Raffaele Romano - Academia.edu (original) (raw)
Papers by Raffaele Romano
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We generalize Bell's hidden variable model describing the singlet state of a two-qubits syste... more We generalize Bell's hidden variable model describing the singlet state of a two-qubits system by extending it to arbitrary states and observables. As in the original work, we assume a uniform, state-independent probability distribution for the hidden variables which are identified with the unit vectors of a 3-dimensional real space. By slightly modifying our model, we provide also a minimal hidden variable description of the two-qubits system, relying on a single hidden variable. We discuss the main features and the implications of the model.
Recently, it has been argued that no extension of quantum theory can have improved predictive pow... more Recently, it has been argued that no extension of quantum theory can have improved predictive power, under a strong assumption of free choice of the experimental settings, and validity of quantum mechanics. Here, under a different free choice assumption, we describe a model which violates this statement for almost all states of a bipartite two-level system, in a possibly experimentally testable way. From consistency with quantum mechanics and the non-signalling principle, we derive a bound on the local averages for the family of deterministic ontological theories our model belongs to.
Physical Review A, 2012
We extend to any maximally entangled state of a bipartite system whose constituents are arbitrari... more We extend to any maximally entangled state of a bipartite system whose constituents are arbitrarily (but finite) dimensional the result, recently derived for two-dimensional constituents, that hidden variable theories cannot have local parts, i.e., that their local averages cannot differ from the quantum mechanical ones.
Journal of Physics A: Mathematical and Theoretical, 2016
In this paper we solve two equivalent time optimal control problems. On one hand, we design the c... more In this paper we solve two equivalent time optimal control problems. On one hand, we design the control field to implement in minimum time the SWAP (or equivalent) operator on a two-level system, assuming that it interacts with an additional, uncontrollable, two-level system. On the other hand, we synthesize the SWAP operator simultaneously, in minimum time, on a pair of twolevel systems subject to opposite drifts. We assume that it is possible to perform three independent control actions, and that the total control strength is bounded. These controls either affect the dynamics of the target system, under the first perspective, or, simultaneously, the dynamics of both systems, in the second view. We obtain our results by using techniques of geometric control theory on Lie groups. In particular, we apply the Pontryagin Maximum Principle, and provide a complete characterization of singular and non-singular extremals. Our analysis shows that the problem can be formulated as the motion of a material point in a central force, a well known system in classical mechanics. Although we focus on obtaining the SWAP operator, many of the ideas and techniques developed in this work apply to the time optimal implementation of an arbitrary unitary operator.
Physical Review A, 2015
We study how to generate in minimum time special unitary transformations for a two-level quantum ... more We study how to generate in minimum time special unitary transformations for a two-level quantum system under the assumptions that: (i) the system is subject to a constant drift, (ii) its dynamics can be affected by three independent, bounded controls, (iii) the bounds on the controls are asymmetric, that is, the constraint on the control in the direction of the drift is independent of that on the controls in the orthogonal plane. Using techniques recently developed for the analysis of SU (2) transformations, we fully characterize the reachable sets of the system, and the optimal control strategies for any possible target transformation.
2015 54th IEEE Conference on Decision and Control (CDC), 2015
We consider the Lindblad-Kossakowski quantum master equation describing the dynamics of an open q... more We consider the Lindblad-Kossakowski quantum master equation describing the dynamics of an open quantum systems in the form originally proposed by Davies and Spohn. This equation contains dissipative corrections, accounting for the interaction with the environment, whose expression strongly depends on the adopted Markov approximation. In the case where a control is present, the rigorous derivation of the Markov approximation in the standard case, the weak coupling limit, shows that the control appears not only in the coherent part of the equation but also in the dissipative correction. This complicates the analysis of the dynamics but also offers the opportunity of indirectly affecting the interaction with the environment through the control. In this paper we study this scenario for a finite dimensional quantum system interacting with a (Bosonic) bath of harmonic oscillators. We prove several control theoretic properties of this system and discuss how the control can be used to effectively shape the influence of the environment and obtain desired features of the dynamics.
In the dynamics of open quantum systems, the interaction with the external environment usually le... more In the dynamics of open quantum systems, the interaction with the external environment usually leads to a contraction of the set of reachable states for the system as time increases, eventually shrinking to a single stationary point. In this contribution we describe to what extent it is possible to modify this asymptotic state by means of indirect control, that is by using an auxiliary system coupled to the target system in order to affect its dynamics, when there is a purely dissipative coupling between the two systems. We prove that, also in this restrictive case, it is possible to modify the asymptotic state of the relevant system, give necessary conditions for that and provide physical examples. Therefore, in indirect control schemes, the environmental action has not only a negative impact on the dynamics of a system, it is rather possible to make use of it for control purposes.
