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David Perez-Garcia

Publications and source records attributed to David Perez-Garcia.

At least 37 records · Page 2Linked to original sources
arXiv2013

Existence of an information unit as a postulate of quantum theory

Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very particular frameworks, like in classical or quantum theory, or more generally, whenever there exists an information unit such that the state of any system can be reversibly encoded in a sufficient number of such units. In this work we show how the abstract formalism of quantum theory can be deduced solely from the existence of an information unit with suitable properties, together with two further natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing the state of a composite system by local measurements. This constitutes a new set of postulates for quantum theory with a simple and direct physical meaning, like the ones of special relativity or thermodynamics, and it articulates a strong connection between physics and information.

quant-ph↗
arXiv2013

Topological order in PEPS: Transfer operator and boundary Hamiltonians

We study the structure of topological phases and their boundaries in the Projected Entangled Pair States (PEPS) formalism. We show how topological order in a system can be identified from the structure of the PEPS transfer operator, and subsequently use these findings to analyze the structure of the boundary Hamiltonian, acting on the bond variables, which reflects the entanglement properties of the system. We find that in a topological phase, the boundary Hamiltonian consists of two parts: A universal non-local part which encodes the nature of the topological phase, and a non-universal part which is local and inherits the symmetries of the topological model, which helps to infer the structure of the boundary Hamiltonian and thus possibly of the physical edge modes.

cond-mat.str-el↗
arXiv2013

Testing microscopic discretization

What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a mathematical theory of the macroscopic fluctuations generated by ensembles of independent microscopic discrete systems. We provide algorithms to decide which multivariate gaussian distributions can be approximated by sums of finitely-valued random vectors. We study non-trivial cases where the microscopic variables have an unbounded range, as well as asymptotic scenarios with infinitely many macroscopic variables. From a foundational point of view, our results imply that bipartite gaussian states of light cannot be understood as beams of independent d-dimensional particle pairs. It is also shown that the classical description of certain macroscopic optical experiments, as opposed to the quantum one, requires variables with infinite cardinality spectra.

quant-ph↗
arXiv2012

Entanglement, fractional magnetization and long-range interactions

Based on the theory of Matrix Product States, we give precise statements and complete analytical proofs of the following claim: a large fractionalization in the magnetization or the need of long-range interactions imply large entanglement in the state of a quantum spin chain.

quant-ph↗
arXiv2012

Preparing topological PEPS on a quantum computer

Simulating of exotic phases of matter that are not amenable to classical techniques is one of the most important potential applications of quantum information processing. We present an efficient algorithm for preparing a large class of topological quantum states -- the G-injective Projected Entangled Pair States (PEPS) -- on a quantum computer. Important examples include the resonant valence bond (RVB) states, conjectured to be topological spin liquids. The runtime of the algorithm scales polynomially with the condition number of the PEPS projectors, and inverse-polynomially in the spectral gap of the PEPS parent Hamiltonian.

quant-ph↗
arXiv2012

Resonating valence bond states in the PEPS formalism

We study resonating valence bond (RVB) states in the Projected Entangled Pair States (PEPS) formalism. Based on symmetries in the PEPS description, we establish relations between the toric code state, the orthogonal dimer state, and the SU(2) singlet RVB state on the kagome lattice: We prove the equivalence of toric code and dimer state, and devise an interpolation between the dimer state and the RVB state. This interpolation corresponds to a continuous path in Hamiltonian space, proving that the RVB state is the four-fold degenerate ground state of a local Hamiltonian on the (finite) kagome lattice. We investigate this interpolation using numerical PEPS methods, studying the decay of correlation functions, the change of overlap, and the entanglement spectrum, none of which exhibits signs of a phase transition.

cond-mat.str-el↗
arXiv2012

An order parameter for symmetry-protected phases in one dimension

We introduce an order parameter for symmetry-protected phases in one dimension which allows to directly identify those phases. The order parameter consists of string-like operators and swaps, but differs from conventional string order operators in that it only depends on the symmetry but not on the state. We verify our framework through numerical simulations for the SO(3) invariant spin-1 bilinear-biquadratic model which exhibits a dimerized and a Haldane phase, and find that the order parameter not only works very well for the dimerized and the Haldane phase, but it also returns a distinct signature for gapless phases. Finally, we discuss possible ways to measure the order parameter in experiments with cold atoms.

cond-mat.str-el↗
arXiv2012

Matrix Product States with long-range Localizable Entanglement

We derive a criterion to determine when a translationally invariant matrix product state (MPS) has long-range localizable entanglement, where that quantity remains finite in the thermodynamic limit. We give examples fulfilling this criterion and eventually use it to obtain all such MPS with bond dimension 2 and 3.

quant-ph↗
arXiv2012

Joint system quantum descriptions arising from local quantumness

Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can always be interpreted as distant measurements of a bipartite quantum state. Here we consider the effect of dropping the assumption of finite dimensionality. Remarkably, we find that the same result holds provided that we relax the tensor structure of space-like separated measurements to mere commutativity. We argue why an extension of this result to tensor representations seems unlikely.

quant-ph↗
arXiv2012

Quantum Steering and Space-Like Separation

In non-relativistic quantum mechanics, measurements performed by separate observers are modeled via tensor products. In Algebraic Quantum Field Theory, though, local observables corresponding to space-like separated parties are just required to commute. The problem of determining whether these two definitions of "separation" lead to the same set of bipartite correlations is known in non-locality as Tsirelson's problem. In this article, we prove that the analog of Tsirelson's problem in steering scenarios is false. That is, there exists a steering inequality that can be violated or not depending on how we define space-like separation at the operator level.

quant-ph↗
arXiv2011

Are problems in Quantum Information Theory (un)decidable?

