Spacetime Replication of Continuous Variable Quantum Information
Grant Salton, Stanford Institute for Theoretical Physics, Stanford University
The theory of relativity requires that no information travel faster than light, whereas the unitarity of quantum mechanics ensures that quantum information cannot be cloned. These conditions provide the basic constraints that appear in information replication tasks, which formalize aspects of the behavior of information in relativistic quantum mechanics. In this article, we provide continuous variable (CV) strategies for spacetime quantum information replication that are directly amenable to optical or mechanical implementation. We use a new class of homologically-constructed CV quantum error correcting codes to provide efficient solutions for the general case of information replication. As compared to schemes encoding qubits, our CV solution requires half as many shares per encoded system. We also provide an optimized five-mode strategy for replicating quantum information in a particular configuration of four spacetime regions designed not to be reducible to previously performed experiments. For this optimized strategy, we provide detailed encoding and decoding procedures using standard optical apparatus and calculate the recovery fidelity when finite squeezing is used. As such we provide a scheme for experimentally realizing quantum information replication using quantum optics.
Vacuum Entanglement Harvesting from the Electromagnetic Field with Hydrogen-like Atoms
Alejandro Pozas-Kerstjens, The Institute of Photonic Sciences (ICFO)
It is known since 1985 that the vacuum state of a scalar quantum field contains both classical and quantum correlations, even between spacelike-separated regions [1,2]. It was later discussed that it is possible to harvest entanglement from the field via locally coupling detectors [3,4,5]. This phenomenon has become known as “vacuum entanglement harvesting”.
In entanglement harvesting, the field-detectors interaction has been earlier modelled via the Unruh-DeWitt Hamiltonian [6]. However, past studies relied on the analysis of simplified scalar fields, which, among other things, fails to capture the features of entanglement harvesting when exchange of angular momentum between detectors and fields is allowed. The proper study of electromagnetic entanglement harvesting requires careful consideration of the shape of the atomic orbitals and the exact gauge-invariant coupling with the field.
In this talk, we will first review some basic interesting features of entanglement harvesting in the usual scalar field-Unruh-DeWitt setup [7], after that we will analyze the harvesting of entanglement from an electromagnetic field beyond the Unruh-DeWitt approximation, considering a realistic interaction through which two fully-featured Hydrogen-like atoms interact with the vacuum state of the (vector) electromagnetic field. Since we carefully considered the angular momentum dynamics in the atom-field interactions we can now discuss, among other features, subtleties that appear due to changes in the relative orientation between the two atoms.
[1] S. J. Summers and R. F. Werner, Phys. Lett. A 110 , 257 (1985). [2] S. J. Summers and R. F. Werner, J. Math. Phys. 28, 2440 (1987). [3] A. Valentini, Phys. Lett. A 153, 321 (1991).
[4] B. Reznik, Foundations of Physics 33, 167 (2003).
[5] B. Reznik, A. Retzker and J. Silman, Phys. Rev. A 71, 042104 (2005).
[6] B. S. DeWitt, S. Hawking, and W. Israel, General Relativity: An Einstein Centenary Survey (Cambridge University Press Cambridge, 1979).
[7] A. PozasKerstjens and E. Martín-Martínez, Phys. Rev. D 92, 064042 (2015).
Work in collaboration with: Eduardo Martín-Martínez
Toward Fermionic Entanglement Harvesting
Allison Sachs, Institute for Quantum Computing, University of Waterloo
The vacuum state of a quantum field, such as the electromagnetic field, possesses correlations, both classical and quantum, between spacelike separated regions [1,2]. By reading out correlations in the vacuum fluctuations, we can gather information about the structure of spacetime [3,4]. Additionally, vacuum correlations can, in principle, be used as a resource for quantum communication and other quantum information tasks. Past works have studied this phenomenon, called entanglement harvesting [5,6], in the case of detectors coupling linearly to a bosonic field, for example, two atoms coupled to the electromagnetic field.
While vacuum entanglement harvesting from a scalar field is well understood, as of today, the entanglement structure of the fermionic vacuum has not been studied in detail. The chief reason is that we lacked an adequate divergence-free equivalent to the Unruh-Dewitt particle detector model for fermionic fields.
Using recently developed renormalized detector models for quadratic coupling to bosonic and fermionic fields [7], we will carry out a comparative study of the phenomenon of entanglement harvesting in different situations. Namely, for detectors coupled linearly to a bosonic vacuum, detectors coupled quadratically to bosonic fields as a lead in to fermionic entanglement harvesting.
