arXiv subjects

Noah Linden

Publications and source records attributed to Noah Linden.

At least 37 records · Page 2Linked to original sources

arXiv2018

Robustness of Measurement, discrimination games and accessible information

We introduce a way of quantifying how informative a quantum measurement is, starting from a resource-theoretic perspective. This quantifier, which we call the robustness of measurement, describes how much `noise' must be added to a measurement before it becomes completely uninformative. We show that this geometric quantifier has operational significance in terms of the advantage the measurement provides over guessing at random in an suitably chosen state discrimination game. We further show that it is the single-shot generalisation of the accessible information of a certain quantum-to-classical channel. Using this insight, we also show that the recently-introduced robustness of coherence is the single-shot generalisation of the accessible information of an ensemble. Finally we discuss more generally the connection between robustness-based measures, discrimination problems and single-shot information theory.

quant-ph↗

arXiv2018

Optimal verification of entangled states with local measurements

Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterise the output state by quantum state tomography; or alternatively to perform some kind of Bell test, tailored to the state of interest. We show here that neither approach is optimal amongst local verification strategies for two qubit states. We find the optimal strategy in this case and show that quadratically fewer total measurements are needed to verify to within a given fidelity than in published results for quantum state tomography, Bell test, or fidelity estimation protocols. We also give efficient verification protocols for any stabilizer state. Additionally, we show that requiring that the strategy be constructed from local, non-adaptive and non-collective measurements only incurs a constant-factor penalty over a strategy without these restrictions.

quant-ph↗

arXiv2017

Equilibration time scales of physically relevant observables

We address the problem of understanding from first principles the conditions under which a quantum system equilibrates rapidly with respect to a concrete observable. On the one hand previously known general upper bounds on the time scales of equilibration were unrealistically long, with times scaling linearly with the dimension of the Hilbert space. These bounds proved to be tight, since particular constructions of observables scaling in this way were found. On the other hand, the computed equilibration time scales for certain classes of typical measurements, or under the evolution of typical Hamiltonians, turn out to be unrealistically short. However neither classes of results cover physically relevant situations, which up to now had only been tractable in specific models. In this paper we provide a new upper bound on the equilibration time scales which, under some physically reasonable conditions, give much more realistic results than previously known. In particular, we apply this result to the paradigmatic case of a system interacting with a thermal bath, where we obtain an upper bound for the equilibration time scale independent of the size of the bath. In this way, we find general conditions that single out observables with realistic equilibration times within a physically relevant setup.

quant-ph↗

arXiv2017

Beyond icosahedral symmetry in packings of proteins in spherical shells

The formation of quasi-spherical cages from protein building blocks is a remarkable self-assembly process in many natural systems, where a small number of elementary building blocks are assembled to build a highly symmetric icosahedral cage. In turn, this has inspired synthetic biologists to design de novo protein cages. We use simple models, on multiple scales, to investigate the self-assembly of a spherical cage, focusing on the regularity of the packing of protein-like objects on the surface. Using building blocks, which are able to pack with icosahedral symmetry, we examine how stable these highly symmetric structures are to perturbations that may arise from the interplay between flexibility of the interacting blocks and entropic effects. We find that, in the presence of those perturbations, icosahedral packing is not the most stable arrangement for a wide range of parameters; rather disordered structures are found to be the most stable. Our results suggest that (i) many designed, or even natural, protein cages may not be regular in the presence of those perturbations, and (ii) that optimizing those flexibilities can be a possible design strategy to obtain regular synthetic cages with full control over their surface properties.

cond-mat.soft↗

arXiv2017

Generating entanglement with linear optics

Entanglement is the basic building block of linear optical quantum computation, and as such understanding how to generate it in detail is of great importance for optical architectures. We prove that Bell states cannot be generated using only 3 photons in the dual-rail encoding, and give strong numerical evidence for the optimality of the existing 4 photon schemes. In a setup with a single photon in each input mode, we find a fundamental limit on the possible entanglement between a single mode Alice and arbitrary Bob. We investigate and compare other setups aimed at characterizing entanglement in settings more general than dual-rail encoding. The results draw attention to the trade-off between the entanglement a state has and the probability of postselecting that state, which can give surprising constant bounds on entanglement even with increasing numbers of photons.

