Simulations of Closed Timelike Curves

Proposed models of closed timelike curves (CTCs) have been shown to enable powerful information-processing protocols. We examine the simulation of models of CTCs both by other models of CTCs and by physical systems without access to CTCs. We prove that the recently proposed transition probability CTCs (T-CTCs) are physically equivalent to postselection CTCs (P-CTCs), in the sense that one model can simulate the other with reasonable overhead. As a consequence, their information-processing capabilities are equivalent. We also describe a method for quantum computers to simulate Deutschian CTCs (but with a reasonable overhead only in some cases). In cases for which the overhead is reasonable, it might be possible to perform the simulation in a table-top experiment. This approach has the benefit of resolving some ambiguities associated with the equivalent circuit model of Ralph et al. Furthermore, we provide an explicit form for the state of the CTC system such that it is a maximum-entropy state, as prescribed by Deutsch.     

Revisiting Consistency Conditions for Quantum States of Systems on Closed Timelike Curves: An Epistemic Perspective

There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use of the dynamical equations developed by Deutsch, which were developed from a consistency condition that assumes that mixed quantum states uniquely describe the physical state of a system. We criticize this choice of consistency condition from an epistemic perspective, i.e., a perspective in which the quantum state represents a state of knowledge about a system. We demonstrate that directly applying Deutsch’s condition when mixed states are treated as representing an observer’s knowledge of a system can conceal time travel paradoxes from the observer, rather than resolving them. To shed further light on the appropriate dynamics for quantum systems traversing CTCs, we make use of a toy epistemic theory with a strictly classical ontology due to Spekkens and show that, in contrast to the results of Deutsch, many of the traditional paradoxical effects of time travel are present.     

A twist in the geometry of rotating black holes: seeking the cause of acausality

We investigate Kerr–Newman black holes in which a rotating charged ring-shaped singularity induces a region which contains closed timelike curves (CTCs). Contrary to popular belief, it turns out that the time orientation of the CTC is opposite to the direction in which the singularity or the ergosphere rotates. In this sense, CTCs “counter-rotate” against the rotating black hole. We have similar results for all spacetimes sufficiently familiar to us in which rotation induces CTCs. This motivates our conjecture that perhaps this counter-rotation is not an accidental oddity particular to Kerr–Newman spacetimes, but instead there may be a general and intuitively comprehensible reason for this.     

Closed timelike curves via postselection: theory and experimental test of consistency

Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can interact with its former self in the past. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we analyze an alternative quantum formulation of CTCs based on teleportation and postselection, and show that it is inequivalent to Deutsch's. The predictions or retrodictions of our theory can be simulated experimentally: we report the results of an experiment illustrating how in our particular theory the "grandfather paradox" is resolved.     

Universal Approximation of Multi-copy States and Universal Quantum Lossless Data Compression

We have proven that there exists a quantum state approximating any multi-copy state universally when we measure the error by means of the normalized relative entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE Trans. IT 46, 810–819 (2009)), the general case has been open for more than ten years. For a deeper analysis, we have solved the mini-max problem concerning ‘approximation error’ up to the second order. Furthermore, we have applied this result to quantum lossless data compression, and have constructed a universal quantum lossless data compression.     

Necessary and sufficient condition for nonzero quantum discord

Quantum discord characterizes "nonclassicality" of correlations in quantum mechanics. It has been proposed as the key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. We obtain a necessary and sufficient condition for the existence of nonzero quantum discord for any dimensional bipartite states. This condition is easily experimentally implementable. Based on this, we propose a geometrical way of quantifying quantum discord. For two qubits this results in a closed form of expression for discord. We apply our results to the model of deterministic quantum computation with one qubit, showing that quantum discord is unlikely to be the reason behind its speedup.     

Modular values and weak values of quantum observables

The concept of a modular value of an observable of a pre- and postselected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an effective interaction when the coupling is weak, it describes a coupling of any strength but only to qubit meters. The generalization of the concept for a coupling of a composite system to a multiqubit meter provides an explanation of some current experiments.     

Multiparty Quantum Key Agreement Based on Three-Photon Entanglement with Unidirectional Qubit Transmission

A multiparty quantum key agreement protocol based on three-photon entangled states is proposed. In this scheme, the quantum channel between all parties is that of a closed loop, in which the qubit transmission is one-way. Each party can obtain the sum of the other parties’ secret key values through the coding rules instead of extracting their private keys. The shared secret key cannot be determined by any subset of all the participants except the universal set and each party makes an equal contribution to the final key. Moreover, the security analysis shows our protocol can resist both outside attacks and inside attacks.

     

The logic of quantum mechanics derived from classical general relativity

For the first time it is shown that the logic of quantum mechanics can be derived from classical physics. An orthomodular lattice of propositions characteristic of quantum logic, is constructed for manifolds in Einstein’s theory of general relativity. A particle is modelled by a topologically non-trivial 4-manifold with closed timelike curves—a 4-geon, rather than as an evolving 3-manifold. It is then possible for both the state preparationand measurement apparatus to constrain the results of experiments. It is shown that propositions about the results of measurements can satisfy a non-distributive logic rather than the Boolean logic of classical systems. Reasonable assumptions about the role of the measurement apparatus leads to an orthomodular lattice of propositions characteristic of quantum logic.     

