renormalization group (DMRG) algorithm. In the 1D ASEP, we present a systematic numerical study of the current cumulant generating function and its derivatives, which serve as dynamical phase order parameters. We further characterize the microscopic structure of the phases from local observables and the entanglement spectrum. In the multi-lane ASEP, which may be viewed as finite width 2D strip, we use the same approach and…
We examine the influence of the Pauli exclusion principle on the scattering properties of composite bosons (cobosons) made of two fermions, such as the exciton quasiparticle. The scattering process incorporates boson-phonon interactions that arise due to lattice vibrations. Composite boson scattering rates increase with the entanglement between the two fermionic constituents, which comes with a larger number of available single-fermion states. An important role is played by probabilities associated with accommodating an incoming boson among the remaining unoccupied Schmidt modes in the initial…
We demonstrate exciting similarities between classical and quantum many body systems whose microscopic dynamics are composed of non-reciprocal three-site facilitated exclusion processes. We show that the quantum analogue of the classical facilitated process engineers an interesting $quantum$ $absorbing$ $transition$ where the quantum particles transit from an unentangled direct-product absorbing phase to an entangled steady state with a finite current at density $ρ=1/2$. In the generalised classical facilitated exclusion process, which includes independent hopping of particles with rate $p$, o…
We address the question of description of qubit system in a formalism based on the nilpotent commuting variables. In this formalism qubits exhibit properties of composite objects being subject of the Pauli exclusion principle, but otherwise behaving boson-like. They are not fundamental particles. In such an approach the classical limit yields the nilpotent mechanics. Using the space of $η$-wavefunctions, generalized Schrödinger equation etc. we study properties of pure qubit systems and also properties of some composed, hybrid models: fermion-qubit, boson-qubit. The fermion-qubit system can be…
The impossibility of ascribing definite states to the constituents of an entangled system restricts the scope of Pauli's principle in this context. We analyze the conceptual and physical aspects of the problem by studying the actual scope of the principle and the possibility of extending the concept of exclusion in correlated systems. When the entanglement is weak, as in the archetypical case of the Helium atom, the principle can be applied in an approximated way. The concept of non-complete set of properties plays a crucial role in the argument, which also clarifies the physical meaning of th…
Geometric quantifier of the incompatibility of single-particle property attribution in indistinguishable boson systems
Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba（科尔多瓦国立大学数学、天文学、物理与计算学院）；Instituto de Física Enrique Gaviola, CONICET - UNC（恩里克·加维亚拉物理研究所，阿根廷国家科学研究委员会-科尔多瓦国立大学）；Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）；Universidad Nacional de Hurlingham (UNAHUR)（乌尔辛汉姆国立大学）
The Pauli exclusion principle gives an upper bound of 1 on the natural occupation numbers. Recently there has been an intriguing amount of theoretical evidence that there is a plethora of additional generalized Pauli restrictions or (in)equalities, of kinematic nature, satisfied by these numbers. Here for the first time a numerical analysis of the nature of such constraints is effected in real atoms. The inequalities are nearly saturated, or quasi-pinned. For rank-six and rank-seven approximations for lithium, the deviation from saturation is smaller than the lowest occupancy number. For a ran…
Fermionic natural occupation numbers (NON) do not only obey Pauli's famous exclusion principle but are even further restricted to a polytope by the generalized Pauli constraints, conditions which follow from the fermionic exchange statistics. Whenever given NON are pinned to the polytope's boundary the corresponding $N$-fermion quantum state $|Ψ_N\rangle$ simplifies due to a selection rule. We show analytically and numerically for the most relevant settings that this rule is stable for NON close to the boundary, if the NON are non-degenerate. In case of degeneracy a modified selection rule is …