This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of entanglement theory and quantum channels turn out to be decidable via quantifier elimination as long as they admit a compact formulation without quantification over integers. For many asymptotically defined properties which have to hold for all or for one integer N, however, effective procedures seem to be difficult if not impossible to find. We review some of the main tools for (dis)proving decidability and apply them to problems in quantum information theory. We find that questions like "can we overcome fidelity 1/2 w.r.t. a two-qubit singlet state?" easily become undecidable. A closer look at such questions might rule out some of the "single-letter" formulas sought in quantum information theory.

quant-ph↗
arXiv2011

Classifying quantum phases using Matrix Product States and PEPS

We give a classification of gapped quantum phases of one-dimensional systems in the framework of Matrix Product States (MPS) and their associated parent Hamiltonians, for systems with unique as well as degenerate ground states, and both in the absence and presence of symmetries. We find that without symmetries, all systems are in the same phase, up to accidental ground state degeneracies. If symmetries are imposed, phases without symmetry breaking (i.e., with unique ground states) are classified by the cohomology classes of the symmetry group, this is, the equivalence classes of its projective representations, a result first derived in [X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B 83, 035107 (2011); arXiv:1008.3745]. For phases with symmetry breaking (i.e., degenerate ground states), we find that the symmetry consists of two parts, one of which acts by permuting the ground states, while the other acts on individual ground states, and phases are labelled by both the permutation action of the former and the cohomology class of the latter. Using Projected Entangled Pair States (PEPS), we subsequently extend our framework to the classification of two-dimensional phases in the neighborhood of a number of important cases, in particular systems with unique ground states, degenerate ground states with a local order parameter, and topological order. We also show that in two dimensions, imposing symmetries does not constrain the phase diagram in the same way it does in one dimension. As a central tool, we introduce the isometric form, a normal form for MPS and PEPS which is a renormalization fixed point. Transforming a state to its isometric form does not change the phase, and thus, we can focus on to the classification of isometric forms.

cond-mat.str-el↗
arXiv2011

A physical approach to Tsirelson's problem

Tsirelson's problem deals with how to model separate measurements in quantum mechanics. In addition to its theoretical importance, the resolution of Tsirelson's problem could have great consequences for device independent quantum key distribution and certified randomness. Unfortunately, understanding present literature on the subject requires a heavy mathematical background. In this paper, we introduce quansality, a new theoretical concept that allows to reinterpret Tsirelson's problem from a foundational point of view. Using quansality as a guide, we recover all known results on Tsirelson's problem in a clear and intuitive way.

quant-ph↗
arXiv2011

Tripartite probability distributions and communication complexity

We show that every tripartite quantum correlation generated with a Schmidt state (in particular every correlation generated with the GHZ state) can be simulated with the sending of two bits of classical communication from Alice to Bob and Charlie plus the sending of two bits of classical communication from Bob to Charlie. This extends recent results which showed that the maximal violation of Bell inequalities attainable by these correlations is uniformly bounded. For simplicity, we state and prove the result for three parties, but the generalization to the case of $n$ parties follows easily. We also show that every $n$-partite probability distribution generated with local resources plus $c$-bits of local communication can violate a Bell inequality by at most a factor of $2^c$.

quant-ph↗
arXiv2010

Sequential Strong Measurements and Heat Vision

We study scenarios where a finite set of non-demolition von-Neumann measurements are available. We note that, in some situations, repeated application of such measurements allows estimating an infinite number of parameters of the initial quantum state, and illustrate the point with a physical example. We then move on to study how the system under observation is perturbed after several rounds of projective measurements. While in the finite dimensional case the effect of this perturbation always saturates, there are some instances of infinite dimensional systems where such a perturbation is accumulative, and the act of retrieving information about the system increases its energy indefinitely (i.e., we have `Heat Vision'). We analyze this effect and discuss a specific physical system with two dichotomic von-Neumann measurements where Heat Vision is expected to show.

quant-ph↗
arXiv2010

PEPS as ground states: degeneracy and topology

We introduce a framework for characterizing Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us to understand how PEPS appear as ground states of local Hamiltonians with finitely degenerate ground states and to characterize the ground state subspace. Subsequently, we apply our framework to show how the topological properties of these ground states can be explained solely from the symmetry: We prove that ground states are locally indistinguishable and can be transformed into each other by acting on a restricted region, we explain the origin of the topological entropy, and we discuss how to renormalize these states based on their symmetries. Finally, we show how the anyonic character of excitations can be understood as a consequence of the underlying symmetries.

quant-ph↗
arXiv2010

The inverse eigenvalue problem for quantum channels

Given a list of n complex numbers, when can it be the spectrum of a quantum channel, i.e., a completely positive trace preserving map? We provide an explicit solution for the n=4 case and show that in general the characterization of the non-zero part of the spectrum can essentially be given in terms of its classical counterpart - the non-zero spectrum of a stochastic matrix. A detailed comparison between the classical and quantum case is given. We discuss applications of our findings in the analysis of time-series and correlation functions and provide a general characterization of the peripheral spectrum, i.e., the set of eigenvalues of modulus one. We show that while the peripheral eigen-system has the same structure for all Schwarz maps, the constraints imposed on the rest of the spectrum change immediately if one departs from complete positivity.

quant-ph↗