We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of d-level systems. The ground state energy eigenvalue and its derivatives, whose non-analyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signalled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.PACS numbers: 03.65. Ud,75.10.Pq Recently, a great deal of effort has been devoted to the understanding of the connections between quantum information [1] and the theory of quantum critical phenomena [2]. A key novel observation is that quantum entanglement can play an important role in a quantum phase transition (QPT) [3,4,5,6,7,8,9,10,11,12,13,14,15,16]. In particular, for a number of spin systems, it has been shown that QPTs are signalled by a critical behavior of bipartite entanglement as measured, for instance, in terms of the concurrence [17]. For the case of second-order QPTs (2QPTs), the critical point was found to be associated to a singularity in the derivative of the ground state concurrence, as first illustrated, for the transverse field Ising chain, in Ref. [3], and generalized in Refs. [4,5,6] (see Refs. [7,8,9,10,11] for an analysis in terms of other entanglement measures). In the case of first-order QPTs (1QPTs), discontinuities in the ground state concurrence were shown to detect the QPT [12,13,14]. The studies conducted to date are based on the analysis of particular many-body models. Hence the general connection between bipartite entanglement and QPTs is not yet well understood. The aim of this work is to discuss, in a general framework, how bipartite entanglement can be related to a QPT characterized by nonanalyticities in the energy.Expectation values and the reduced density matrix.-The most general Hamiltonian of non-identical particles, up to two-body interactions, readswhere {|α i } is a basis for the Hilbert space, α, β, γ, δ ∈ {0, 1, ..., d − 1}, and i, j enumerate N "qudits" (dlevel systems).Let E = ψ|H|ψ be the energy in a non-degenerate eigenstate |ψ of the Hamiltonian. The two-spin reduced density operatorρ ij is given byρ ij = m m|ψ ψ|m , with m running over all the d N −2 orthonormal basis vectors, excluding qudits i and j.ρ ij has a d 2 × d 2 matrix representation ρ ij , with elements ρ with U(ij) denoting a d 2 × d 2 matrix whose elements are, where N i is the number of qudits that qudit i interacts with, and δ j βδ is the Kronecker symbol on qudit j. Clearly, Eq. (2) holds not only for the Hamiltonian operator but for any observable. Indeed, it turns out that the expectation value (or eigenvalue, for an eigenstate) of any two-qudit observable in an arbitrary state |ψ is a ...

We show how to realize, by means of non-abelian quantum holonomies, a set of universal quantum gates acting on decoherence-free subspaces and subsystems. In this manner we bring together the quantum coherence stabilization virtues of decoherence-free subspaces and the fault-tolerance of all-geometric holonomic control. We discuss the implementation of this scheme in the context of quantum information processing using trapped ions and quantum dots. Introduction.-The implementation of quantum information processing (QIP) poses an unprecedented challenge to our capabilities of controlling the dynamics of quantum systems. The challenge is twofold and somewhat contradictory. On the one hand one must (i) maintain as much as possible the isolation of the computing degrees of freedom from the environment, in order to preserve their "quantumness"; on the other hand (ii) their dynamical evolution must be enacted with extreme precision in order to avoid errors whose propagation would quickly spoil the whole quantum computational process. To cope with the decoherence problem (i), active strategies such as quantum error correcting codes [1], as well as passive ones such as error avoiding codes [2], have been contrived. The latter are based on the symmetry structure of the system-environment interaction, which under certain circumstances allows for the existence of decoherence-free subspaces (DFS), i.e., subspaces of the system Hilbert state-space over which the dynamics is still unitary. DFSs have been experimentally demonstrated in a host of physical systems (e.g., [3,4]). The DFS idea of symmetry-aided protection has been generalized to noiseless subsystems [5], experimentally tested in Ref. [6].