quant-ph↗

arXiv2016

Quantum speedup of the Travelling Salesman Problem for bounded-degree graphs

The Travelling Salesman Problem is one of the most famous problems in graph theory. However, little is currently known about the extent to which quantum computers could speed up algorithms for the problem. In this paper, we prove a quadratic quantum speedup when the degree of each vertex is at most 3 by applying a quantum backtracking algorithm to a classical algorithm by Xiao and Nagamochi. We then use similar techniques to accelerate a classical algorithm for when the degree of each vertex is at most 4, before speeding up higher-degree graphs via reductions to these instances.

quant-ph↗

arXiv2016

Universal Refocusing of Systematic Quantum Noise

Refocusing of a quantum system in NMR and quantum information processing can be achieved by application of short pulses according to the methods of spin echo and dynamical decoupling. However, these methods are strongly limited by the requirement that the evolution of the system between pulses be suitably small. Here we show how refocusing may be achieved for arbitrary (but time-independent) evolution of the system between pulses. We first illustrate the procedure with one-qubit systems, and then generalize to $d$-dimensional quantum systems. We also give an application of this result to quantum computation, proving a new version of the Solovay-Kitaev theorem that does not require inverse gates.

quant-ph↗

arXiv2015

Rapid spatial equilibration of a particle in a box

We study the equilibration behaviour of a quantum particle in a one-dimensional box, with respect to a coarse grained position measurement (whether it lies in a certain spatial window or not). We show that equilibration in this context indeed takes place and does so very rapidly, in a time comparable to the time for the initial wave packet to reach the edges of the box. We also show that, for this situation, the equilibration behaviour is relatively insensitive to the precise choice of position measurements or initial condition.

quant-ph↗

arXiv2014

Quantum Systems Equilibrate Rapidly for Most Observables

Considering any Hamiltonian, any initial state, and measurements with a small number of possible outcomes compared to the dimension, we show that most measurements are already equilibrated. To investigate non-trivial equilibration we therefore consider a restricted set of measurements. When the initial state is spread over many energy levels, and we consider the set of observables for which this state is an eigenstate, most observables are initially out of equilibrium yet equilibrate rapidly. Moreover, all two-outcome measurements, where one of the projectors is of low rank, equilibrate rapidly.

quant-ph↗

arXiv2014

Entanglement enhances cooling in microscopic quantum fridges

Small self-contained quantum thermal machines function without external source of work or control, but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned---fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.

quant-ph↗

arXiv2013

Pre- and post-selected quantum states: density matrices, tomography, and Kraus operators

We present a general formalism for charecterizing 2-time quantum states, describing pre- and post-selected quantum systems. The most general 2-time state is characterized by a `density vector' that is independent of measurements performed between the preparation and post-selection. We provide a method for performing tomography of an unknown 2-time density vector. This procedure, which cannot be implemented by weak or projective measurements, brings new insight to the fundamental role played by Kraus operators in quantum measurements. Finally, after showing that general states and measurements are isomorphic, we show that any measurement on a 2-time state can be mapped to a measurement on a preselected bipartite state.

quant-ph↗

arXiv2013

Inequalities for the Ranks of Quantum States

We investigate relations between the ranks of marginals of multipartite quantum states. These are the Schmidt ranks across all possible bipartitions and constitute a natural quantification of multipartite entanglement dimensionality. We show that there exist inequalities constraining the possible distribution of ranks. This is analogous to the case of von Neumann entropy (α-Rényi entropy for α=1), where nontrivial inequalities constraining the distribution of entropies (such as e.g. strong subadditivity) are known. It was also recently discovered that all other α-Rényi entropies for $α\in(0,1)\cup(1,\infty)$ satisfy only one trivial linear inequality (non-negativity) and the distribution of entropies for $α\in(0,1)$ is completely unconstrained beyond non-negativity. Our result resolves an important open question by showing that also the case of α=0 (logarithm of the rank) is restricted by nontrivial linear relations and thus the cases of von Neumann entropy (i.e., α=1) and 0-Rényi entropy are exceptionally interesting measures of entanglement in the multipartite setting.

