Well-known Nuclear Magnetic Resonance experiments show that the time evolution according to (truncated) dipole-dipole interactions between n spins can be inverted by simple pulse sequences. Independent of n, the reversed evolution is only two times slower than the original one. Here we consider more general spin-spin couplings with long range. We prove that some are considerably more complex to invert since the number of required time steps and the slow-down of the reversed evolutions are necessarily of the order n. Furthermore, the spins have to be addressed separately. We show for which values of the coupling parameters the phase transition between simple and complex time-reversal schemes occurs.
Two approaches toward the arrow of time for scattering processes have been proposed in rigged Hilbert space quantum mechanics. One, due to Arno Bohm, involves preparations and registrations in laboratory operations and results in two semigroups oriented in the forward direction of time. The other, employed by the Brussels-Austin group, is more general, involving excitations and de-excitations of systems, and apparently results in two semigroups oriented in opposite directions of time. It turns out that these two time arrows can be related to each other via Wigner's extensions of the spacetime …
The connection between the micro and macro-arrow of time is discussed in the frame of the stochastic quantum hydrodynamic analogy (SQHA). The presence of fluctuations that in the case on non-linear interactions leads to the breaking of the quantum mechanics on large scale and then to the macroscopic irreversibility with a defined arrow of time, gives also rise to the time reversal breaking in the micro-scale quantum evolution (micro-arrow of time). The quantum irreversibility with time reversal asymmetry is briefly discussed.
One of the stunning consequences of quantum correlations in thermodynamics is the reversal of the arrow of time, recently shown experimentally in [K. Micadei, et al., Nat. Commun. 10:2456 (2019)], and manifesting itself by a reversal of the heat flow (from the cold system to the hot one). Here, we show that contrary to what could have been expected, heat flow reversal can happen without reversal of the arrow of time. Moreover, contrasting with previous studies, no initial correlations between system and bath is required. Instead, the heat flow reversal only relies on internal quantum coherence…
Microscopic physical laws are time-symmetric, hence, a priori there exists no preferential temporal direction. However, the second law of thermodynamics allows one to associate the "forward" temporal direction to a positive variation of the total entropy produced in a thermodynamic process, and a negative variation with its "time-reversal" counterpart. This definition of a temporal axis is normally considered to apply in both classical and quantum contexts. Yet, quantum physics admits also superpositions between forward and time-reversal processes, whereby the thermodynamic arrow of time becom…
We expand the time reversal symmetry arguments of quantum mechanics, originally proposed by Wigner in the context of unitary dynamics, to contain situations including generalized measurements for monitored quantum systems. We propose a scheme to derive the time reversed measurement operators by considering the Schrödinger picture dynamics of a qubit coupled to a measuring device, and show that the time reversed measurement operators form a Positive Operator Valued Measure (POVM) set. We present three particular examples to illustrate time reversal of measurement operators: (1) the Gaussian spi…
There is an incompatibility between the symmetries of causal structure in relativity theory and the signaling abilities of probabilistic devices with inputs and outputs: while time-reversal in relativity will not introduce the ability to signal between spacelike separated regions, this is not the case for probabilistic devices with space-like separated input-output pairs. We explicitly describe a non-signaling device which becomes a perfect signaling device under time-reversal, where time-reversal can be conceptualized as playing backwards a videotape of an agent manipulating the device. This …
Open quantum systems are often represented by non-Hermitian effective Hamiltonians that have complex eigenvalues associated with resonances. In previous work we showed that the evolution of tight-binding open systems can be represented by an explicitly time-reversal symmetric expansion involving all the discrete eigenstates of the effective Hamiltonian. These eigenstates include complex-conjugate pairs of resonant and anti-resonant states. An initially time-reversal-symmetric state contains equal contributions from the resonant and anti-resonant states. Here we show that as the state evolves i…
