Study of nonlocal correlations in term of Hardy's argument has been quite popular in quantum mechanics. Recently Hardy's argument of non-locality has been studied in the context of generalized non-signaling theory as well as theory respecting information causality. Information causality condition significantly reduces the success probability for Hardy's argument when compared to the result based on non-signaling condition. Here motivated by the fact that maximally entangled state in quantum mechanics does not exhibit Hardy's non-local correlation, we do a qualitative study of the property of local randomness of measured observable on each side reproducing Hardy's non-locality correlation,in the context of information causality condition. On applying the necessary condition for respecting the principle of information causality, we find that there are severe restrictions on the local randomness of measured observable in contrast to results obtained from no-signaling condition.Still, there are some restrictions imposed by quantum mechanics that are not obtained from information causality condition.
Recently,the principle of nonviolation of information causality [Nature 461,1101 (2009)], has been proposed as one of the foundational properties of nature. We explore the Hardy's nonlocality theorem for two qubit systems, in the context of generalised probability theory, restricted by the principle of nonviolation of information causality. Applying, a sufficient condition for information causality violation, we derive an upper bound on the maximum success probability of Hardy's nonlocality argument. We find that the bound achieved here is higher than that allowed by quantum mechanics,but stil…
The principle of non-violation of "information causality", has been proposed as one of the foundational properties of nature\cite{nature}. The main goal of the paper is to explore the gap between quantum mechanical correlations and those allowed by "information causality" in the context of local randomness by using Cabello's nonlocality argument. This is interesting because the gap is slightly different than in the context of Hardy's similar nonlocality argument\cite{gazi}
Hardy's paradox was originally presented as a demonstration, without inequalities, of the incompatibility between quantum mechanics and the hypothesis of local causality. Equipped with newly developed tools that allow for a quantitative assessment of realism, here we revisit Hardy's paradox and argue that non-local causality is not mandatory for its solution; quantum irrealism suffices.
Device-Independent (DI) security is the best form of quantum cryptography, providing information-theoretic security based on the very laws of nature. In its highest form, security is guaranteed against adversaries limited only by the no-superluminal signalling rule of relativity. The task of randomness amplification, to generate secure fully uniform bits starting from weakly random seeds, is of both cryptographic and foundational interest, being important for the generation of cryptographically secure random numbers as well as bringing deep connections to the existence of free-will. DI no-sign…
In this paper, we study the Hardy nonlocal argument (HNA) and the Cabello nonlocal argument (CNA) under the Information Causality, Macroscopic Locality and Local Orthogonality principles in the context of Local Randomness. We see that, in the context of all the possibilities of local randomness, the gap between the quantum mechanics and the above principles, in the Cabello's nonlocality argument is larger than the Hardy's case. Therefore the CNA is stronger control than the HNA for detecting post-quantum nosignalling correlations.
We give a analytic quantitative relation between Hardy's non-locality and Bell operator. We find that Hardy's non-locality is a sufficient condition for violation of Bell inequality, the upper bound of Hardy's non-locality allowed by information causality just correspond to Tsirelson bound of Bell inequality, and the upper bound of Hardy's non-locality allowed by the principle of no-signaling just correspond to the algebraic maximum of Bell operator. Then we study the Cabello's argument of Hardy's non-locality (a generalization of Hardy's argument) and find a similar relation between it and vi…
Quantum statistics originate from the physics of state preparation. It is therefore wrong to think of quantum states as fundamental. In fact, quantum states are merely summaries of dynamical processes that randomize the properties of the system by drawing on the inexhaustible reservoir of quantum fluctuations provided by the physical tools used to control the quantum system. The mathematical form of the "state vector" is actually an expression of the laws of causality which describe the relations between physical properties in terms of the action of transformations. These laws of causality dir…
The set of multiparty correlations that respect all bi-partite principles has been conjectured to be same as the set of time-ordered-bi-local correlations. Based on this conjuncture we find the maximum value of success probability of tri-partite Hardy's correlation respecting all bi-partite physical principles. Unlike in quantum mechanics, the no-signaling principle does not reveal any gap in Hardy's maximum success probability for bi-partite and tri-partite system. Information causality principle is shown to be successful in qualitatively revealing this quantum feature and this result is inde…
