arXiv subjects

N. Canosa

Publications and source records attributed to N. Canosa.

At least 19 recordsLinked to original sources

arXiv2026

History state formalism for time series with application to finance

We present a method for analyzing general time series by employing the history state formalism of quantum mechanics. This formalism allows us to describe a complete evolution based on a single quantum state, the history state, which simultaneously includes -also as a quantum system- the reference clock. It naturally leads to the concept of system-time entanglement, with the ensuing entanglement entropy constituting a measure of the effective number of distinguishable states visited in the history. Through a quantum coherent state embedding of the time series data, it is then possible to associate a quantum history state to the series. The gaussian overlap between these coherent states provides thus a smooth measure of distinguishability between the series data. The eigenvalues of the corresponding overlap matrix determine in fact the entanglement spectrum and entropy of the history state, which provide a rigorous characterization of the evolution. As illustration, the formalism is applied to typical financial time-series data. Through the entanglement entropy and spectrum, different evolution regimes can be identified. Entanglement based volatility indicators are also derived, and compared with standard volatility measures.

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arXiv2023

Covariance-based method for eigenstate factorization and generalized singlets

We derive a general method for determining the necessary and sufficient conditions for exact factorization $|\Psi\rangle=\otimes_p |\psi_p\rangle$ of an eigenstate of a many-body Hamiltonian $H$, based on the quantum covariance matrix of the relevant local operators building the Hamiltonian. The "site" $p$ can be either a single component or a group of subsystems. The formalism is then used to derive exact dimerization and clusterization conditions in spin systems, covering from spin-$s$ singlets and clusters coupled to $0$ total spin to general nonmaximally entangled spin-$s$ dimers (generalized singlets). New results for field induced dimerization in anisotropic $XYZ$ arrays under a magnetic field are obtained.

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arXiv2022

History states of one-dimensional quantum walks

We analyze the application of the history state formalism to quantum walks. The formalism allows one to describe the whole walk through a pure quantum history state, which can be derived from a timeless eigenvalue equation. It naturally leads to the notion of system-time entanglement of the walk, which can be considered as a measure of the number of orthogonal states visited in the walk. We then focus on one-dimensional discrete quantum walks, where it is shown that such entanglement is independent of the initial spin orientation for real Hadamard-type coin operators and real initial states (in the standard basis) with definite site parity. Moreover, in the case of an initially localized particle it can be identified with the entanglement of the unitary global operator that generates the whole history state, which is related to its entangling power and can be analytically evaluated. Besides, it is shown that the evolution of the spin subsystem can also be described through a spin history state with an extended clock. A connection between its average entanglement (over all initial states) and that of the operator generating this state is also derived. A quantum circuit for generating the quantum walk history state is provided as well.

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arXiv2022

Ground state separability and criticality in interacting many-particle systems

We analyze exact ground state (GS) separability in general $N$ particle systems with two-site couplings. General necessary and sufficient conditions for full separability, in the form of one and two-site eigenvalue equations, are first derived. The formalism is then applied to a class of $SU(n)$-type interacting systems, where each constituent has access to $n$ local levels, and where the total number parity of each level is preserved. Explicit factorization conditions for parity-breaking GS's are obtained, which generalize those for $XYZ$ spin systems and correspond to a fundamental GS multilevel parity transition where the lowest $2^{n-1}$ energy levels cross. We also identify a multicritical factorization point with exceptional high degeneracy proportional to $N^{n-1}$, arising when the total occupation number of each level is preserved, in which any uniform product state is an exact GS. Critical entanglement properties (like full range pairwise entanglement) are shown to emerge in the immediate vicinity of factorization. Illustrative examples are provided.