It is well-known that the 4-rotation in the 4-dimensional space-time is equivalent to the CPT-transformation (C is the charge conjugation, P is the space inversion and T is the time-reversal). The standard definition of the T-reversal includes the change of the sign of time variable and replacement of the initial state of the particle (system of particles) by the final state and vice versa. Since the time-reversal operation changes the state of a particle, the particle's wave function cannot be the eigenfunction of the corresponding operator with a certain eigenvalue, as in the case of space p…
It is one of the most important and long-standing issues of physics to derive the irreversibility out of a time-reversal symmetric equation of motion. The present paper considers the breaking of the time-reversal symmetry in open quantum systems and the emergence of an arrow of time. We claim that the time-reversal symmetric Schrödinger equation can have eigenstates that break the time-reversal symmetry if the system is open in the sense that it has at least a countably infinite number of states. Such eigenstates, namely the resonant and anti-resonant states, have complex eigenvalues. We show …
For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is set by the measurement procedure and that the time reversal requires complex conjugation of the wave function, which is overly complex to spontaneously appear in nature. Building on this Landau-Wigner conjecture, it became possible to demonstrate that time reversal is exponentially improbable in a virgin nature and to design an algorithm artificially reversin…
Uncovering the origin of the arrow of time remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the second law of thermodynamics, which declares that entropy growth proceeds from the system's entanglement with the environment. It remains to be seen, however, whether the irreversibility of time is a fundamental law of nature or whether, on the contrary, it might be circumvented. Here we show that, while in nature the complex conjugation needed for time reversal is exponentially improbable, one can design a quantum…
Dynamical decoupling (DD) is a technique for preserving the coherence of quantum mechanical states in the presence of a noisy environment. It uses sequences of inversion pulses to suppress the environmental perturbations by periodically refocusing them. It has been shown that different sequences of inversion pulses show vastly different performance, in particular also concerning the correction of experimental pulse imperfections. Here, we investigate specifically the role of time-reversal symmetry in the building-blocks of the pulse sequence. We show that using time symmetric building blocks o…
Time's apparent passage has long been debated by philosophers, with no decisive argument for or against its objective existence. In this paper we show that introducing the issue of determinism gives the debate a new, empirical twist. We prove that any theory that states that the basic laws of physics are time-symmetric must be strictly deterministic. It is only determinism that enables time reversal, whether theoretical or experimental, of anyentropy-increasing process. A contradiction therefore arises between Hawking's argument that physical law is time-symmetric and his controversial claim t…
We discuss quantum entanglement in the context of the thermodynamic arrow of time. We review the role of correlations in entropy-decreasing events and prove that the occurrence of a transformation between two thermodynamic states constitutes a new type of entanglement witness, one not defined as a separating plane in state space between separable and entangled states, but as a physical process dependent on the local initial properties of the states. Extending work by Partovi, we consider a general entangled multipartite system that allows large reversals of the thermodynamic arrow of time. We …
Modern approaches to causal modeling give a central role to interventions, which require the active input of an observer and introduces an explicit `causal arrow of time'. Causal models typically adopt a mechanistic interpretation, according to which the direction of the causal arrow is intrinsic to the process being studied. Here we investigate whether the direction of the causal arrow might be a contribution from the observer, rather than an intrinsic property of the process. Working within a counterfactual and non-mechanistic interpretation of causal modeling developed in arXiv:1806.00895, …
Fundamental interactions are either fully or nearly symmetric under time reversal. But macroscopic phenomena have a definite arrow of time. Though there is no convergence on the origin of time's preferential direction, many researchers believe that the direction of time is towards increasing entropy. In this paper, we provide an alternate point of view. In driven-dissipative nonequilibrium systems forced at large scale, the energy flows from large scales to dissipative scales. This generic and multiscale process breaks time reversal symmetry and principle of detailed balance, thus can yield an…
