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Quantum Telepathy and the Analysis of Particle Presence
The field of quantum mechanics has revolutionised physics as a subject. Areas such as information theory, computer science and physical sensing have all been affected by the tremendous successes of various quantum protocols. In this thesis I present my contribution to the development of such non-classical protocols.
In classical communication theory a message is always carried by physical particles that interact with a transmitter, after which they travel to a receiver. In this thesis I outline a quantum protocol which allows a receiver to obtain a message without receiving any physical object or particles that have interacted with the transmitter—that is, counterfactually. I build my protocol for counterfactual communication on the principles of interaction-free measurements, ensuring that information always propagates in the opposite direction to the protocol particles. The protocol shows how quantum mechanics breaks the previous premise of communication theory. From the perspective of local observers, it is a beautiful manifestation of the non-locality of interaction-free measurements. Furthermore, it is highly robust against experimental errors and external disturbances. The majority of this part of the thesis is based on my published article ‘Quantum counterfactual communication without a weak trace’ [Phys. Rev. A 94, 062303 (2016)].
Previous to my work, Salih et al. attempted to design a counterfactual communication protocol [Phys. Rev. Lett. 110, 170502 (2013)]. This protocol has been highly controversial. As counterfactual phenomena impose restrictions on the inter-measurement paths of quantum particles, and the physical reality of such paths lacks description in the Copenhagen interpretation of quantum mechanics, an extension of current quantum theory is required to facilitate a discussion. In this thesis I present an operational and interpretation-independent methodology, enabling the discussion of inter-measurement paths of quantum particles. I start by considering the interferometers of counterfactual protocols, making the basic assumption that any quantum evolution naturally involves uncontrolled weak interactions. I then show how the Fisher information of these weak interactions, available at the output of counterfactual experiments, can be used to discuss the pre-measurement past of the particles. Based on this analysis, the protocol developed by Salih et al. is found to strongly violate counterfactuality. However, my protocol is more flexible in that it allows particles to propagate in the opposite direction to the message. This leads to counterfactuality being satisfied—even in the presence of large experimental errors. These results are observed both analytically and numerically. This part of the thesis is based on my article ‘Evaluation of counterfactuality in counterfactual communication protocols’ [Phys. Rev. A 96, 062316 (2017)]. The numerical methods are inspired by another of my publications: ‘Protocol for fermionic positive-operator-valued measures’ [Phys. Rev. A 96, 052305 (2017)].
Finally, as the Fisher information measure is found to be useful in evaluating counterfactual protocols, I extend my work by investigating the quantum Fisher information in experiments with general discrete quantum circuits. I prove that the quantum Fisher information of a two-level interaction in a quantum circuit can be expressed by a simple formula. Under certain phase-relations, the formula provides a straightforward connection between the abstract concept of the inter-measurement wavefunction and the quantum Fisher information at the output. With regard to how the information obtained from a certain volume of space influences our perception of classical objects, I argue that the quantum Fisher information measure is highly useful in describing quantum objects. If this measure is applied to observers with a limited set of the experimental measurement outcomes, a quantum object can appear to follow non-classical discontinuous paths. This supports the remarkable conclusion that our perception of the past of a quantum object is subjectively dependent on the measurement we conduct on it
Characterizing the geometry of the Kirkwood-Dirac positive states
The Kirkwood-Dirac (KD) quasiprobability distribution can describe any
quantum state with respect to the eigenbases of two observables and . KD
distributions behave similarly to classical joint probability distributions but
can assume negative and nonreal values. In recent years, KD distributions have
proven instrumental in mapping out nonclassical phenomena and quantum
advantages. These quantum features have been connected to nonpositive entries
of KD distributions. Consequently, it is important to understand the geometry
of the KD-positive and -nonpositive states. Until now, there has been no
thorough analysis of the KD positivity of mixed states. Here, we characterize
how the full convex set of states with positive KD distributions depends on the
eigenbases of and . In particular, we identify three regimes where
convex combinations of the eigenprojectors of and constitute the only
KD-positive states: any system in dimension ; an open and dense
set of bases in dimension ; and the discrete-Fourier-transform bases
in prime dimension. Finally, we investigate if there can exist mixed
KD-positive states that cannot be written as convex combinations of pure
KD-positive states. We show that for some choices of observables and
this phenomenon does indeed occur. We explicitly construct such states for a
spin- system.Comment: 35 pages, 2 figure
Quantum simulations of time travel can power nonclassical metrology
Gambling agencies forbid late bets, placed after the winning horse crosses
the finish line. A time-traveling gambler could cheat the system. We construct
a gamble that one can win by simulating time travel with experimentally
feasible entanglement manipulation. Our gamble echoes a common metrology
protocol: A gambler must prepare probes to input into a metrology experiment.
The goal is to infer as much information per probe as possible about a
parameter's value. If the input is optimal, the information gained per probe
can exceed any value achievable classically. The gambler chooses the input
state analogously to choosing a horse. However, only after the probes are
measured does the gambler learn which input would have been optimal. The
gambler can "place a late bet" by effectively teleporting the optimal input
back in time, via entanglement manipulation. Our Gedankenexperiment
demonstrates that not only true time travel, but even a simulation offers a
quantum advantage in metrology.Comment: 5+1 pages. 2 figures. Comments are welcomed
Dynamic-ADAPT-QAOA: An algorithm with shallow and noise-resilient circuits
The quantum approximate optimization algorithm (QAOA) is an appealing
proposal to solve NP problems on noisy intermediate-scale quantum (NISQ)
hardware. Making NISQ implementations of the QAOA resilient to noise requires
short ansatz circuits with as few CNOT gates as possible. Here, we present
Dynamic-ADAPT-QAOA. Our algorithm significantly reduces the circuit depth and
the CNOT count of standard ADAPT-QAOA, a leading proposal for near-term
implementations of the QAOA. Throughout our algorithm, the decision to apply
CNOT-intensive operations is made dynamically, based on algorithmic benefits.
Using density-matrix simulations, we benchmark the noise resilience of
ADAPT-QAOA and Dynamic-ADAPT-QAOA. We compute the gate-error probability
below which these algorithms provide, on average, more
accurate solutions than the classical, polynomial-time approximation algorithm
by Goemans and Williamson. For small systems with qubits, we show that
for Dynamic-ADAPT-QAOA. Compared to standard
ADAPT-QAOA, this constitutes an order-of-magnitude improvement in noise
resilience. This improvement should make Dynamic-ADAPT-QAOA viable for
implementations on superconducting NISQ hardware, even in the absence of error
mitigation.Comment: 15 pages, 9 figure