SIAM Journal on Control and Optimization, 2015
ABSTRACT In coherent quantum feedback control schemes, a target quantum system S is put in contac... more ABSTRACT In coherent quantum feedback control schemes, a target quantum system S is put in contact with an auxiliary system A and the coherent control can directly affect only A. The system S is controlled 'indirectly' through the interaction with A. The system S is said to be indirectly controllable if every unitary transformation can be performed on the state of S with this scheme. The indirect controllability of S will depend on the `dynamical Lie algebra' L characterizing the dynamics of the total system S+A and on the initial state of the auxiliary system A. In this paper we describe this characterization exactly. A natural assumption is that the auxiliary system A is minimal which means that there is no part of A which is uncoupled to S, and we denote by n_A the dimension of such a minimal A, which we assume to be fully controllable. We show that, if n_A is greater than or equal to 3, indirect controllability of S is verified if and only if complete controllability of the total system S+A is verified, i.e., L=su(n_Sn_A) or L=u(n_Sn_A), where n_S denotes the dimension of the system S. If n_A=2, it is possible to have indirect controllability without having complete controllability. The exact condition for that to happen is given in terms of a Lie algebra L_S which describes the evolution on the system S only. We prove that indirect controllability is verified if and only if L_S=u(n_S), and the initial state of the auxiliary system A is pure.
In a recent paper, Kalamidas has advanced a new proposal of faster than light communication which... more In a recent paper, Kalamidas has advanced a new proposal of faster than light communication which has not yet been proved invalid. In this paper, by strictly sticking to the standard quantum formalism we prove that, as all previous proposals, it does not work.
Physical Review Letters
Recently, it has been argued that no extension of quantum theory can have improved predictive pow... more Recently, it has been argued that no extension of quantum theory can have improved predictive power, under a strong assumption of free choice of the experimental settings, and validity of quantum mechanics. Here, under a different free choice assumption, we describe a model which violates this statement for almost all states of a bipartite two-level system, in a possibly experimentally testable way. From consistency with quantum mechanics and the non-signalling principle, we derive a bound on the local averages for the family of deterministic ontological theories our model belongs to.
In a recent paper, Kalamidas has advanced a new proposal of faster than light communication which... more In a recent paper, Kalamidas has advanced a new proposal of faster than light communication which has not yet been proved invalid. In this paper we show that, as all previous proposals, it does not work. The mistake arises from an inappropriate use of some approximations.
In view of the remarkable interest raised by the introduction of the so called PR-box we analyze ... more In view of the remarkable interest raised by the introduction of the so called PR-box we analyze its nonlocal features from the point of view of Parameter and Outcome Dependence.
Lecture Notes in Physics, 2002
ABSTRACT The property of complete positivity is reviewed in connection with dissipation in elemen... more ABSTRACT The property of complete positivity is reviewed in connection with dissipation in elementary particle physics and neutron interferometry.
Physics Letters A, 2003
We derive an optimal entropic uncertainty relation for an arbitrary pair of observables in a two-... more We derive an optimal entropic uncertainty relation for an arbitrary pair of observables in a two-dimensional Hilbert space. Such a result, for the simple case we are considering, definitively improves all the entropic uncertainty relations which have appeared in the literature.
Physical Review A, 2014
We consider the problem of controlling in minimum time a two-level quantum system which can be su... more We consider the problem of controlling in minimum time a two-level quantum system which can be subject to a drift. The control is assumed to be bounded in magnitude, and to affect two or three independent generators of the dynamics. We describe the time optimal trajectories in SU (2), the Lie group of possible evolutions for the system, by means of a particularly simple parametrization of the group. A key ingredient of our analysis is the introduction of the optimal front line. This tool allows us to fully characterize the time-evolution of the reachable sets, and to derive the worst-case operators and the corresponding times. The analysis is performed in any regime: controlled dynamics stronger, of the same magnitude or weaker than the drift term, and gives a method to synthesize quantum logic operations on a two-level system in minimum time.
Physical Review A, 2007
Pure states are fundamental for the implementation of quantum technologies, and several methods f... more Pure states are fundamental for the implementation of quantum technologies, and several methods for the purification of the state of a quantum system S have been developed in the past years. In this letter we present a new approach, based on the interaction of S with an auxiliary system P , having a wide range of applicability. Considering two-level systems S and P and assuming a particular interaction between them, we prove that complete purifications can be obtained under suitable conditions on the parameters characterizing P. Using analytical and numerical tools, we show that the purification process exhibits a resonant behavior in both the cases of system isolated from the external environment or not.
