Quantum Foundations

When utilized appropriately, the path-integral offers an alternative to the ordinary quantum formalism of state-vectors, selfadjoint operators, and external observers -- an alternative that seems closer to the underlying reality and more in tune with quantum gravity. The basic dynamical relationships are then expressed, not by a propagator, but by the quantum measure, a set-function $\mu$ that assigns to every (suitably regular) set $E$ of histories its generalized measure $\mu(E)$. (The idea is that $\mu$ is to quantum mechanics what Wiener-measure is to Brownian motion.) Except in special cases, $\mu(E)$ cannot be interpreted as a probability, as it is neither additive nor bounded above by unity. Nor, in general, can it be interpreted as the expectation value of a projection operator (or POVM). Nevertheless, I will describe how one can ascertain $\mu(E)$ experimentally for any specified $E$, by means of an arrangement which, in a well-defined sense, acts as an $E$-pass filter. This raises the question whether in certain circumstances we can claim to know that the event $E$ actually did occur.

REFERENCE:

Alvaro Mozota Frauca and Rafael Dolnick Sorkin, How to Measure the Quantum Measure, Int J Theor Phys 56: 232-258 (2017), arxiv:1610.02087

In this talk I will discuss how we might go about about performing a Bell experiment in which humans are used to decide the settings at each end.  The radical possibility we wish to investigate is that, when humans are used to decide the settings (rather than various types of random number generators), we might then expect to see a violation of Quantum Theory in agreement with the relevant Bell inequality.  Such a result, while very unlikely, would be tremendously significant for our understanding of the world (and I will discuss some interpretations).  

Possible radical implications aside, performing an experiment like this would push the development of new technologies.  The biggest problem would be to get sufficiently high rates wherein there has been a human induced switch at each end before a signal as to the new value of the setting could be communicated to the other end and, at the same time, a photon pair is detected.   It looks like an experiment like this, while challenging, is just about feasible with current technologies.  

The fact that in physics concepts such as space, time, mass and energy are considered to be foundational has been conveniently serving a set of higher-level physical theories.

However, this keeps us from gaining a deeper understanding of such concepts which can in turn help us build a theory based on truly foundational concepts.

In this talk I introduce an alternate description of physical reality based on a simple foundational concept that there exist things that influence one another.

A network of objects that influence one another form a partially-ordered set (poset) that is called the influence network is considered. By consistently quantifying such a network with respect to a distinguished chain of events that is called an embedded observer, I demonstrate in relevant special cases that influence events can only be quantified by the familiar mathematics of space-time (Minkowski metric and Lorentz transformations), influence gives rise to basic concepts in Euclidean geometry such as direction, dimension and subspaces as well as the Pythagorean theorem, the dot product and geometrical figures. Thus a discrete version of some of the Euclidean geometry’s fundamental concepts is derived in this picture. Finally I talk about the concept of influence in quantum mechanics and how the case of a free particle is identical to the Feynman checkerboard problem for the electron which is known to give rise to the Dirac equation.

The study of thermodynamics in the quantum regime has in recent years experienced somewhat of a renaissance in our community. This excitement is fueled both by the fundamental nature of the subject as well as the potential for heat machines designed with quantum advantages. Here, I will suggest the study of quantum thermodynamics restricted to a Gaussian regime, with two primary goals in mind. The first is to understand just how restrictive Gaussian states and operations are in a thermodynamic context; as such operations are often the most easily implemented in the laboratory it is pertinent to understand what limitations they impose on us. The second is to use the computational simplicity of Gaussian quantum mechanics to examine thermodynamics under less ideal but more realistic assumptions, such as with finite bath sizes and time scales. We will present two works in this seminar, one focusing on each of these motivations.

Hayden and Van Dam showed that starting with a separable state in Alice and Bob’s state space and a shared entangled state in a common bipartite resource space, then using local unitary operations, it is possible to produce an entangled pair in the state space while at the same time only perturbing the shared entangled state by a small amount, which can be made arbitrarily small as the dimension of the resource space grows. They referred to this as “embezzling entanglement” since numerically it “appears" that the resource state was returned exactly.

It is natural to wonder if using an infinite dimensional resource space and local operations, one can return the resource state exactly while producing an entangled state in their state space. Whether or not you can achieve this phenomenon of “perfect embezzlement of an entangled state” depends on which mathematical model one uses to describe “local”.

We prove that perfect embezzlement is impossible in the tensor model but is possible in the commuting model. We then relate this to current work on the conjectures of Connes and Tsirelson about different models for quantum conditional probabilities.

This talk is based on joint work with R. Cleve, L. Liu and S. Harris.

Anomalies are a ubiquitous phenomenon in quantum mechanics whereby a classical
symmetry is irrevocably violated by quantization. Anomalies not only constrain the
space of classical theories than are consistent with quantum mechanics but are
responsible for rich, surprising and experimentally tested physical phenomena.
In this talk I will give a non-technical, bird's eye introduction to anomalies.

