Reduction of the Wavepacket: How Long Does it Take?

We show that the ``reduction of the wavepacket'' caused by the interaction with the environment occurs on a timescale which is typically many orders of magnitude shorter than the relaxation timescale $\tau$. In particular, we show that in a system interacting with a ``canonical'' heat bath of harmonic oscillators decorrelation timescale of two pieces of the wave-packet separated by $N$ thermal de Broglie wavelengths is approximately $\tau/N^2$. Therefore, in the classical limit $\hbar \to 0$ dynamical reversibility $(\tau \to \infty)$ is compatible with ``instantaneous'' coherence loss.Comment: 7 pages. This paper introduced what is now known as "decoherence timescale" and gave a now broadly used estimate, Eq.(1), for quantum Brownian motio

Quantum Discord and Maxwell's Demons

Quantum discord was proposed as an information theoretic measure of the ``quantumness'' of correlations. I show that discord determines the difference between the efficiency of quantum and classical Maxwell's demons in extracting work from collections of correlated quantum systems

Relative States and the Environment: Einselection, Envariance, Quantum Darwinism, and the Existential Interpretation

Starting with basic axioms of quantum theory I revisit "Relative State Interpretation'' set out 50 years ago by Hugh Everett

Maxwell's Demon, Szilard's Engine and Quantum Measurements

We propose and analyze a quantum version of Szilard's ``one-molecule engine.'' In particular, we recover, in the quantum context, Szilard's conclusion concerning the free energy ``cost'' of measurements: $\Delta F \geq k_B T\ln2$ per bit of information.Comment: 9 pages, 1 figur

Entanglement Symmetry, Amplitudes, and Probabilities: Inverting Born's Rule

Symmetry of entangled states under a swap of outcomes ("envariance") implies their equiprobability, and leads to Born's rule. Here I show that the amplitude of a state given by a superposition of sequences of events that share same total count (e.g., n detections of 0 and m of 1 in a spin 1/2 measurement) is proportional to the square root of the fraction - square root of the relative frequency - of all the equiprobable sequences of 0's and 1's with that n and m.Comment: Submitted to Physical Review Letter

Decoherence, chaos, quantum-classical correspondence, and the algorithmic arrow of time

The environment -- external or internal degrees of freedom coupled to the system -- can, in effect, monitor some of its observables. As a result, the eigenstates of these observables decohere and behave like classical states: Continuous destruction of superpositions leads to environment-induced superselection (einselection). Here I investigate it in the context of quantum chaos (i. e., quantum dynamics of systems which are classically chaotic).Comment: 26 pages in Tex, 3 figure

Quantum Theory of the Classical: Quantum Jumps, Born's Rule, and Objective Classical Reality via Quantum Darwinism

Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with derivation of preferred sets of states that help define what exists - our everyday classical reality. They emerge as a result of breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification - of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection. Pointer states obtained this way determine what can happen - define events - without appealing to Born's rule for probabilities. Therefore, Born's rule can be now deduced from the entanglement-assisted invariance, or envariance - a symmetry of entangled quantum states. With probabilities at hand one also gains new insights into foundations of quantum statistical physics. Moreover, one can now analyze information flows responsible for decoherence. These information flows explain how perception of objective classical reality arises from the quantum substrate: Effective amplification they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment - through quantum Darwinism

Preferred Observables, Predictability, Classicality, and the Environment-Induced Decoherence

Selection of the preferred classical set of states in the process of decoherence -- so important for cosmological considerations -- is discussed with an emphasis on the role of information loss and entropy. {\it Persistence of correlations} between the observables of two systems (for instance, a record and a state of a system evolved from the initial conditions described by that record) in the presence of the environment is used to define classical behavior. From the viewpoint of an observer (or any system capable of maintaining records) {\it predictability} is a measure of such persistence. {\it Predictability sieve} -- a procedure which employs both the statistical and algorithmic entropies to systematically explore all of the Hilbert space of an open system in order to eliminate the majority of the unpredictable and non-classical states and to locate the islands of predictability including the preferred {\it pointer basis} is proposed. Predictably evolving states of decohering systems along with the time-ordered sequences of records of their evolution define the effectively classical branches of the universal wavefunction in the context of the ``Many Worlds Interpretation". The relation between the consistent histories approach and the preferred basis is considered. It is demonstrated that histories of sequences of events corresponding to projections onto the states of the pointer basis are consistent.Comment: to appear in ``The Physical Origins of Time Asymmetry'' ed by J.J. Halliwell et al., Cambridge Univ. Press. 38 Pages, Preprint LA-UR-92-2051. Content-Length: 12308

Quantum Reversibility Is Relative, Or Do Quantum Measurements Reset Initial Conditions?

I compare the role of the information in the classical and quantum dynamics by examining the relation between information flows in measurements and the ability of observers to reverse evolutions. I show that in the Newtonian dynamics reversibility is unaffected by the observer's retention of the information about the measurement outcome. By contrast -- even though quantum dynamics is unitary, hence, reversible -- reversing quantum evolution that led to a measurement becomes in principle impossible for an observer who keeps the record of its outcome. Thus, quantum irreversibility can result from the information gain rather than just its loss -- rather than just an increase of the (von Neumann) entropy. Recording of the outcome of the measurement resets, in effect, initial conditions within the observer's (branch of) the Universe. Nevertheless, I also show that observer's friend -- an agent who knows what measurement was successfully carried out and can confirm that the observer knows the outcome but resists his curiosity and does not find out the result -- can, in principle, undo the measurement. This relativity of quantum reversibility sheds new light on the origin of the arrow of time and elucidates the role of information in classical and quantum physics. Quantum discord appears as a natural measure of the extent to which dissemination of information about the outcome affects the ability to reverse the measurement

Wave-packet collapse and the core quantum postulates: Discreteness of quantum jumps from unitarity, repeatability, and actionable information

An unknown quantum state of a single system cannot be discovered, as a measured system is reprepare: it jumps into an eigenstate of the measured observable. This impossibility of finding the quantum state and other symptoms usually blamed on wave-packet collapse follow (as was recently demonstrated for pure states of measured systems) from unitarity (which does not, however, allow for a literal collapse) and from the repeatability of measurements: Continuous unitary evolution and repeatability suffice to establish the discreteness that underlies quantum jumps. Here we consider mixed states of a macroscopic, open system (such as an apparatus), and we allow its microscopic state to change when, e.g., measured by an observer, provided that its salient features remain unchanged and that observers regard macroscopic state of the pointer as representing the same record. We conclude that repeatably accessible states of macroscopic systems (such as the states of the apparatus pointer) must correspond to orthogonal subspaces in the Hilbert space. The symmetry breaking we exhibit defies the egalitarian quantum superposition principle and unitary symmetry of the Hilbert space, as it singles out preferred subspaces. We conclude that the resulting discreteness (which underlies quantum jumps) emerges from the continuity of the core quantum postulates plus repeatability also in macroscopic and open, but ultimately quantum systems such as measuring devices accessed by observers, where (in contrast with pure states of microsystems) repeatability is paramount.Comment: Changes in the presentation, figure added, et