A long sequence of tosses of a classical coin produces an apparently random bit string, but classical randomness is an illusion: the algorithmic information content of a classically-generated bit string lies almost entirely in the description of initial conditions. This letter presents a simple argument that, by contrast, a sequence of bits produced by tossing a quantum coin is, almost certainly, genuinely (algorithmically) random. This result can be interpreted as a strengthening of Bell's no-hidden-variables theorem, and relies on causality and quantum entanglement in a manner similar to Bel…
A new interpretation of quantum mechanics, similar to the Copenhagen interpretation, is developed from time-symmetry arguments and commonly held principles concerning time and causality. These principles, which are grounded in ideas outside of quantum mechanics, suggest that the strange features and paradoxes of quantum mechanics come from backward causation, in which future events can change the past. Using these principles this paper gives a better understanding of (and reasons for) stationary states, tunneling, wave-particle duality, the measurement problem with the collapse of the state ve…
The amount of nonlocality in quantum theory is limited compared to that allowed in generalized no-signaling theory [Found. Phys. 24, 379 (1994)]. This feature, for example, gets manifested in the amount of Bell inequality violation as well as in the degree of success probability of Hardy's (Cabello's) nonlocality argument. Physical principles like information causality and macroscopic locality have been proposed for analyzing restricted nonlocality in quantum mechanics---viz. explaining the Cirel'son bound. However, these principles are not that much successful in explaining the maximum succes…
The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of consequences. First, the usual definitions of randomness depend on a causal structure and turn meaningless. So motivated, we propose an intrinsic, physically motivated measure for the randomness of a string of bits: its length minus its normalized work value, a quantity we closely relate to its Kolmogorov complexity (the length of the shortest program makin…
Relativistic causality, namely, the impossibility of signaling at superluminal speeds, restricts the kinds of correlations which can occur between different parts of a composite physical system. Here we establish the basic restrictions which relativistic causality imposes on the joint probabilities involved in an experiment of the Einstein-Podolsky-Rosen-Bohm type. Quantum mechanics, on the other hand, places further restrictions beyond those required by general considerations like causality and consistency. We illustrate this fact by considering the sum of correlations involved in the CHSH in…
Information causality states that the information obtainable by a receiver cannot be greater than the communication bits from a sender, even if they utilize no-signaling resources. This physical principle successfully explains some boundaries between quantum and post-quantum nonlocal correlations, where the obtainable information reaches the maximum limit. We show that no-signaling resources of pure partially entangled states produce randomness (or noise) in the communication bits, and achievement of the maximum limit is impossible, i.e., the information causality principle is insufficient for…
After a review of the arrows of time, we describe the possibilities of a time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is time-symmetric, the rigged Hilbert space formulation, which arose from Dirac's bra-ket formalism, allows the choice of asymmetric boundary conditions analogous to the retarded solutions of the Maxwell equations for the radiation arrow of time. This led to irreversibility on the microphysical level as exemplified by decaying states or resonances. Resonances are mathematically represented by Gamow kets, functionals over a space of very well-behaved…
In quantum mechanical experiments one distinguishes between the state of an experimental system and an observable measured in it. Heuristically, the distinction between states and observables is also suggested in scattering theory or when one expresses causality. We explain how this distinction can be made also mathematically. The result is a theory with asymmetric time evolution and for which decaying states are exactly unified with resonances. A consequence of the asymmetric time evolution is a beginning of time. The meaning of this beginning of time can be understood by identifying it in da…
It is shown that for quantum ensembles consisting of equal particles, the collective micro-causality does not contradict the quantum theory. The amplitudes of the states of such an ensemble can be divided into small portions, for each of which evolution in time will be accurately determined, without any randomness. For ensembles of dissimilar particles, whose Hamiltonian is represented as a sum of operators belonging to homogeneous systems, micro-causality will take place on separate small segments, on which only the selected component will act. In this case, the duration of the terms for diff…
In this work, we propose device independent true random numbers generation protocols based on non-inequality paradoxes such as Hardy's and Cabello's non-locality argument. The efficiency of generating randomness in our protocols are far better than any other proposed protocols certified by CHSH inequality or other non-locality test involving inequalities. Thus, highlighting non-inequality paradox as an important resource for device independent quantum information processing in particular generating true randomness. As a byproduct, we find that the non-local bound of the Cabello's argument with…