We expect that these studies will shed some light on the nature of fermionic field vacuum entanglement, which displays distinctive features not present in the bosonic case as observed in the study of the Unruh effect [8,9].
Work in collaboration with: Eduardo Martín-Martínez and Robert B. Mann.
[1] S. J. Summers and R. F. Werner, Phys. Lett. A 110 , 257 (1985).
[2] S. J. Summers and R. F. Werner, J. Math. Phys. 28, 2
[3] G. V. Steeg and N. C. Menicucci, Phys. Rev. D 79, 044027 (2009).
[4] E. Martin-Martinez, A. R. H. Smith, D. R. Terno, Phys. Rev. D 93, 044001 (2016) [5] A. Valentini, Physics Letters A 153, 321 (1991).
[6] B. Reznik, Foundations of Physics 33, 167 (2003). [7]D .Hümmer,E.Martín-Martínez,andA.Kempf P hys.Rev.D93,024019(2015)
[8] P. M. Alsing, I. Fuentes-Schuller, R. B. Mann, and T. E. Tessier, Phys. Rev. A, 74, 032326 (2006)
[9] N. Friis, P. Köhler, Eduardo Martín-Martínez, and Reinhold A. Bertlmann Phys. Rev. A 84, 062111 (2011), M. Montero and E. Martín-Martínez Phys. Rev. A 83, 062323 (2011), [11] M. Miguel Montero, J. León, and Eduardo Martín-Martínez Phys. Rev. A 84, 042320 (2011)
Emergent Open Dynamics Under General Repeated Interactions
Daniel Grimmer, Institute of Quantum Computing, University of Waterloo
The dynamics of open quantum systems, i.e., of systems interacting with an environment, forms the basis of numerous active areas of research. For instance, understanding and controlling open quantum systems is essential to the development of quantum technologies, such as quantum computers, simulators and sensors, in which the decohering effects of the environment must be suppressed. Open dynamics are also central to more foundational questions such as the quantum measurement problem: whether the formalism of projective measurements must be postulated or whether it emerges naturally from the complex interplay of a quantum system, a detector, and an environment.
We will discuss the emergent open dynamics of a quantum system which undergoes repeated unitary interactions with a sequence of ancillary systems. We will review under what general circumstances the dynamics emerging out of these fast repeated interaction is unitary [1] and how decoherence appears when we consider a quantum system ‘bombarded’ by a set of ancillas which, in the most general case, are taken from an ensemble of quantum systems of different dimensions, prepared in different states, and possibly interacting with the system through different Hamiltonians.
We will show how a rich variety of phenomena in open dynamics (including projection, thermalization, purification, and dephasing) emerge out of our general model of repeated interaction. Remarkably, the strength of the dissipative part of the dynamics is intrinsically linked with the fundamental ``unpredictability'' in the system-ancilla interaction.
We will explore some of the possible applications of this formalism ranging from the measurement problem, quantum thermodynamics, and (relativistic) quantum computing all the way to gravity-induced decoherence.
Work in collaboration with: David Layden, Robert B. Mann and Eduardo Martín-Martínez
A Generalized Model of Repeated Quantum Interactions
Paulina Corona Ugalde, Institute of Quantum Computing, University of Waterloo
We study the different scenarios that repeated quantum interactions between a system S and an ancillary system Sm induces on the former. These latter systems play the role of measurement devices, or meters. Distinct dynamics emerge depending on various limits that can be taken for the ancillae.
Of special interest is the case where induced effective interactions between subsystems of a composite system arise due to their repeated interactions with a common set of meters, which we use to investigate the possibility of describing gravity as a classical channel, or in other words, that gravity arises as an effective force that cannot transmit quantum information.
Non-Local Measurements Via Quantum Erasure
Aharon Brodutch, Institute of Quantum Computing, University of Waterloo
Relativistic constrains impose limits on the type of projective measurements that can be carried out instantaneously. In general, instantaneous projective measurements of non-local observables are difficult and often impossible to perform instantaneously (or in an arbitrarily short period of time) even when unlimited entanglement resources are available. Surprisingly this is true even when the non-local observables can be described as a product of local observables. While the constraint can be traced back to issues with causality, it can be described as a problem of having too much local information during the measurement. To overcome this issue we propose a measurement method that includes a component that erases the redundant information. The protocol allows a projective measurement of any non-local product observable and a large class of more general non-local observables. The interplay between relativistic causality, measurement uncertainty and the requirement for projective measurements leads to a probabilistic protocol that can be made deterministic in some special cases or if the requirement for instantaneous measurements is relaxed.
