The optimal allocation of resources is a crucial task for their efficient use in a wide range of ... more The optimal allocation of resources is a crucial task for their efficient use in a wide range of practical applications in science and engineering. This paper investigates the optimal allocation of resources in multipartite quantum systems. In particular, we show the relevance of proportional fairness and optimal reliability criteria for the application of quantum resources. Moreover, we present optimal allocation solutions for an arbitrary number of qudits using measurement incompatibility as an exemplary resource theory. Besides, we study the criterion of optimal equitability and demonstrate its relevance to scenarios involving several resource theories such as nonlocality vs local contextuality. Finally, we highlight the potential impact of our results for quantum networks and other multi-party quantum information processing, in particular to the future Quantum Internet.
Distinguishing physical processes is one of the fundamental problems in quantum physics. Although... more Distinguishing physical processes is one of the fundamental problems in quantum physics. Although distinguishability of quantum preparations and quantum channels have been studied considerably, distinguishability of quantum measurements remains largely unexplored. We investigate the problem of single-shot discrimination of quantum measurements using two strategies, one based on single quantum systems and the other one based on entangled quantum systems. First, we formally define both scenarios. We then construct sets of measurements (including non-projective) in arbitrary finite dimensions that are perfectly distinguishable within the second scenario using quantum entanglement, while not in the one based on single quantum systems. Furthermore, we show that any advantage in measurement discrimination tasks over single systems is a demonstration of Einstein–Podolsky–Rosen ‘quantum steering’. Alongside, we prove that all pure two-qubit entangled states provide an advantage in a measure...
The second law of thermodynamics uses change in free energy of macroscopic systems to set a bound... more The second law of thermodynamics uses change in free energy of macroscopic systems to set a bound on performed work. Ergotropy plays a similar role in microscopic scenarios, and is defined as the maximum amount of energy that can be extracted from a system by a unitary operation. In this analysis, we quantify how much ergotropy can be induced on a system as a result of system's interaction with a thermal bath, with a perspective of using it as a source of work performed by microscopic machines. We provide the fundamental bound on the amount of ergotropy which can be extracted from environment in this way. The bound is expressed in terms of the non-equilibrium free energy difference and can be saturated in the limit of infinite dimension of the system's Hamiltonian. The ergotropy extraction process leading to this saturation is numerically analyzed for finite dimensional systems. Furthermore, we apply the idea of extraction of ergotropy from environment in a design of a new c...
The fluctuation-dissipation theorem is a fundamental result in statistical physics that establish... more The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, we first characterise optimal thermodynamic distillation processes, and then prove a relation between the amount of free energy dissipated in such processes and the free energy fluctuations of the initial state of the system. Our results apply to initial states given by either asymptotically many identical pure systems or arbitrary number of independent energy-incoherent systems, and allow not only for a state transformation, but also for the change of Hamiltonian. The fluctuation-dissipation relations we derive enable us to find the optimal performance of thermodynamic protocols such as work extraction, information erasure and thermodynamically-free communication, up to second-order asymptotics in the number N of processed systems. We thus provide a first rigorous analysis of these thermodynamic protocols for quantum states with coherence between different energy eigenstates in the intermediate regime of large but finite N .
For any resource theory it is essential to identify tasks for which resource objects offer advant... more For any resource theory it is essential to identify tasks for which resource objects offer advantage over free objects. We show that this identification can always be accomplished for resource theories of quantum measurements in which free objects form a convex subset of measurements on a given Hilbert space. To this aim we prove that every resourceful measurement offers advantage for some quantum state discrimination task. Moreover, we give an operational interpretation of robustness, which quantifies the minimal amount of noise that must be added to a measurement to make it free. Specifically, we show that this geometric quantity is related to the maximal relative advantage that a resourceful measurement offers in a class of minimal-error state discrimination (MESD) problems. Finally, we apply our results to two classes of free measurements: incoherent measurements (measurements that are diagonal in the fixed basis) and separable measurements (measurements whose effects are separa...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017
Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed a... more Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. ( Phys. Rev. Lett. 113 , 140401. (doi:10.1103/PhysRevLett.113.140401)), following Åberg ( http://arxiv.org/abs/quant-ph/0612146 ), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by ana...