Landauer's principle claims that "Information is Physical." It is not surprising that its conceptual antithesis, Wheeler's "It from Bit," has been more popular among computer scientists --- in the form of the Church-Turing hypothesis: All natural processes can be computed by a universal Turing machine; physical laws then become descriptions of subsets of observable, as opposed to merely possible, computations. Switching back and forth between the two traditional styles of thought, motivated by quantum-physical Bell correlations and the doubts they raise about fundamental space-time causality, …
Non-local observables play an important role in quantum theory, from Bell inequalities and various post-selection paradoxes to quantum error correction codes. Instantaneous measurement of these observables is known to be a difficult problem, especially when the measurements are projective. The standard von Neumann Hamiltonian used to model projective measurements cannot be implemented directly in a non-local scenario and can, in some cases, violate causality. We present a scheme for effectively generating the von Neumann Hamiltonian for non-local observables without the need to communicate and…
We derive a device-independent quantum key distribution protocol based on synchronous correlations and their Bell inequalities. This protocol offers several advantages over other device-independent schemes including symmetry between the two users and no need for preshared randomness. We close a "synchronicity" loophole by showing that an almost synchronous correlation inherits the self-testing property of the associated synchronous correlation. We also pose a new security assumption that closes the "locality" (or "causality") loophole: an unbounded adversary with even a small uncertainty about…
We describe new unconditionally secure bit commitment schemes whose security is based on Minkowski causality and the monogamy of quantum entanglement. We first describe an ideal scheme that is purely deterministic, in the sense that neither party needs to generate any secret randomness at any stage. We also describe a variant that allows the committer to proceed deterministically, requires only local randomness generation from the receiver, and allows the commitment to be verified in the neighbourhood of the unveiling point. We show that these schemes still offer near-perfect security in the p…
In quantum physics, disturbance due to a measurement is not negligible. This requires the time parameter $t$ in the Schrödinger or Heisenberg equation to be considered differently from a time continuum of experimenter's clock $T$ on which physical events are recorded. It will be shown that $t$ represents an ensemble of time intervals on $T$ during which a microsystem travels undisturbed. In particular $t=0$ represents the ensemble of preparation events that we refer to as the ensemble of beginnings of time. This restricts $t$ to be $0\leq t<\infty$. But such a time evolution of quantum states …
A slight modification of one axiom of quantum theory changes a reversible theory into a time asymmetric theory. Whereas the standard Hilbert space axiom does not distinguish mathematically between the space of states (in-states of scattering theory) and the space of observables (out-``states'' of scattering theory) the new axiom associates states and observables to two different Hardy subspaces which are dense in the same Hilbert space and analytic in the lower and upper complex energy plane, respectively. As a consequence of this new axiom the dynamical equations (Schrödinger or Heisenberg) i…
This work is concerned with the issue of applications of the semi-definite programming (SDP) in the field of quantum information science. Our results of the analysis of certain quantum information protocols using this optimization technique are presented, and an implementation of a relevant numerical tool is introduced. The key method used is NPA discovered by Navascues et al. [Phys. Rev. Lett. 98, 010401 (2007)]. In chapter 1 a brief overview of mathematical methods used in this work is presented. In chapter 2 an introduction to quantum information science is given. Chapter 3 concerns the dev…
The classical notions of continuity and mechanical causality are left in order to refor- mulate the Quantum Theory starting from two principles: I) the intrinsic randomness of quantum process at microphysical level, II) the projective representations of sym- metries of the system. The second principle determines the geometry and then a new logic for describing the history of events (Feynman's paths) that modifies the rules of classical probabilistic calculus. The notion of classical trajectory is replaced by a history of spontaneous, random an discontinuous events. So the theory is reduced to …
This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except the very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single real…
The Rigged Hilbert Space (RHS) theory of resonance scattering and decay is reviewed and contrasted with the standard Hilbert space (HS) theory of quantum mechanics. The main difference is in the choice of boundary conditions. Whereas the conventional theory allows for the in-states $ϕ^+$ and the out-states (observables) $ψ^-$ of the S-matrix elements $(ψ^-,ϕ^+)=(ψ^{out},S ϕ^{in})$ any elements of the HS $\H$, $\{ψ^-\}=\{ϕ^+\}(=\H)$, the RHS theory chooses the boundary conditions~: $ϕ^+\inΦ_-\subset\H\subsetΦ_-^\times$, $ψ^-\inΦ_+\subset \H\subset Φ_+^\times$, where $Φ_-$ ($Φ_+$) are Hardy clas…
"Nonlocality-of-a-single-photon" based Quantum Key Distribution and Random Number Generation schemes and their device-independent security analysis
University of Gdańsk（格但斯克大学）；Technology Innovation Institute（技术创新研究所）；Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）；Institute of Theoretical and Applied Informatics, Polish Academy of Sciences（波兰科学院理论与应用数学研究所）