Seminal work of Steve Lack showed that universal algebraic theories (PROPs) may be composed to produce more sophisticated theories.  I’ll apply this method to construct an axiomatic version of the theory of a pair of complementary observables starting from the theory of monoids.  How far can we get with this?  Quite far!  We’ll get a large chunk of finite dimensional quantum theory this way —but the fact that quantum systems have non-trivial dynamics means that it’s (always) possible to present the resulting theory as a composite PROP in Lack’s sense.  If time permits, I’ll also discuss how this approach can serve as a way of constructing toy models with specific properties.
TRIGGER WARNING: category theory, blasphemy.

Analyzing characteristics of an unknown quantum system in a device-independent manner, i.e., using only the measurement statistics, is a fundamental task in quantum physics and quantum information theory. For example, device-independence is a very important feature in the study of quantum cryptography where the quantum devices may not be trusted. In this talk, I will discuss the ability to characterize the state that Alice and Bob share in various physical scenarios using only the correlation data. I first give a lower bound on the dimension of the underlying Hilbert spaces required by Alice and Bob to generate a given correlation in the Bell scenario. Also, I give two properties that the Schmidt coefficients of their shared state must satisfy. I’ll provide examples showing that our results can be tight, and examine when the shared pure state is characterized completely. Lastly, I will discuss these ideas in the Prepare-and-Measure scenario. 

This is joint work with Antonios Varvitsiotis and Zhaohui Wei. 

References: 

Phys. Rev. Lett. 117, 060401, 

Phys. Rev. A, to appear. (ArXiv:1606.03878), 

ArXiv:1609.01030. 

A geometric approach to investigation of quantum entanglement is advocated.
We discuss first the geometry of the (N^2-1)--dimensional convex body
of  mixed quantum states acting  on an N--dimensional Hilbert space
and study projections of this set into 2- and 3-dimensional spaces.
For composed dimensions, N=K^2, one consideres the subset
of separable states and shows that it has a positive measure.
Analyzing its properties contributes to our understanding of
quantum entanglement and its time evolution.

To describe observed phenomena in the lab and to apply superposition principle to gravity, quantum theory needs to be generalized to incorporate indefinite causal structure. Practically, indefinite causal structure offers advantage in communication and computation. Fundamentally, superposing causal structure is one approach to quantize gravity (spacetime metric is equivalent to causal structure plus conformal factor, so quantizing causal structure effectively quantizes gravity). 

We develop a framework to do Operational Probabilistic Theories (OPT) with indefinite causal structure. For the interest of quantum gravity, this framework gives a general prescription to quantize causal structure, assuming linearity is intact. For the interest of quantum foundations, this framework can support new experimental tests about the validity of quantum theory in complex Hilbert space. It also offers opportunities for constructing new OPT models to substitute ordinary quantum theory. Along this direction, we identify principles that single out the complex Hilbert space theory within the general framework.

The on-demand generation of bright entangled photon pairs is highly needed in quantum optics and emerging quantum information applications. However, a quantum light source combining both high fidelity and on-demand bright emission has proven elusive with current leading photon technologies. In this work we present a new bright nanoscale source of strongly entangled photon pairs generated with a position controlled nanowire quantum dot. The major breakthrough in the nanowire growth to achieve both bright photon emission and highly entangled photon pairs will be discussed [2, 3]. Recent experiments show the entanglement fidelity approaching unity, while enhancing the photon pair efficiency beyond state-of-the-art. We further demonstrate violation of the famous Clauser-Horne-Shimony-Holt inequality in the traditional linear basis [4]. This is the first bright nanoscale source of entangled photon pairs capable of violating Bell`s inequalities, opening up future experiments in quantum optics and developments in quantum information applications.

For long-distance quantum communication we convert polarization entangled photons generated by a single quantum dot into time-bin entangled photons by sending them through a polarization-time-bin interface [5]. Importantly, this conversion is performed without loss of entanglement strength. Time-bin entanglement is more robust for long-distance quantum communication than polarization entanglement, since time-bin entangled photons are insensitive to thermal and mechanical disturbances in optical fibers.

References

[1]      M. A. M. Versteegh, M. E Reimer, K. D Jöns, D. Dalacu, P. J. Poole, A. Gulinatti, A. Giudice, and V. Zwiller, Nature Commun. 5, 5298 (2014).

[2]      D. Dalacu, K. Mnaymneh, J. Lapointe, X. Wu, P. J. Poole, G. Bulgarini, V. Zwiller, and M. E. Reimer, Nano Lett. 12 (11), 5919-5923 (2012).

[3]      M. E. Reimer et al., Phys. Rev. B 93, 195316 (2016).

[4]      K. D. Jöns et al., arXiv:1510.03897 (2015).

[5]      M. A. M. Versteegh, M. E. Reimer, A. A. van den Berg, G. Juska, V. Dimastrodonato, A. Gocalinska, E. Pelucchi, and V. Zwiller, Phys. Rev. A 92, 033802 (2015).