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arXiv2020

Nonlinear effects on the dynamics of quantum harmonic modes coupled through angular momentum

We investigate nonlinear effects on the dynamics of entanglement and other quantum observables in a system of two harmonic modes coupled through angular momentum. The nonlinearity arises from a quartic anharmonic term in each mode. The emergence and evolution of entanglement, non-gaussianity, photon number, photon antibunching and squeezing are examined for different initial product coherent states and couplings, through exact diagonalization in a truncated basis. It is shown that the anharmonic terms, even if weak, can lead to very significant effects for such initial states, considerably enhancing and stabilizing entanglement and leading to a non negligible non-gaussianity of the evolved states. They also affect other observables, stabilizing the dynamics after an initial transient regime, for not too small initial average populations of each mode. Analytic short-time approximate expressions are also provided.

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arXiv2020

Separability and parity transitions in $XYZ$ spin systems under nonuniform fields

We examine the existence of completely separable ground states (GS) in finite spin-$s$ arrays with anisotropic $XYZ$ couplings, immersed in a non-uniform magnetic field along one of the principal axes. The general conditions for their existence are determined. The analytic expressions for the separability curve in field space, and for the ensuing factorized state and GS energy, are then derived for alternating solutions, valid for any spin and size. They generalize results for uniform fields and show that nonuniform fields can induce GS factorization also in systems which do not exhibit this phenomenon in a uniform field. It is also shown that such curve corresponds to a fundamental $S_z$-parity transition of the GS, present for any spin and size, and that two different types of GS parity diagrams can emerge, according to the anisotropy. The role of factorization in the magnetization and entanglement of these systems is also analyzed, and analytic expressions at the borders of the factorizing curve are provided. Illustrative examples for spin pairs and chains are as well discussed.

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arXiv2019

Conditional states and entropy in qudit-qubit 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 post-measurement qudit states lie on the surface of an ellipsoid, for a measurement at the qudit we show that the set of post-measurement 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 cone-like and triangle-like 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.

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arXiv2019

Inducing critical phenomena in spin chains through sparse alternating fields

We analyze the phase diagram of the exact ground state (GS) of spin-$s$ chains with ferromagnetic $XXZ$ couplings under $n$-alternating field configurations, i.e, sparse alternating fields having nodes at $n-1$ contiguous sites. It is shown that such systems can exhibit a non-trivial magnetic behavior, which can differ significantly from that of the standard ($n=1$) alternating case and enable mechanisms for controlling their magnetic and entanglement properties. The boundary in field space of the fully aligned phase can be determined analytically $\forall\,n$, and shows that it becomes reachable only above a threshold value of the coupling anisotropy $J_z/J$, which depends on $n$ but is independent of the system size. Below this value the maximum attainable magnetization becomes much smaller. We then show that the GS can exhibit significant magnetization plateaus, persistent for large systems, at which the magnetization per site $m$ obeys the quantization rule $2n(s-m)=integer$, consistent with the Oshikawa, Yamanaka and Affleck (OYA) criterion. We also identify the emergence of field induced spin polymerization, which explains the presence of such plateaus. Entanglement and field induced frustration effects are also analyzed.

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arXiv2017

Quantum Discord and entropic measures of quantum correlations: Optimization and behavior in finite $XY$ spin chains

We discuss a generalization of the conditional entropy and one-way information deficit in quantum systems, based on general entropic forms. The formalism allows to consider simple entropic forms for which a closed evaluation of the associated optimization problem in qudit-qubit systems is shown to become feasible, allowing to approximate that of the quantum discord. As application, we examine quantum correlations of spin pairs in the exact ground state of finite $XY$ spin chains in a magnetic field through the quantum discord and information deficit. While these quantities show a similar behavior, their optimizing measurements exhibit significant differences, which can be understood and predicted through the previous approximations. The remarkable behavior of these quantities in the vicinity of transverse and non-transverse factorizing fields is also discussed.

