Session D30: Focus Session: Quantum Information for Quantum Foundations - Entanglement and Causal Structure

Quantum measurement bounds beyond uncertainty relations

Quantum measurements are limited by bounds such as the Heisenberg uncertainty relations which limit the accuracy of measuring a quantity via the standard deviation of the conjugate one. This talk shows that the accuracy of measuring a quantity such as phase or time is limited by the expectation value of the conjugate quantity. This result proves the long-standing conjecture -- recently challenged -- that the ultimate phase-precision limit in interferometry is lower bounded by the inverse of the total number of photons employed in the estimation process.   

Quantum sharability: Entanglement is less monogamous than you think

One of the essential features of entanglement is monogamy. However, is it well known that there are entangled states which are not monogamous. A generalization of the monogamy property is provided by the concept of sharability. For bipartite states, we say a state (or relationship) is $1$-$n$ sharable if a subsystem can simultaneously share this relationship with $n$ other subsystems. Any state with a limited sharing capacity is entangled, and the strictness of the limit corresponds to how entangled the state is. We present the most interesting findings of sharability of bipartite qubit and qudit states and describe an application to quantum teleportation.   

New entanglement properties in systems of higher-spin particles

We describe a new entanglement property of four-qutrit states that is inaccessable to any number of qubits. In such states, every particle is equally entangled with all others, as in GHZ states, but the entanglement is more robust than that of any four-qubit state. We describe the entanglement properties of related generalized graph states of three-state and five-state particles, and show how these suggest that new entanglement properties will emerge more generally for systems of p+1 particles, each having p states, where p is a prime number.   

Optimal Probabilistic Simulation of Quantum Channels from the Future to the Past

We introduce the study of probabilistic protocols that simulate quantum channels transforming input states in the future into output states in the past. The maximum probability for such a simulation is set by causality and, we claim, depends on the amount and type (classical or quantum) of information the given channel can transmit. In particular, we focus on probabilistic teleportation with multiple copies of input and output. We show that as the number of input copies increases, the maximum probability of successful teleportation increases, a feature that is impossible in classical physics. As the number of input copies tends to infinity, the teleportation probability converges to the maximum probability for the simulation of an ideal classical channel from the future to the past.   

The asymmetry properties of pure quantum states

The \emph{asymmetry properties} of a state relative to some symmetry group specify how and to what extent the given symmetry is broken by the state. Characterizing these is found to be surprisingly useful for addressing a very common problem: to determine what follows from a system's dynamics (possibly open) having that symmetry. We demonstrate and exploit the fact that the asymmetry properties of a state can be understood in terms of information-theoretic concepts. We show that for a pure state $\psi$ and a symmetry group $G$, they are completely specified by the characteristic function of the state, defined as $\chi_{\psi}(g)\equiv \langle \psi|U(g)|\psi\rangle$ where $g\in G$ and $U$ is the unitary representation of interest. Based on this observation, we study several important problems about the interconversion of pure states under symmetric dynamics such as determining the conditions for reversible transformations, deterministic irreversible transformations and asymptotic transformations.   

Equilibration of Global Observables to Microcanoical Measure for Complex Systems

In the last few years we have seen significant progress in understanding how the canonical features of quantum statistical mechanics can be derived rigorously from an exact treatment of the underlying quantum mechanical system. Here we consider a related problem: we determine sufficient conditions under which one can derive an effective equilibration to the microcanonical ensemble for the measurement statistics of the global observables of a closed system. Our central assumption is that the unitary time-evolution operator of the system is sufficiently complex when expressed in the eigenbasis of the observable of interest that its eigenstates can be modeled by a typical unitary chosen from the Haar measure (or Circular Unitary Ensemble). This assumption is well-motivated from numerical studies in the field of quantum chaos where this property has been observed for simple model systems whose classical counterparts are globally chaotic. Further, we discuss the time scale on which equilibration occurs in the context of two models for the eigenvalues of the dynamical system. We argue that our results are a natural consequence of an epistemic view of pure quantum states, but may be surpising or even controversial for adherents of other interpretational perspectives.   

Coarse-graining makes it hard to see micro-macro entanglement

Observing quantum effects such as superpositions and entanglement in macroscopic systems requires not only a system that is well protected against environmental decoherence, but also sufficient measurement precision. Motivated by recent experiments, we study the effects of coarse-graining in photon number measurements on the observability of micro-macro entanglement that is created by greatly amplifying one photon from an entangled pair. We compare the results obtained for a unitary quantum cloner, which generates micro-macro entanglement, and for a measure-and-prepare cloner, which produces a separable micro-macro state. We show that the distance between the probability distributions of results for the two cloners approaches zero for a fixed moderate amount of coarse-graining. Proving the presence of micro-macro entanglement therefore becomes progressively harder as the system size increases.   

On the quantification of resourcefulness in quantum information

Quantum information processing tasks cannot be performed for free; several types of informational resource must be consumed. Such resources are often expensive: entanglement, for example, is quite difficult to distribute between distant parties. Efficient consumption of informational resources is therefore desirable for practical quantum information processing. Determination of the efficiency of a given protocol requires some method of quantifying the resources present before and after the implementation of a protocol. In the prototypical case of entanglement, one or several entanglement monotones are often used to determine the entanglement cost of a protocol. The mathematical definition of an entanglement monotone has undergone multiple revisions since its formal introduction by Vidal. Currently, a real-valued function of quantum states is considered an entanglement monotone if the function is monotonically decreasing under application of channels that can be enacted using only local operations with classical communication. In this lecture, I argue that even this simple definition is unnecessarily restrictive for fully characterising the entanglement of a state and propose a more general scheme of relative quantifiers of entanglement.   