The talk is based on work reported in [A. Brodutch and E. Cohen Phys. Rev. Lett. 116, 070404 (2016)]
Tools for Relativistic Quantum Reference Frames
Alexander Smith, University of Waterloo and Macquarie University
Progress in physics, from Aristotelian physics, to Galilean and Newtonian physics, and then to both special and general relativity, can be viewed as a continual refinement of the notion of a reference frame. The next natural step in this progression is the idea of a quantum reference frame. In this talk, I will introduce the basic tools that have been developed to study quantum reference frames and examine how they may be applied to relativistic scenarios.
Reference frames naturally have a group structure associated with them, as changes of reference frame form a group. Most of the literature to date has focused on quantum reference frames associated with compact groups, such as reference frames indicating a direction. However, if we would like to treat quantum reference frames relativistically, for which the relevant group is the Poincare group, we need tools to treat reference frames associated with non-compact groups. I will propose three different ways to overcome the issues that arise when considering reference frames associated with non-compact groups.
Alexander R. H. Smith, Marco Piani, and Robert B. Mann, Quantum reference frames associated with non- compact groups: the case of translations and boosts, and the role of mass; arXiv:1602.07696. Submitted to Physical Review A, AQ11435.
Mehdi Ahmadi, Alexander R. H. Smith, and Andrzej Dragan, Communication between inertial observers with partially correlated reference frames; Physical Review A 92, 062319 (2015)
DOI: 10.1103/PhysRevA.92.062319
Communication Between Inertial Observers with Partially Correlated Reference Frames
Mehdi Ahmadi, University of Calgary
In quantum communication protocols the existence of a shared reference frame between two spatially separated parties is normally presumed. However, in many practical situations we are faced with the problem of misaligned reference frames. In this paper, we study communication between two inertial observers who have partial knowledge about the Lorentz transformation that relates their frames of reference. Since every Lorentz transformation can be decomposed into a pure boost followed by a rotation, we begin by analyzing the effects on communication when the parties have partial knowledge about the transformation relating their frames, when the transformation is either a rotation or a pure boost. This then enables us to investigate how the efficiency of communication is affected due to partially correlated inertial reference frames related by an arbitrary Lorentz transformation. Furthermore, we show how the results of previous studies where reference frames are completely uncorrelated are recovered from our results in appropriate limits.
Gravity as an Emergent Quantum Measurement: Cosmological Applications
Natacha Altamirano, Perimeter Institute for Theoretical Physics and University of Waterloo
Much effort has been devoted into understanding the quantum mechanical properties of gravitational interactions. Here we explore the recent suggestion that gravitational interactions are a fundamentally classical channel that is described by continuous quantum measurements and feedforward (CQMF). Specifically, we investigate the possibility that some properties of our universe, modelled using a Friedman-Robertson-Walker metric, can emerge from CQMF by introducing an underlying quantum system for the dynamical variables, avoiding well known difficulties in trying to quantize the spacetime itself. We show that the quantum decoherence, necessary in such a measurement model, manifests itself as a type of dark energy in the resulting space time. The dark energy asymptotes to exactly the bound required for a non-accelerating universe, regardless of the spatial curvature.
Quantum Decoherence During Inflation Due to Gravity
Elliot Nelson, Perimeter Institute for Theoretical Physics
We study the inflationary quantum-to-classical transition for scalar curvature (or inflation) fluctuations due to quantum decoherence from gravitational nonlinearities. We evolve the quantum state Ψ in the Schrodinger picture, for a generic coupling of curvature (or inflation) modes to additional environment degrees of freedom. Focusing on the case of minimal gravitational interactions, we find the evolution of the reduced density matrix for a given long-wavelength fluctuation by tracing out the other (mostly shorter- wavelength) modes as an environment. We show that inflation produces phase oscillations in the wave functional Ψ[ζ(x)], which suppress off-diagonal components of the reduced density matrix, leaving a diagonal mixture of different classical configurations. Gravitational nonlinearities thus provide a minimal mechanism for generating classical stochastic perturbations from inflation. We identify the time when decoherence occurs, which is delayed after modes redshift beyond the Hubble scale due to the weak coupling, and we identify Hubble-scale modes as the decohering environment.
We comment on the related case of inflationary gravitational waves, the role of gravity in quantum measurement, and the possible absence of non- gravitational sources of decoherence during inflation.