Vlatko Vedral

University of Oxford, Oxford, England, United Kingdom

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Publications (302)1313.13 Total impact

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    ABSTRACT: The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more interesting quantity in general. We show that an expression that quantifies majorization determines the optimal guaranteed work. We argue it should therefore be the central quantity of statistical mechanics, rather than the von Neumann entropy. In the limit of many identical and independent subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered but in the non-equilbrium regime the optimal guaranteed work can be radically different to the optimal average. Moreover our measure of majorization governs which evolutions can be realized via thermal interactions, whereas the non-decrease of the von Neumann entropy is not sufficiently restrictive. Our results are inspired by single-shot information theory.
    New Journal of Physics 07/2015; 17(7). DOI:10.1088/1367-2630/17/7/073001 · 3.67 Impact Factor
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    ABSTRACT: Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, one between quantum states, and one between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity R\'enyi divergence is proportional to the maximum dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics.
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    ABSTRACT: The tunneling experiment is a key technique for detecting Majorana fermion (MF) in solid state systems. We use Keldysh non-equilibrium Green function method to study two-lead tunneling in superconducting nanowire with Rashba and Dresselhaus spin-orbit couplings. A zero-bias dc conductance peak appears in our setup which signifies the existence of MF and is in accordance with previous experimental results on InSb nanowire. Interestingly, due to the exotic property of MF, there exists a hole transmission channel which makes the currents asymmetric at the left and right leads. The ac current response mediated by MF is also studied here. To discuss the impacts of Coulomb interaction and disorder on the transport property of Majorana nanowire, we use the renormalization group method to study the phase diagram of the wire. It is found that there is a topological phase transition under the interplay of superconductivity and disorder. We find that the Majorana transport is preserved in the superconducting-dominated topological phase and destroyed in the disorder-dominated non-topological insulator phase.
    Journal of Physics Condensed Matter 05/2015; 27(22):225302. DOI:10.1088/0953-8984/27/22/225302 · 2.35 Impact Factor
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    Benjamin Yadin, Vlatko Vedral
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    ABSTRACT: We suggest that quantum macroscopicity should be quantified in terms of coherence, and propose a set of conditions that should be satisfied by any measure of macroscopic coherence. We show that this enables a rigorous justification of a previously proposed measure of macroscopicity based on the quantum Fisher information, while another measure does not satisfy important monotonicity criteria.
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    ABSTRACT: We derive an equality for non-equilibrium statistical mechanics. The equality concerns the worst-case work output of a time-dependent Hamiltonian protocol in the presence of a Markovian heat bath. It has the form "worst-case work = penalty - optimum". The equality holds for all rates of changing the Hamiltonian and can be used to derive the optimum by setting the penalty to 0. The optimum term contains the max entropy of the initial state, rather than the von Neumann entropy, thus recovering recent results from single-shot statistical mechanics. We apply the equality to an electron box.
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    Yu-Xin Wang, Liang-Zhu Mu, Vlatko Vedral, Heng Fan
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    ABSTRACT: Entanglement can be well quantified by R\'{e}nyi $\alpha$-entropy which is a generalization of the standard von Neumann entropy. Here we study the measure of entanglement R\'{e}nyi $\alpha$-entropy for arbitrary two-qubit states. We show that entanglement of two states may be incomparable, contrary to other well-accepted entanglement measures. These facts impose constraint on the convertibility of entangled states by local operations and classical communication. We find that when $\alpha $ is larger than a critical value, the entanglement measure by R\'{e}nyi $\alpha$-entropy is determined solely by concurrence which is a well accepted measure of entanglement. When $\alpha $ is small, the entanglement R\'{e}nyi $\alpha$-entropy of Werner state is obtained. Interestingly, we show that entanglement R\'{e}nyi $\alpha$-entropy of Werner state is always less than any pure entangled state when $\alpha $ is close to zero, even this Werner state is close to a maximally entangled state and the concurrence is larger. We also conclude that the optimal decomposition of a general mixed state cannot be the same for all $\alpha $.
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    ABSTRACT: The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area law for entanglement entropy and the exponential decay of correlations between spatially separated observables. In this letter we present a novel characterization of locality in quantum states, which we call `local reversibility'. It characterizes the type of operations that are needed to reverse the action of a general disturbance on the state. We prove that unique ground states of gapped local Hamiltonian are locally reversible. This way, we identify new fundamental features of many-body ground states, which cannot be derived from the aforementioned properties. We use local reversibility to distinguish between states enjoying microscopic and macroscopic quantum phenomena. To demonstrate the potential of our approach, we prove specific properties of ground states, which are relevant both to critical and non-critical theories.
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    ABSTRACT: We investigate the notion of quantumness based on the non-commutativity of the algebra of observables and introduce a measure of quantumness based on the mutual incompatibility of quantum states. Since it relies on the full algebra of observables, our measure for composed systems is partition independent and witnesses the global quantum nature of a state. We show that such quantity can be experimentally measured with an interferometric setup and that, when an arbitrary bipartition is introduced, it detects the one-way quantum correlations restricted to one of the two subsystems. We finally show that, by combining only two projective measurements and carrying out the interference procedure, our measure becomes an efficient universal witness of quantum discord and non-classical correlations.
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    ABSTRACT: In general relativity, closed timelike curves can break causality with remarkable and unsettling consequences. At the classical level, they induce causal paradoxes disturbing enough to motivate conjectures that explicitly prevent their existence. At the quantum level, resolving such paradoxes induce radical benefits - from cloning unknown quantum states to solving problems intractable to quantum computers. Instinctively, one expects these benefits to vanish if causality is respected. Here we show that in harnessing entanglement, we can efficiently solve NP-complete problems and clone arbitrary quantum states - even when all time-travelling systems are completely isolated from the past. Thus, the many defining benefits of closed timelike curves can still be harnessed, even when causality is preserved. Our results unveil the subtle interplay between entanglement and general relativity, and significantly improve the potential of probing the radical effects that may exist at the interface between relativity and quantum theory.
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    ABSTRACT: Maxwell's daemon is a popular personification of a principle connecting information gain and extractable work in thermodynamics. A Szilard Engine is a particular hypothetical realization of Maxwell's daemon, which is able to extract work from a single thermal reservoir by measuring the position of particle(s) within the system. Here we investigate the role of particle statistics in the whole process; namely, how the extractable work changes if instead of classical particles fermions or bosons are used as the working medium. We give a unifying argument for the optimal work in the different cases: the extractable work is determined solely by the information gain of the initial measurement, as measured by the mutual information, regardless of the number and type of particles which constitute the working substance.