Closed Timelike Curves and Time Travel: Dispelling the Myth

G?del’s contention that closed timelike curves (CTC’s) are a necessary consequence of the Einstein equations for his metric is challenged. It is seen that the imposition of periodicity in a timelike coordinate is the actual source of CTC’s rather than the physics of general relativity. This conclusion is supported by the creation of G?del-like CTC’s in flat space by the correct choice of coordinate system and identifications. Thus, the indications are that the notion of a time machine remains exclusively an aspect of science fiction fantasy. The element of the identification of spacetime points is also seen to be the essential factor in the modern creation of CTC’s in the Gott model of moving cosmic strings.     

The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory

The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel’s entanglement assisted classical capacity. In this paper, we provide a new proof of this theorem, which has previously been proved by Bennett, Devetak, Harrow, Shor, and Winter. Our proof has a clear structure being based on two recent information-theoretic results: one-shot Quantum State Merging and the Post-Selection Technique for quantum channels.     

Experimental implementation of the optimal linear-optical controlled phase gate

We report on the first experimental realization of optimal linear-optical controlled phase gates for arbitrary phases. The realized scheme is entirely flexible in that the phase shift can be tuned to any given value. All such controlled phase gates are optimal in the sense that they operate at the maximum possible success probabilities that are achievable within the framework of postselected linear-optical implementations with vacuum ancillas. The quantum gate is implemented by using bulk optical elements and polarization encoding of qubit states. We have experimentally explored the remarkable observation that the optimum success probability is not monotone in the phase.     

Detecting the classical harmonic vibrations of micro amplitudes and low frequencies with an atomic Mach–Zehnder interferometer

Here we present an example of an axially symmetric spacetime, representing pure radiation, and admitting circular closed timelike curves (CTCs) on the $z= \hbox {constant plane}$ . The spacetime is regular everywhere, having no curvature singularities and is locally isometric to (non-vacuum) pp wave spacetimes. The stability of the CTCs under linear perturbations is studied and they are found to be stable from a calculation of the Lyapunov exponent for the deviation vector. We also demonstrate that the spacetime also admits non-circular CTCs which do not lie in this plane. A modification of the metric is also studied and we find that a region of this spacetime behaves like a time-machine where CTCs appear after a certain instant of time.     

Closed Timelike Curves—Time and Again

Sixty years ago, in 1949, Kurt Gödel published a paper dedicated to Albert Einstein on the occasion of his 70th birthday. Gödel presented a solution of Einstein’s field equations for a rotating, homogeneous, stationary universe with negative cosmological constant. Among various surprising properties this universe allows closed timelike curves (CTC), i.e. travel into the past and into the future. Until today many papers have been published concerning physical, logical and philosophical consequences of these results and the existence of closed timelike worldlines in the General Theory of Relativity. Starting from a short survey on Gödel’s work we proceed to elucidate more modern interpretations of the existence of CTCs.     

Relativistic quantum coin tossing

A relativistic quantum exchange protocol enabling “coin tossing at a distance” between two participants is proposed. The exchange protocol is based on the fact that to distinguish a pair of orthogonal states with certainty in relativistic quantum mechanics requires a finite time that depends on the structure of the states themselves. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 10, 684–689 (25 November 1999)     

A Physical Approach to Tsirelson’s Problem

Tsirelson’s problem deals with how to model separate measurements in quantum mechanics. In addition to its theoretical importance, the resolution of Tsirelson’s problem could have great consequences for device independent quantum key distribution and certified randomness. Unfortunately, understanding present literature on the subject requires a heavy mathematical background. In this paper, we introduce quansality, a new theoretical concept that allows to reinterpret Tsirelson’s problem from a foundational point of view. Using quansality as a guide, we recover all known results on Tsirelson’s problem in a clear and intuitive way.     

Simple family of nonadditive quantum codes

Most known quantum codes are additive, meaning the code can be described as the simultaneous eigenspace of an Abelian subgroup of the Pauli group. While in some scenarios such codes are strictly suboptimal, very little is understood about how to construct nonadditive codes with good performance. Here we present a family of distance 2 nonadditive quantum codes for all odd block lengths n, that has a particularly simple form. Our codes detect single qubit errors (or correct single qubit erasures) while encoding a higher dimensional space than is possible with an additive code or, for n> or =11, any previous codes. We exhibit the encoding circuits and automorphism group for our codes as well.     

A Quantum Weak Energy Inequality¶for Dirac Fields in Curved Spacetime

Quantum fields are well known to violate the weak energy condition of general relativity: the renormalised energy density at any given point is unbounded from below as a function of the quantum state. By contrast, for the scalar and electromagnetic fields it has been shown that weighted averages of the energy density along timelike curves satisfy “quantum weak energy inequalities” (QWEIs) which constitute lower bounds on these quantities. Previously, Dirac QWEIs have been obtained only for massless fields in two-dimensional spacetimes. In this paper we establish QWEIs for the Dirac and Majorana fields of mass m≥ 0 on general four-dimensional globally hyperbolic spacetimes, averaging along arbitrary smooth timelike curves with respect to any of a large class of smooth compactly supported positive weights. Our proof makes essential use of the microlocal characterisation of the class of Hadamard states, for which the energy density may be defined by point-splitting. Received: 21 May 2001 / Accepted: 23 August 2001