quant-ph↗

arXiv2013

The Quantum Entropy Cone of Stabiliser States

We investigate the universal linear inequalities that hold for the von Neumann entropies in a multi-party system, prepared in a stabiliser state. We demonstrate here that entropy vectors for stabiliser states satisfy, in addition to the classic inequalities, a type of linear rank inequalities associated with the combinatorial structure of normal subgroups of certain matrix groups. In the 4-party case, there is only one such inequality, the so-called Ingleton inequality. For these systems we show that strong subadditivity, weak monotonicity and Ingleton inequality exactly characterize the entropy cone for stabiliser states.

quant-ph↗

arXiv2012

The structure of Renyi entropic inequalities

We investigate the universal inequalities relating the alpha-Renyi entropies of the marginals of a multi-partite quantum state. This is in analogy to the same question for the Shannon and von Neumann entropy (alpha=1) which are known to satisfy several non-trivial inequalities such as strong subadditivity. Somewhat surprisingly, we find for 0 1 we show analogously that there are no non-trivial homogeneous (in particular no linear) inequalities. On the other hand, it is known that there are further, non-linear and indeed non-homogeneous, inequalities delimiting the alpha-entropies of a general quantum state. Finally, we also treat the case of Renyi entropies restricted to classical states (i.e. probability distributions), which in addition to non-negativity are also subject to monotonicity. For alpha different from 0 and 1 we show that this is the only other homogeneous relation.

quant-ph↗

arXiv2012

Efficient Distributed Quantum Computing

We provide algorithms for efficiently addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with low overhead by the more realistic model of a distributed quantum computer. As a result, the circuit model can be used by algorithm designers without worrying whether the underlying architecture supports the connectivity of the circuit. In addition, we apply our results to existing memory intensive quantum algorithms. We present a parallel quantum search algorithm and improve the time-space trade-off for the Element Distinctness and Collision problems.

quant-ph↗

arXiv2012

Measurement entropy in Generalized Non-Signalling Theory cannot detect bipartite non-locality

We consider entropy in Generalized Non-Signalling Theory (also known as box world) where the most common definition of entropy is the measurement entropy. In this setting, we completely characterize the set of allowed entropies for a bipartite state. We find that the only inequalities amongst these entropies are subadditivity and non-negativity. What is surprising is that non-locality does not play a role - in fact any bipartite entropy vector can be achieved by separable states of the theory. This is in stark contrast to the case of the von Neumann entropy in quantum theory, where only entangled states satisfy S(AB)<S(A).

quant-ph↗

arXiv2012

Bell nonlocality and Bayesian game theory

We discuss a connection between Bell nonlocality and Bayesian games. This link offers interesting perspectives for Bayesian games, namely to allow the players to receive advice in the form of nonlocal correlations, for instance using entangled quantum particles or more general no-signaling boxes. The possibility of having such 'nonlocal advice' will lead to novel joint strategies, impossible to achieve in the classical setting. This implies that quantum resources, or more general no-signaling resources, offer a genuine advantage over classical ones. Moreover, some of these strategies can represent equilibrium points, leading to the notion of quantum/no-signaling Nash equilibrium. Finally we describe new types of question in the study of nonlocality, namely the consideration of non-local advantage when there is a set of Bell expressions.

quant-ph↗

arXiv2012

Virtual qubits, virtual temperatures, and the foundations of thermodynamics

We argue that thermal machines can be understood from the perspective of `virtual qubits' at `virtual temperatures': The relevant way to view the two heat baths which drive a thermal machine is as a composite system. Virtual qubits are two-level subsystems of this composite, and their virtual temperatures can take on any value, positive or negative. Thermal machines act upon an external system by placing it in thermal contact with a well-selected range of virtual qubits and temperatures. We demonstrate these claims by studying the smallest thermal machines. We show further that this perspective provides a powerful way to view thermodynamics, by analysing a number of phenomena. This includes approaching Carnot efficiency (where we find that all machines do so essentially by becoming equivalent to the smallest thermal machines), entropy production in irreversible machines, and a way to view work in terms of negative temperature and population inversion. Moreover we introduce the idea of "genuine" thermal machines and are led to considering the concept of "strength" of work.

quant-ph↗