Quantifying high dimensional entanglement with two mutually unbiased bases

We derive a framework for quantifying entanglement in multipartite and high dimensional systems using only correlations in two unbiased bases. We furthermore develop such bounds in cases where the second basis is not characterized beyond being unbiased, thus enabling entanglement quantification with minimal assumptions. Furthermore, we show that it is feasible to experimentally implement our method with readily available equipment and even conservative estimates of physical parameters.Comment: 17 pages, 1 figur

Fundamental accuracy-resolution trade-off for timekeeping devices

From a thermodynamic point of view, all clocks are driven by irreversible processes. Additionally, one can use oscillatory systems to temporally modulate the thermodynamic flux towards equilibrium. Focusing on the most elementary thermalization events, this modulation can be thought of as a temporal probability concentration for these events. There are two fundamental factors limiting the performance of clocks: On the one level, the inevitable drifts of the oscillatory system, which are addressed by finding stable atomic or nuclear transitions that lead to astounding precision of today's clocks. On the other level, there is the intrinsically stochastic nature of the irreversible events upon which the clock's operation is based. This becomes relevant when seeking to maximize a clock's resolution at high accuracy, which is ultimately limited by the number of such stochastic events per reference time unit. We address this essential trade-off between clock accuracy and resolution, proving a universal bound for all clocks whose elementary thermalization events are memoryless.Comment: 5 + 7 pages, 8 figures, published versio

Autonomous Quantum Processing Unit: What does it take to construct a self-contained model for quantum computation?

Computation is an input-output process, where a program encoding a problem to be solved is inserted into a machine that outputs a solution. Whilst a formalism for quantum Turing machines which lifts this input-output feature into the quantum domain has been developed, this is not how quantum computation is physically conceived. Usually, such a quantum computation is enacted by the manipulation of macroscopic control interactions according to a program executed by a classical system. To understand the fundamental limits of computation, especially in relation to the resources required, it is pivotal to work with a fully self-contained description of a quantum computation where computational and thermodynamic resources are not be obscured by the classical control. To this end, we answer the question; "Can we build a physical model for quantum computation that is fully autonomous?", i.e., where the program to be executed as well as the control are both quantum. We do so by developing a framework that we dub the autonomous Quantum Processing Unit (aQPU). This machine, consisting of a timekeeping mechanism, instruction register and computational system allows an agent to input their problem and receive the solution as an output, autonomously. Using the theory of open quantum systems and results from the field of quantum clocks we are able to use the aQPU as a formalism to investigate relationships between the thermodynamics, complexity, speed and fidelity of a desired quantum computation.Comment: 21 + 18 pages, 1 table, 6 figures. Comments welcom

The Impact of Imperfect Timekeeping on Quantum Control

In order to unitarily evolve a quantum system, an agent requires knowledge of time, a parameter which no physical clock can ever perfectly characterise. In this letter, we study how limitations on acquiring knowledge of time impact controlled quantum operations in different paradigms. We show that the quality of timekeeping an agent has access to limits the gate complexity they are able to achieve within circuit-based quantum computation. It also exponentially impacts state preparation for measurement-based quantum computation. Another area where quantum control is relevant is quantum thermodynamics. In that context, we show that cooling a qubit can be achieved using a timer of arbitrary quality for control: timekeeping error only impacts the rate of cooling and not the achievable temperature. Our analysis combines techniques from the study of autonomous quantum clocks and the theory of quantum channels to understand the effect of imperfect timekeeping on controlled quantum dynamics.Comment: 5 + 7 pages, 2 figure

DiVincenzo-like criteria for autonomous quantum machines

Controlled quantum machines have matured significantly. A natural next step is to grant them autonomy, freeing them from timed external control. For example, autonomy could unfetter quantum computers from classical control wires that heat and decohere them; and an autonomous quantum refrigerator recently reset superconducting qubits to near their ground states, as is necessary before a computation. What conditions are necessary for realizing useful autonomous quantum machines? Inspired by recent quantum thermodynamics and chemistry, we posit conditions analogous to DiVincenzo's criteria for quantum computing. Our criteria are intended to foment and guide the development of useful autonomous quantum machines.Comment: 7 pages (2 figures + 1 table) + appendi