Einstein held that the formalism of Quantum Mechanics (QM) entails "spooky actions at a distance". Indeed, in the 60's Bell showed that the predictions of QM disagree with the results of any locally causal description. Accepting non-local descriptions while retaining causality leads to a clash with the theory of relativity. Furthermore, the causal arrow of time by definition contradicts time-reversal symmetry. For these reasons, some authors (Feynman and Wheeler, Costa de Beauregard, Cramer, Price) have advocated abandoning microscopic causality. In the present article, a simplistic but concre…
In order to describe the quantum electrodynamic measurement process in a relativistic observer-participant manner, an operator symmetry of "microscopic observer-participation" called Measurement Color (MC) is incorporated into the field theoretic structure of Quantum Electrodynamics (QED) in the Heisenberg Picture. It is found that the resultant Measurement Color Quantum Electrodynamics (MC-QED) contains a microscopic quantum electrodynamic arrow of time that emerges dynamically, independent of any thermodynamic or cosmological assumptions. This occurs because the photon has a negative time pa…
The nature of time has beguiled philosophers for nearly three millennia. There are myriad types of time including cosmological time, biological time, psychological time, physical time, historical time, and even theological time. My brief essay concerns time in physics and I hope that the pragmatism of an experimental physicist might help provide a perspective that is often absent in treatises by contemporary philosophers and physicists. This is especially the case for the notion of the arrow of time. The paradox of the arrow of time arises because the laws of physics are invariably time revers…
We develop a simple protocol for a one-shot version of quantum state redistribution, which is the most general two-terminal source coding problem. The protocol is simplified from a combination of protocols for the fully quantum reverse Shannon and fully quantum Slepian-Wolf problems, with its time-reversal symmetry being apparent. When the protocol is applied to the case where the redistributed states have a tensor power structure, more natural resource rates are obtained.
In this work we experimentally study the efficiency of various dynamical decoupling sequences for suppressing decoherence of single as well as multiple quantum coherences on large spin-clusters. The system involves crystallites of a powdered sample containing a large number of molecular protons interacting via long-range dipole-dipole interaction. The multiple quantum coherences are prepared by progressively creating correlations in the spin lattice using standard pulse sequences implementing two-quantum average Hamiltonian. The spin system is then subjected to various dynamical decoupling seq…
A theory is developed which attempts to reconcile the measurements of nonlocal quantum observables with special relativity and quantum mechanics. The collapse of a wave function, which coincides with a nonlocal measurement by some macroscopic measuring device, is associated with the triggering of an absorber mechanism due to the interaction of the apparatus with the charges in the rest of the universe. The standard retarded electromagnetic field plus radiation damping is converted, for a short time during the collapse of the wave function, to an advanced field plus radiation. The reversal of t…
In the understanding of the fundamental interactions, the origin of an arrow of time is viewed as problematic. However, quantum field theory has an arrow of causality, which tells us which time direction is the past lightcone and which is the future. This direction is tied to the conventions used in the quantization procedures. The different possible causal directions have related physics - in this sense they are covariant under time-reversal. However, only one causal direction emerges for a given set of conventions. This causal arrow tells us the direction that scattering reactions proceed. T…
The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems, leading to well-defined time arrows. Associated with these time arrows are semigroups bearing time orientations. Usually, when time symmetry is broken, two time-oriented semigroups result, one directed toward the future and one directed toward the past. If time-reversed states and evolutions are excluded due to resonances, then the status of these states and their associated backwards-in-tim…
The second law of thermodynamics points to the existence of an `arrow of time', along which entropy only increases. This arises despite the time-reversal symmetry (TRS) of the microscopic laws of nature. Within quantum theory, TRS underpins many interesting phenomena, most notably topological insulators and the Haldane phase of quantum magnets. Here, we demonstrate that such TRS-protected effects are fundamentally unstable against coupling to an environment. Irrespective of the microscopic symmetries, interactions between a quantum system and its surroundings facilitate processes which would b…