We generalize Bell's hidden variable model describing the singlet state of a two-qubits syste... more We generalize Bell's hidden variable model describing the singlet state of a two-qubits system by extending it to arbitrary states and observables. As in the original work, we assume a uniform, state-independent probability distribution for the hidden variables which are identified with the unit vectors of a 3-dimensional real space. By slightly modifying our model, we provide also a minimal hidden variable description of the two-qubits system, relying on a single hidden variable. We discuss the main features and the implications of the model.
Recently, it has been argued that no extension of quantum theory can have improved predictive pow... more Recently, it has been argued that no extension of quantum theory can have improved predictive power, under a strong assumption of free choice of the experimental settings, and validity of quantum mechanics. Here, under a different free choice assumption, we describe a model which violates this statement for almost all states of a bipartite two-level system, in a possibly experimentally testable way. From consistency with quantum mechanics and the non-signalling principle, we derive a bound on the local averages for the family of deterministic ontological theories our model belongs to.
Physical Review A, 2012
We extend to any maximally entangled state of a bipartite system whose constituents are arbitrari... more We extend to any maximally entangled state of a bipartite system whose constituents are arbitrarily (but finite) dimensional the result, recently derived for two-dimensional constituents, that hidden variable theories cannot have local parts, i.e., that their local averages cannot differ from the quantum mechanical ones.
Journal of Physics A: Mathematical and Theoretical, 2016
In this paper we solve two equivalent time optimal control problems. On one hand, we design the c... more In this paper we solve two equivalent time optimal control problems. On one hand, we design the control field to implement in minimum time the SWAP (or equivalent) operator on a two-level system, assuming that it interacts with an additional, uncontrollable, two-level system. On the other hand, we synthesize the SWAP operator simultaneously, in minimum time, on a pair of twolevel systems subject to opposite drifts. We assume that it is possible to perform three independent control actions, and that the total control strength is bounded. These controls either affect the dynamics of the target system, under the first perspective, or, simultaneously, the dynamics of both systems, in the second view. We obtain our results by using techniques of geometric control theory on Lie groups. In particular, we apply the Pontryagin Maximum Principle, and provide a complete characterization of singular and non-singular extremals. Our analysis shows that the problem can be formulated as the motion of a material point in a central force, a well known system in classical mechanics. Although we focus on obtaining the SWAP operator, many of the ideas and techniques developed in this work apply to the time optimal implementation of an arbitrary unitary operator.
Physical Review A, 2015
We study how to generate in minimum time special unitary transformations for a two-level quantum ... more We study how to generate in minimum time special unitary transformations for a two-level quantum system under the assumptions that: (i) the system is subject to a constant drift, (ii) its dynamics can be affected by three independent, bounded controls, (iii) the bounds on the controls are asymmetric, that is, the constraint on the control in the direction of the drift is independent of that on the controls in the orthogonal plane. Using techniques recently developed for the analysis of SU (2) transformations, we fully characterize the reachable sets of the system, and the optimal control strategies for any possible target transformation.
2015 54th IEEE Conference on Decision and Control (CDC), 2015
We consider the Lindblad-Kossakowski quantum master equation describing the dynamics of an open q... more We consider the Lindblad-Kossakowski quantum master equation describing the dynamics of an open quantum systems in the form originally proposed by Davies and Spohn. This equation contains dissipative corrections, accounting for the interaction with the environment, whose expression strongly depends on the adopted Markov approximation. In the case where a control is present, the rigorous derivation of the Markov approximation in the standard case, the weak coupling limit, shows that the control appears not only in the coherent part of the equation but also in the dissipative correction. This complicates the analysis of the dynamics but also offers the opportunity of indirectly affecting the interaction with the environment through the control. In this paper we study this scenario for a finite dimensional quantum system interacting with a (Bosonic) bath of harmonic oscillators. We prove several control theoretic properties of this system and discuss how the control can be used to effectively shape the influence of the environment and obtain desired features of the dynamics.
In the dynamics of open quantum systems, the interaction with the external environment usually le... more In the dynamics of open quantum systems, the interaction with the external environment usually leads to a contraction of the set of reachable states for the system as time increases, eventually shrinking to a single stationary point. In this contribution we describe to what extent it is possible to modify this asymptotic state by means of indirect control, that is by using an auxiliary system coupled to the target system in order to affect its dynamics, when there is a purely dissipative coupling between the two systems. We prove that, also in this restrictive case, it is possible to modify the asymptotic state of the relevant system, give necessary conditions for that and provide physical examples. Therefore, in indirect control schemes, the environmental action has not only a negative impact on the dynamics of a system, it is rather possible to make use of it for control purposes.