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arXiv2017

Factorization and criticality in finite XXZ systems of arbitrary spin

We analyze ground state (GS) factorization in general arrays of spins $s_i$ with $XXZ$ couplings immersed in nonuniform fields. It is shown that an exceptionally degenerate set of completely separable symmetry-breaking GS's can arise for a wide range of field configurations, at a quantum critical point where all GS magnetization plateaus merge. Such configurations include alternating fields as well as zero bulk field solutions with edge fields only and intermediate solutions with zero field at specific sites, valid for $d$-dimensional arrays. The definite magnetization projected GS's at factorization can be analytically determined and depend only on the exchange anisotropies, exhibiting critical entanglement properties. We also show that some factorization compatible field configurations may result in field-induced frustration and nontrivial behavior at strong fields.

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arXiv2017

Entanglement and coherence in a spin-s XXZ system under non-uniform fields

We investigate entanglement and coherence in an $XXZ$ spin-$s$ pair immersed in a non-uniform transverse magnetic field. The ground state and thermal entanglement phase diagrams are analyzed in detail in both the ferromagnetic and antiferromagnetic cases. It is shown that a non-uniform field enables to control the energy levels and the entanglement of the corresponding eigenstates, making it possible to entangle the system for any value of the exchange couplings, both at zero and finite temperatures. Moreover, the limit temperature for entanglement is shown to depend only on the difference $|h_1-h_2|$ between the fields applied at each spin, leading for $T>0$ to a separability stripe in the $(h_1,h_2)$ field plane such that the system becomes entangled above a threshold value of $|h_1-h_2|$. These results are demonstrated to be rigorously valid for any spin $s$. On the other hand, the relative entropy of coherence in the standard basis, which coincides with the ground state entanglement entropy at $T=0$ for any $s$, becomes non-zero for any value of the fields at $T>0$, decreasing uniformly for sufficiently high $T$. A special critical point arising at $T=0$ for non-uniform fields in the ferromagnetic case is also discussed

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arXiv2016

Pair entanglement in dimerized spin-s chains

We examine the pair entanglement in the ground state of finite dimerized spin-$s$ chains interacting through anisotropic $XY$ couplings immersed in a transverse magnetic field, by means of a self-consistent pair mean field approximation. The approach, which makes no a priori assumptions on the pair states, predicts, for sufficiently low coupling between pairs, $2s$ distinct dimerized phases for increasing fields below the pair factorizing field, separated by spin parity breaking phases. The dimerized phases lead to approximate magnetization and pair entanglement plateaus, while the parity breaking phases are characterized by weak pair entanglement but non-negligible entanglement of the pair with the rest of the system. These predictions are confirmed by the exact results obtained in finite $s=1$ and $s=3/2$ chains. It is also shown that for increasing values of the spin $s$, the entanglement of an isolated pair, as measured by the negativity, rapidly saturates in the anisotropic $XY$ case but increases as $s^{1/2}$ in the $XX$ case, reflecting a distinct single spin entanglement spectrum.

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arXiv2016

Factorization in XYZ spin systems under general fields and separable ground state engineering

We discuss ground state factorization schemes in spin $S$ arrays with general $XYZ$ couplings under general magnetic fields, not necessarily uniform or transverse. It is first shown that given arbitrary spin alignment directions at each site, nonzero couplings between any pair and fields at each site always exist such that the ensuing Hamiltonian has an exactly separable eigenstate with the spins pointing along the specified directions. Furthermore, by suitable tuning of the fields this eigenstate can always be cooled down to a nondegenerate ground state. It is also shown that in open one-dimensional systems with arbitrary $XYZ$ first neighbor couplings, at least one separable eigenstate compatible with an arbitrarily chosen spin direction at one site is always feasible if the fields at each site can be tuned. We demonstrate as well that in the vicinity of factorization, i.e., for small perturbations in the fields or couplings, pairwise entanglement reaches full range. Some noticeable examples of factorized eigenstates for uniform couplings are unveiled. The present results open the way for separable ground state engineering. A notation to quantify the complexity of a given type of solution according to the required control on the system couplings and fields is introduced.