Here we present the time-bidirectional state formalism (TBSF) unifying in a general manner the standard quantum mechanical formalism with no postselection and the time-symmetrized two-state (density) vector formalism, which deals with postselected states. In the proposed approach, a quantum particle's state, called a time-bidirectional state, is equivalent to a joined state of two particles propagating in opposite time directions. For a general time-bidirectional state, we derive outcome probabilities of generalized measurements, as well as mean and weak values of Hermitian observables. We als…
Is a spontaneous perpetual reversal of the arrow of time possible? The out-of-time-ordered correlator (OTOC) is a standard measure of irreversibility, quantum scrambling, and the arrow of time. The question may be thus formulated more precisely and conveniently: can spatially-ordered perpetual OTOC oscillations exist in many-body systems? Here we give a rigorous lower bound on the amplitude of OTOC oscillations in terms of a strictly local dynamical algebra allowing for identification of systems that are out-of-time-ordered (OTO) crystals. While OTOC oscillations are possible for few-body syst…
The discussion on time-reversal in quantum mechanics exists at least since Wigner's ``Uber die Operation der Zeitumkehr in der Quantenmechanik'' paper in 1932. If and how the dynamics of the quantum world is time-reversible has been the subject of many controversies. Some have seen quantum mechanics as fundamentally time-irreversible, see for example von Neumann, and some have seen in that the ultimate cause of time's arrow and second law behavior. In his best-selling book ``The Emperor's New Mind'', Roger Penrose argues similarly and concludes that ``our sought-for quantum gravity must be a t…
Avoiding the loss of coherence of quantum mechanical states is an important prerequisite for quantum information processing. Dynamical decoupling (DD) is one of the most effective experimental methods for maintaining coherence, especially when one can access only the qubit-system and not its environment (bath). It involves the application of pulses to the system whose net effect is a reversal of the system-environment interaction. In any real system, however, the environment is not static, and therefore the reversal of the system-environment interaction becomes imperfect if the spacing between…
In previous papers we have considered mutual simulation of n-partite pair-interaction Hamiltonians. We have focussed on the running time overhead of general simulations, while considering the required number of time steps only for special cases (decoupling and time-reversal). These two complexity measures differ significantly. Here we derive lower bounds on the number of time steps for general simulations. In particular, the simulation of interaction graphs with irrational spectrum requires at least n steps. We discuss as examples graphs that correspond to graph codes and nearest neighbor inte…
Error-resilient Reversal of Quantum Chaotic Dynamics Enabled by Scramblons
University of Science and Technology of China（中国科学技术大学）；Tsinghua University（清华大学）；The Chinese University of Hong Kong（香港中文大学）；Hefei National Laboratory（合肥国家实验室）
Echo protocols provide a means to investigate the arrow of time in macroscopic processes. Starting from a nonequilibrium state, the many-body quantum system under study is evolved for a certain period of time $τ$. Thereafter, an (effective) time reversal is performed that would -- if implemented perfectly -- take the system back to the initial state after another time period $τ$. Typical examples are nuclear magnetic resonance imaging and polarization echo experiments. The presence of small, uncontrolled inaccuracies during the backward propagation results in deviations of the "echo signal" fr…
The Heisenberg exchange interaction between neighboring quantum dots allows precise voltage control over spin dynamics, due to the ability to precisely control the overlap of orbital wavefunctions by gate electrodes. This allows the study of fundamental electronic phenomena and finds applications in quantum information processing. Although spin-based quantum circuits based on short-range exchange interactions are possible, the development of scalable, longer-range coupling schemes constitutes a critical challenge within the spin-qubit community. Approaches based on capacitative coupling and ca…
General physical background of Peres-Horodecki positive partial transpose (ppt-) separability criterion is revealed. Especially, the physical sense of partial transpose operation is shown to be equivalent to the "local causality reversal" (LCR-) procedure for all separable quantum systems or to the uncertainty in a global time arrow direction in all entangled cases. Using these universal causal considerations the heuristic causal separability criterion has been proposed for arbitrary $ D^{N} \times D^{N}$ density matrices acting in $ \mathcal{H}_{D}^{\otimes N} $ Hilbert spaces which describe …