    Scientific Reports 11/2014; 4:6995. DOI:10.1038/srep06995 · 5.58 Impact Factor
  • Mile Gu, Vlatko Vedral
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    ABSTRACT: We investigate the thermodynamical properties of quantum fields in curved spacetime. Our approach is to consider quantum fields in curved spacetime as a quantum system undergoing an out-of-equilibrium transformation. The non-equilibrium features are studied by using a formalism which has been developed to derive fluctuation relations and emergent irreversible features beyond the linear response regime. We apply these ideas to an expanding universe scenario, therefore avoiding assumptions on the relation between entropy and quantum matter. We provide a fluctuation theorem which allows us to understand particle production due to the expansion of the universe as an entropic increase. Our results pave the way towards a different understanding of the thermodynamics of relativistic and quantum systems in our universe.
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    ABSTRACT: Fluctuation-dissipation relations, such as Crooks' Theorem and Jarzynski's Equality, are powerful tools in quantum and classical nonequilibrium statistical mechanics. We link these relations to a newer approach known as "one-shot statistical mechanics." Rooted in one-shot information theory, one-shot statistical mechanics concerns statements true of every implementation of a protocol, not only of averages. We show that two general models for work extraction in the presence of heat baths obey fluctuation relations and one-shot results. We demonstrate the usefulness of this bridge between frameworks in several ways. Using Crooks' Theorem, we derive a bound on one-shot work quantities. These bounds are tighter, in certain parameter regimes, than a bound in the fluctuation literature and a bound in the one-shot literature. Our bounds withstand tests by numerical simulations of an information-theoretic Carnot engine. By analyzing data from DNA-hairpin experiments, we show that experiments used to test fluctuation theorems also test one-shot results. Additionally, we derive one-shot analogs of a known equality between a relative entropy and the average work dissipated as heat. Our unification of experimentally tested fluctuation relations with one-shot statistical mechanics is intended to bridge one-shot theory to applications.
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    ABSTRACT: Recently, a novel operational strategy to access quantum correlation functions of the form Tr[A rho B] was provided in [F. Buscemi, M. Dall'Arno, M. Ozawa, and V. Vedral, arXiv:1312.4240]. Here we propose a realization scheme, that we call partial expectation values, implementing such strategy in terms of a unitary interaction with an ancillary system followed by the measurement of an observable on the ancilla. Our scheme is universal, being independent of rho, A, and B, and it is optimal in a statistical sense. Our scheme is suitable for implementation with present quantum optical technology, and provides a new way to test uncertainty relations.
    International Journal of Quantum Information 09/2014; 12(07n08). DOI:10.1142/S0219749915600023 · 0.99 Impact Factor
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    Vlatko Vedral
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    ABSTRACT: We present arguments to the effect that time and temperature can be viewed as a form of quantum entanglement. Furthermore, if temperature is thought of as arising from the quantum mechanical tunneling probability this then offers us a way of dynamically "converting" time into temperature based on the entanglement between the transmitted and reflected modes. We then show how similar entanglement-based logic can be applied to the dynamics of cosmological inflation and discuss the possibility of having observable effects of the early gravitational entanglement at the level of the universe.
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    ABSTRACT: The quantum uncertainty principle stipulates that when one observable is predictable there must be some other observables that are unpredictable. The principle is viewed as holding the key to many quantum phenomena and understanding it deeper is of great interest in the study of the foundations of quantum theory. Here we show that apart from being restrictive, the principle also plays a positive role as the enabler of non-classical dynamics in an interferometer. First we note that instantaneous action at a distance should not be possible. We show that for general probabilistic theories this heavily curtails the non-classical dynamics. We prove that there is a trade-off with the uncertainty principle that allows theories to evade this restriction. On one extreme, non-classical theories with maximal certainty have their non-classical dynamics absolutely restricted to only the identity operation. On the other extreme, quantum theory minimizes certainty in return for maximal non-classical dynamics.
    Nature Communications 08/2014; 5:4592. DOI:10.1038/ncomms5592 · 10.74 Impact Factor
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    Benjamin Yadin, Vlatko Vedral
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    ABSTRACT: There have recently been a number of proposals for measures to describe the extent to which the quantum behaviour of a system extends to the macroscopic scale. We argue that measures for systems of qubits should be extended to classify a larger set of states (including two-dimensional cluster states and certain topological states) as macroscopically quantum. This is motivated by the ability to use local measurements to distil a Schroedinger's cat state from states which are not macroscopically quantum according to current measures. We also investigate the role played by imperfect measurements.
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    Tristan Farrow, Vlatko Vedral
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    ABSTRACT: A generic and intuitive model for coherent energy transport in multiple minima systems coupled to a quantum mechanical bath is shown. Using a simple spin-boson system, we illustrate how a generic donor-acceptor system can be brought into resonance using a narrow band of vibrational modes, such that the transfer efficiency of an electron-hole pair (exciton) is made arbitrarily high. Coherent transport phenomena in nature are of renewed interest since the discovery that a photon captured by the light-harvesting complex (LHC) in photosynthetic organisms can be conveyed to a chemical reaction centre with near-perfect efficiency. Classical explanations of the transfer use stochastic diffusion to model the hopping motion of a photo-excited exciton. This accounts inadequately for the speed and efficiency of the energy transfer measured in a series of recent landmark experiments. Taking a quantum mechanical perspective can help capture the salient features of the efficient part of that transfer. To show the versatility of the model, we extend it to a multiple minima system comprising seven-sites, reminiscent of the widely studied Fenna-Matthews-Olson (FMO) light-harvesting complex. We show that an idealised transport model for multiple minima coupled to a narrow-band phonon can transport energy with arbitrarily high efficiency.
    Scientific Reports 06/2014; 4. DOI:10.1038/srep05520 · 5.58 Impact Factor
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    ABSTRACT: We introduce a simple and efficient technique to verify quantum discord in unknown Gaussian states and certain class of non-Gaussian states. We also demonstrate that discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interaction.
    CLEO: QELS_Fundamental Science; 06/2014
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    Tristan Farrow, Vlatko Vedral
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    ABSTRACT: We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of systems differ so widely, we use a case by case approach to identifying the different parameters and criteria that capture their behaviour in a quantum mechanical framework. We find it helpful to categorise systems into three broad classes defined by mass, spatio-temporal coherence, and number of particles. The classes are not mutually exclusive and in fact the properties of some systems fit into several classes. We discuss experiments by turn, starting with interference of massive objects like macromolecules and micro-mechanical resonators, followed by self-interference of single particles in complex molecules, before examining the striking advances made with superconducting qubits. Finally, we propose a theoretical basis for quantifying the macroscopic features of a system to lay the ground for a more systematic comparison of the quantum properties in disparate systems.
    Optics Communications 06/2014; 337. DOI:10.1016/j.optcom.2014.06.042 · 1.54 Impact Factor