SIAM Journal on Control and Optimization, 2015
ABSTRACT In coherent quantum feedback control schemes, a target quantum system S is put in contac... more ABSTRACT In coherent quantum feedback control schemes, a target quantum system S is put in contact with an auxiliary system A and the coherent control can directly affect only A. The system S is controlled 'indirectly' through the interaction with A. The system S is said to be indirectly controllable if every unitary transformation can be performed on the state of S with this scheme. The indirect controllability of S will depend on the `dynamical Lie algebra' L characterizing the dynamics of the total system S+A and on the initial state of the auxiliary system A. In this paper we describe this characterization exactly. A natural assumption is that the auxiliary system A is minimal which means that there is no part of A which is uncoupled to S, and we denote by n_A the dimension of such a minimal A, which we assume to be fully controllable. We show that, if n_A is greater than or equal to 3, indirect controllability of S is verified if and only if complete controllability of the total system S+A is verified, i.e., L=su(n_Sn_A) or L=u(n_Sn_A), where n_S denotes the dimension of the system S. If n_A=2, it is possible to have indirect controllability without having complete controllability. The exact condition for that to happen is given in terms of a Lie algebra L_S which describes the evolution on the system S only. We prove that indirect controllability is verified if and only if L_S=u(n_S), and the initial state of the auxiliary system A is pure.
In a recent paper, Kalamidas has advanced a new proposal of faster than light communication which... more In a recent paper, Kalamidas has advanced a new proposal of faster than light communication which has not yet been proved invalid. In this paper, by strictly sticking to the standard quantum formalism we prove that, as all previous proposals, it does not work.
Physical Review Letters
Recently, it has been argued that no extension of quantum theory can have improved predictive pow... more Recently, it has been argued that no extension of quantum theory can have improved predictive power, under a strong assumption of free choice of the experimental settings, and validity of quantum mechanics. Here, under a different free choice assumption, we describe a model which violates this statement for almost all states of a bipartite two-level system, in a possibly experimentally testable way. From consistency with quantum mechanics and the non-signalling principle, we derive a bound on the local averages for the family of deterministic ontological theories our model belongs to.
In a recent paper, Kalamidas has advanced a new proposal of faster than light communication which... more In a recent paper, Kalamidas has advanced a new proposal of faster than light communication which has not yet been proved invalid. In this paper we show that, as all previous proposals, it does not work. The mistake arises from an inappropriate use of some approximations.
In view of the remarkable interest raised by the introduction of the so called PR-box we analyze ... more In view of the remarkable interest raised by the introduction of the so called PR-box we analyze its nonlocal features from the point of view of Parameter and Outcome Dependence.
Lecture Notes in Physics, 2002
ABSTRACT The property of complete positivity is reviewed in connection with dissipation in elemen... more ABSTRACT The property of complete positivity is reviewed in connection with dissipation in elementary particle physics and neutron interferometry.
Physics Letters A, 2003
We derive an optimal entropic uncertainty relation for an arbitrary pair of observables in a two-... more We derive an optimal entropic uncertainty relation for an arbitrary pair of observables in a two-dimensional Hilbert space. Such a result, for the simple case we are considering, definitively improves all the entropic uncertainty relations which have appeared in the literature.
Physical Review A, 2014
We consider the problem of controlling in minimum time a two-level quantum system which can be su... more We consider the problem of controlling in minimum time a two-level quantum system which can be subject to a drift. The control is assumed to be bounded in magnitude, and to affect two or three independent generators of the dynamics. We describe the time optimal trajectories in SU (2), the Lie group of possible evolutions for the system, by means of a particularly simple parametrization of the group. A key ingredient of our analysis is the introduction of the optimal front line. This tool allows us to fully characterize the time-evolution of the reachable sets, and to derive the worst-case operators and the corresponding times. The analysis is performed in any regime: controlled dynamics stronger, of the same magnitude or weaker than the drift term, and gives a method to synthesize quantum logic operations on a two-level system in minimum time.
Physical Review A, 2007
Pure states are fundamental for the implementation of quantum technologies, and several methods f... more Pure states are fundamental for the implementation of quantum technologies, and several methods for the purification of the state of a quantum system S have been developed in the past years. In this letter we present a new approach, based on the interaction of S with an auxiliary system P , having a wide range of applicability. Considering two-level systems S and P and assuming a particular interaction between them, we prove that complete purifications can be obtained under suitable conditions on the parameters characterizing P. Using analytical and numerical tools, we show that the purification process exhibits a resonant behavior in both the cases of system isolated from the external environment or not.