Scalar Fields via Causal Tapestries

Causal tapestries provide a framework for implementing an explicit Process Theory approach to quantum foundations which models information flow within a physical system. We consider event-transition tapestry pairs. An event tapestry ${\rm O}$ is a 4-tuple (L, K, M, \underline {I}$_{p })$ where K is an index set of cardinality $\kappa $, M = $M$ x F($M)$ x D x P($M')$ a mathematical structure with $M$ a causal space, F($M)$ a function space, D a descriptor space, P($M')$ either a Lie algebra or tangent space on a manifold $M'$, \underline {I}$_{p }$ an event tapestry. L consists of elements of the form [$n$]$<$\textit{$\alpha $}$>${\{}$G${\}}, $n$ in K, \textit{$\alpha $} in M and $G$ an acyclic directed graph whose vertex set is a subset of L$_{p}$ Likewise, a transition tapestry $\Pi $ is a 4-tuple (L', K', M', \underline {I'}$_{p })$ where M' = $M'$ x F($M')$ x D' x P'($M)$. The dynamic generates a consistent succession of ${\rm O}-\Pi $ pairs by means of a game based on the technique of forcing used in logic to generate models. This dynamic has previously been shown to be compatible with Lorentz invariance. An application of this approach to model scalar fields is presented in which each informon is associated with a function of the form $_{ }$ f($\pi $k$_{1 }$/$\sigma _{1 }$,{\ldots},$\pi $k$_{N }$/$\sigma _{N}$ )sin ( $\sigma _{1 }$t$_{1 }$--$\pi $k$_{1 })$/ ( $\sigma _{1 }$t$_{1 }$--$\pi $k$_{1 })$ {\ldots}.sin ( $\sigma _{N }$t$_{N }$--$\pi $k$_{N })$/ ( $\sigma _{N }$t$_{N }$--$\pi $k$_{N })$ and the WSK interpolation theorem is used to generate the resulting scalar field on the causal manifold.   

Topology of Quantum Discord

Quantum discord is arguably a more sensitive measure of quantum correlations than quantum entanglement, and may be able to serve as a resource for quantum computation. All quantum correlations are subject to destruction by external noise. The route by which this destruction takes place depends on the shape of the hypersurface of zero discord in the space of generalized Bloch vectors. In the case of 2 qubits, we show that, except at the origin, this hypersurface is a 9-dimensional manifold with boundary embedded in a 15-dimensional background space. This is done by computing the tangent vectors explicitly and verifying that there are no self-intersections. We discuss the implications for the time evolution of discord in physical models, which contrasts sharply with the evolution of entanglement.   

Quantumness versus entanglement in quantum measurements

We analyze a hierarchy of quantumness measures for composite systems, defined in terms of the entanglement necessarily created between systems and apparata during local measurements. We prove that the quantumness so defined is always greater than intra-systems entanglement, establishing a firm ordering relation between different non-classical features of correlations. We analyze qualitatively and quantitatively the flow of correlations in iterated measurements, showing that quantumness and entanglement can never decrease along von Neumann chains. Our results provide a comprehensive framework to understand and quantify general signatures of quantumness in multipartite states, and prove how useful the broader study of the quantumness of correlations can be to shed light on issues in quantum information processing, in the quantum theory of measurement and in quantum foundations.   

Operational interpretation of the G-asymmetry for Abelian groups

In a reference frame alignment protocol the sender, Alice, prepares a quantum system in a state $ket{\psi}$, that serves as a token of her reference frame, and sends this system to a receiver, Bob, who performs a measurement and learns about the reference frame. We derive the state and measurement that maximize the accessible information in a reference frame alignment protocol. We show that in the limit where a large number of systems are sent, the accessible information per copy equals the Holevo bound. The latter was shown to be equal to the relative entropy of frameness, or $G$-asymmetry, of the state $ket{\psi}$, a measure of resourcefulness analogous to the relative entropy of entanglement. We show that for a reference frame alignment protocol, associated with a finite abelian group, $Z_N$, or the continuous group $U(1)$, associated with the important case of photon number super-selection, the rate of accessible information is quantified by the linearized, regularized $G$-asymmetry. Our result provides an information theoretic operational interpretation for the $G$-asymmetry that has been thus far lacking.   

Considerations of Closed Systems that Measure Particles

The Measurement Problem has been of fundamental concern since the discovery of Schrodinger's equation. We have been developing a framework for which this problem can be considered under the assumption that the detector is a closed system. Considerations that such systems satisfy will be presented. Questions of whether or not such a framework is possible for which the various considerations can be met will be presented. Related existing work in the literature will be presented.   

Is entanglement signaling really impossible?

Quantum entanglement cannot be used as a communication channel without an auxiliary light speed limited classical key to unlock the message at the receiver? Hermitian observables guarantee orthogonal sender base states that erase any nonlocal influence of the sender settings on the detection probabilities at the receiver. However, this is no longer true when the entangled whole has different macro-quantum coherent Glauber sender states. Glauber states are non-orthogonal eigenstates of the non-Hermitian photon destruction operator. The Born probability interpretation breaks down because of ``phase rigidity'' (P.W. Anderson's ``More is different''). This is a new regime that is to orthodox quantum theory what general relativity is to special relativity. Antony Valentini has argued that the breakdown of the Born probability rule entails ``signal non locality'' (aka entanglement signals). The space-time interval between the sending and the receiving irreversible measurements is irrelevant depending only on the free will of the local observers. That is, this is a pre-metrical topological information effect. There is asymmetry between the sending and the receiving. Therefore, there is no ambiguity between active (retro) cause and passive effect.