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arXiv2016

Conditional purity and quantum correlation measures in two qubit mixed states

We analyze and show experimental results of the conditional purity, the quantum discord and other related measures of quantum correlation in mixed two-qubit states constructed from a pair of photons in identical polarization states. The considered states are relevant for the description of spin pair states in interacting spin chains in a transverse magnetic field. We derive clean analytical expressions for the conditional local purity and other correlation measures obtained as a result of a remote local projective measurement, which are fully verified by the experimental results. A simple exact expression for the quantum discord of these states in terms of the maximum conditional purity is also derived.

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arXiv2016

Separability conditions and limit temperatures for entanglement detection in two qubit Heisenberg XYZ models

We examine the entanglement of general mixed states of a two qubit Heisenberg XYZ chain in the presence of a magnetic field, and its detection by means of different criteria. Both the exact separability conditions and the weaker conditions implied by the disorder and the von Neumann entropic criteria are analyzed. The ensuing limit temperatures for entanglement in thermal states of different XYZ models are then examined and compared with the limit temperature of the symmetry-breaking solution in a mean field type approximation. The latter, though generally lower, can also be higher than the exact limit temperature for entanglement in certain cases, indicating that symmetry-breaking does not necessarily entail entanglement. The reentry of entanglement for increasing temperatures is also discussed.

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arXiv2015

Non-transverse factorizing fields and entanglement in finite spin systems

We determine the conditions for the existence of non-transverse factorizing magnetic fields in general spin arrays with anisotropic XYZ couplings of arbitrary range. It is first shown that a uniform maximally aligned completely separable eigenstate can exist just for fields ${h}_s$ parallel to a principal plane and forming four straight lines in field space, with the alignment direction different from that of ${h}_s$ and determined by the anisotropy. Such state always becomes a non-degenerate ground state (GS) for sufficiently strong (yet finite) fields along these lines, in both ferromagnetic (FM) and antiferromagnetic (AFM) type systems. In AFM chains, this field coexists with the non-transverse factorizing field ${h}'_s$ associated with a degenerate Néel-type separable GS, which is shown to arise at a level crossing in a finite chain. It is also demonstrated for arbitrary spin that pairwise entanglement reaches full range in the vicinity of both ${h}_s$ and ${h}'_s$, vanishing at ${h}_s$ but approaching small yet finite side-limits at ${h}'_s$, which are analytically determined. The behavior of the block entropy and entanglement spectrum in their vicinity is also analyzed.

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arXiv2015

Exact dynamics and squeezing in two harmonic modes coupled through angular momentum

We investigate the exact dynamics of a system of two independent harmonic oscillators coupled through their angular momentum. The exact analytic solution of the equations of motion for the field operators is derived, and the conditions for dynamical stability are obtained. As application, we examine the emergence of squeezing and mode entanglement for an arbitrary separable coherent initial state. It is shown that close to instability, the system develops considerable entanglement, which is accompanied with simultaneous squeezing in the coordinate of one oscillator and the momentum of the other oscillator. In contrast, for weak coupling away from instability, the generated entanglement is small, with weak alternating squeezing in the coordinate and momentum of each oscillator. Approximate expressions describing these regimes are also provided.

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arXiv2015

Generalized entropic criterion for separability

We discuss the entropic criterion for separability of compound quantum systems for general non-additive entropic forms based on arbitrary concave functions $f$. For any separable state, the generalized entropy of the whole system is shown to be not smaller than that of the subsystems, for any choice of $f$, providing thus a necessary criterion for separability. Nevertheless, the criterion is not sufficient and examples of entangled states with the same property are provided. This entails, in particular, that the conjecture about the positivity of the conditional Tsallis entropy for all $q$, a more stringent requirement than the positivity of the conditional von Neumann entropy, is actually a necessary but not sufficient condition for separability in general. The direct relation between the entropic criterion and the largest eigenvalues of the full and reduced density operators of the system is also discussed.

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