A decoherence-free subspace (DFS) isolates quantum information from deleterious environmental interactions. We give explicit sequences of strong and fast ("bang-bang", BB) pulses that create the conditions allowing for the existence of DFSs that support scalable, universal quantum computation. One such example is the creation of the conditions for collective decoherence, wherein all system particles are coupled in an identical manner to their environment. The BB pulses needed for this are generated using only the Heisenberg exchange interaction. In conjunction with previous results, this shows that Heisenberg exchange is all by itself an enabler of universal fault tolerant quantum computation on DFSs.Since the discovery of quantum error correcting codes (QECCs) [1], an arsenal of powerful methods has been developed for overcoming the problem of decoherence that plagues quantum computers (QCs). A QECC is a closedloop procedure, that involves frequent error identification via non-destructive measurements, and concommitant recovery steps. Alternatively, decoherence-free subspaces (DFSs) [2][3][4] and subsystems [5], and dynamical decoupling, or "bang-bang" (BB) [6][7][8][9][10][11], are open-loop methods. A DFS is subspace of the system Hilbert space which is isolated, by virtue of a dynamical symmetry, from the system-bath interaction. The BB method is a close cousin of the spin-echo effect. All decoherencereduction methods make assumptions about the system (S)-bath (B) coupling, embodied in a Hamiltonian of the general form H = H S ⊗ I B + H SB + I S ⊗ H B . Here I is an identity operator and H SB is the system-bath interaction term, which can be expanded as a sum over linear, bilinear, and higher order coupling terms:Specializing to qubits, a typical assumption is p = 1,where α ∀i), important, respectively for the QECC and DFS methods. The bilinear terms are in general descibed by a second-rank tensor G ij , so that H ij = σ i ·G ij · σ j . One of the main problems in applying the various decoherence-countering strategies is that, typically, the conditions under which they apply are not wholly satisfied experimentally [12]. This problem is particularly severe for the DFS method, since it demands a high degree of symmetry in the systembath interaction. Two main cases are known that admit scalable DFSs (i.e., subspaces that occupy a finite fraction of the system Hilbert space): collective decoherence [2-4] and the model of "multiple qubit errors" (MQE) [13]. Collective decoherence, as defined above, assumes qubit-permutation-invariant system-bath coupling. This may be satisfied at ultralow temperatures in solid-state QC implementations, provided the dominant decoherence mechanism is due to coupling to a long-wavelength reservoir, e.g., phonons [14,15]. MQE assumes that the system terms appearing in H SB generate an Abelian group under multiplication (referred to below as the "error group"). This is a somewhat artificial model that typically imposes severe restrictions on B i and G ij (examples are given below). On...

Density functional theory (DFT) is shown to provide a novel conceptual and computational framework for entanglement in interacting many-body quantum systems. DFT can, in particular, shed light on the intriguing relationship between quantum phase transitions and entanglement. We use DFT concepts to express entanglement measures in terms of the first or second derivative of the ground state energy. We illustrate the versatility of the DFT approach via a variety of analytically solvable models. As a further application we discuss entanglement and quantum phase transitions in the case of mean field approximations for realistic models of many-body systems.

We analytically identify sufficient conditions for manifesting thermal rectification in two-terminal junctions, including a subsystem connected to two reservoirs, within the quantum master equation formalism. We recognize two classes of rectifiers. In type A rectifiers, the reservoirs' energy structure is dissimilar. In type B rectifiers, the baths are identical but include particles whose statistics differ from that of the subsystem, to which they asymmetrically couple. Our study applies to various hybrid junctions including metals, dielectrics, and spins.

We review the quantum adiabatic approximation for closed systems, and its recently introduced generalization to open systems (M.S. Sarandy and D.A. Lidar, e-print quant-ph/0404147). We also critically examine a recent argument claiming that there is an inconsistency in the adiabatic theorem for closed quantum systems [K.P. Marzlin and B.C. Sanders, Phys. Rev. Lett. 93, 160408 (2004)] and point out how an incorrect manipulation of the adiabatic theorem may lead one to obtain such an inconsistent result.

The severe acute respiratory syndrome virus 2 (SARS-CoV-2) invades host cells by interacting with receptors/co-receptors, as well as other co-factors, via its spike (S) protein that further mediates the fusion between viral and cellular membranes. The host membrane protein angiotensin-converting enzyme 2 (ACE2) is the major receptor for SARS-CoV-2 and a critical determinant for its cross-species transmission. Additionally, some auxiliary receptors and co-factors are also involved which would expand the host/tissue tropism of SARS-CoV-2. After receptor engagement, certain proteases are required to cleave the S protein to trigger its fusogenic activity. In this review, we discuss the recent advancement in understanding the molecular events during SARS-CoV-2 entry which would contribute to developing vaccines and therapeutics.

Inherent gate errors can arise in quantum computation when the actual system Hamiltonian or Hilbert space deviates from the desired one. Two important examples we address are spin-coupled quantum dots in the presence of spin-orbit perturbations to the Heisenberg exchange interaction, and off-resonant transitions of a qubit embedded in a multilevel Hilbert space. We propose a ``dressed qubit'' transformation for dealing with such inherent errors. Unlike quantum error correction, the dressed qubits method does not require additional operations or encoding redundancy, is insenstitive to error magnitude, and imposes no new experimental constraints.Comment: Replaced with published versio