The optimal allocation of resources is a crucial task for their efficient use in a wide range of ... more The optimal allocation of resources is a crucial task for their efficient use in a wide range of practical applications in science and engineering. This paper investigates the optimal allocation of resources in multipartite quantum systems. In particular, we show the relevance of proportional fairness and optimal reliability criteria for the application of quantum resources. Moreover, we present optimal allocation solutions for an arbitrary number of qudits using measurement incompatibility as an exemplary resource theory. Besides, we study the criterion of optimal equitability and demonstrate its relevance to scenarios involving several resource theories such as nonlocality vs local contextuality. Finally, we highlight the potential impact of our results for quantum networks and other multi-party quantum information processing, in particular to the future Quantum Internet.
Distinguishing physical processes is one of the fundamental problems in quantum physics. Although... more Distinguishing physical processes is one of the fundamental problems in quantum physics. Although distinguishability of quantum preparations and quantum channels have been studied considerably, distinguishability of quantum measurements remains largely unexplored. We investigate the problem of single-shot discrimination of quantum measurements using two strategies, one based on single quantum systems and the other one based on entangled quantum systems. First, we formally define both scenarios. We then construct sets of measurements (including non-projective) in arbitrary finite dimensions that are perfectly distinguishable within the second scenario using quantum entanglement, while not in the one based on single quantum systems. Furthermore, we show that any advantage in measurement discrimination tasks over single systems is a demonstration of Einstein–Podolsky–Rosen ‘quantum steering’. Alongside, we prove that all pure two-qubit entangled states provide an advantage in a measure...
The second law of thermodynamics uses change in free energy of macroscopic systems to set a bound... more The second law of thermodynamics uses change in free energy of macroscopic systems to set a bound on performed work. Ergotropy plays a similar role in microscopic scenarios, and is defined as the maximum amount of energy that can be extracted from a system by a unitary operation. In this analysis, we quantify how much ergotropy can be induced on a system as a result of system's interaction with a thermal bath, with a perspective of using it as a source of work performed by microscopic machines. We provide the fundamental bound on the amount of ergotropy which can be extracted from environment in this way. The bound is expressed in terms of the non-equilibrium free energy difference and can be saturated in the limit of infinite dimension of the system's Hamiltonian. The ergotropy extraction process leading to this saturation is numerically analyzed for finite dimensional systems. Furthermore, we apply the idea of extraction of ergotropy from environment in a design of a new c...
The fluctuation-dissipation theorem is a fundamental result in statistical physics that establish... more The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, we first characterise optimal thermodynamic distillation processes, and then prove a relation between the amount of free energy dissipated in such processes and the free energy fluctuations of the initial state of the system. Our results apply to initial states given by either asymptotically many identical pure systems or arbitrary number of independent energy-incoherent systems, and allow not only for a state transformation, but also for the change of Hamiltonian. The fluctuation-dissipation relations we derive enable us to find the optimal performance of thermodynamic protocols such as work extraction, information erasure and thermodynamically-free communication, up to second-order asymptotics in the number N of processed systems. We thus provide a first rigorous analysis of these thermodynamic protocols for quantum states with coherence between different energy eigenstates in the intermediate regime of large but finite N .
For any resource theory it is essential to identify tasks for which resource objects offer advant... more For any resource theory it is essential to identify tasks for which resource objects offer advantage over free objects. We show that this identification can always be accomplished for resource theories of quantum measurements in which free objects form a convex subset of measurements on a given Hilbert space. To this aim we prove that every resourceful measurement offers advantage for some quantum state discrimination task. Moreover, we give an operational interpretation of robustness, which quantifies the minimal amount of noise that must be added to a measurement to make it free. Specifically, we show that this geometric quantity is related to the maximal relative advantage that a resourceful measurement offers in a class of minimal-error state discrimination (MESD) problems. Finally, we apply our results to two classes of free measurements: incoherent measurements (measurements that are diagonal in the fixed basis) and separable measurements (measurements whose effects are separa...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017
Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed a... more Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. ( Phys. Rev. Lett. 113 , 140401. (doi:10.1103/PhysRevLett.113.140401)), following Åberg ( http://arxiv.org/abs/quant-ph/0612146 ), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by ana...
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Papers by Tanmoy Biswas