Publication Stats

14k Citations
1,313.13 Total Impact Points

Institutions

  • 1995–2015
    • University of Oxford
      • Department of Physics
      Oxford, England, United Kingdom
  • 2007–2014
    • Università degli Studi di Palermo
      • Dipartimento di Fisica e Chimica
      Palermo, Sicily, Italy
    • Indian Institute of Technology Madras
      • Department of Electrical Engineering
      Chennai, State of Tamil Nadu, India
  • 2013
    • Masaryk University
      • Faculty of Informatics
      Brünn, South Moravian, Czech Republic
  • 2011
    • National University of Singapore
      Tumasik, Singapore
    • Federal University of Pernambuco
      • Department of Physics
      Arrecife, Pernambuco, Brazil
  • 2004–2011
    • University of Leeds
      • School of Physics and Astronomy
      Leeds, ENG, United Kingdom
  • 2006
    • University of Vienna
      • Basic Experimental Physics Training and Didactics Group
      Wien, Vienna, Austria
    • University of Cambridge
      • Department of Applied Mathematics and Theoretical Physics
      Cambridge, England, United Kingdom
    • Federal University of Minas Gerais
      • Departamento de Física
      Cidade de Minas, Minas Gerais, Brazil
  • 1996–2005
    • Imperial College London
      • Section of Statistics
      Londinium, England, United Kingdom