scholarly journals ARE QUANTUM STATES REAL?

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345012 ◽  
Author(s):  
LUCIEN HARDY
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Single Copy ◽  
Quantum States ◽  
Real Thing ◽  
Basic Assumptions ◽  
Pure Quantum State ◽  
Pure States

In this paper we consider theories in which reality is described by some underlying variables, λ. Each value these variables can take represents an ontic state (a particular state of reality). The preparation of a quantum state corresponds to a distribution over the ontic states, λ. If we make three basic assumptions, we can show that the distributions over ontic states corresponding to distinct pure states are nonoverlapping. This means that we can deduce the quantum state from a knowledge of the ontic state. Hence, if these assumptions are correct, we can claim that the quantum state is a real thing (it is written into the underlying variables that describe reality). The key assumption we use in this proof is ontic indifference — that quantum transformations that do not affect a given pure quantum state can be implemented in such a way that they do not affect the ontic states in the support of that state. In fact this assumption is violated in the Spekkens toy model (which captures many aspects of quantum theory and in which different pure states of the model have overlapping distributions over ontic states). This paper proves that ontic indifference must be violated in any model reproducing quantum theory in which the quantum state is not a real thing. The argument presented in this paper is different from that given in a recent paper by Pusey, Barrett and Rudolph. It uses a different key assumption and it pertains to a single copy of the system in question.

Thresholds for reduction-related entanglement criteria in quantum information theory

2015 ◽  
Vol 15 (13&14) ◽  
pp. 1165-1184
Author(s):  
Maria A. Jivulescu ◽  
Nicolae Lupa ◽  
Ion Nechita
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum State ◽  
Random Matrix ◽  
Matrix Theory ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Absolute Reduction ◽  
Open Questions ◽  
Pure Quantum State

We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the resulting bipartite quantum state satisfies the reduction criterion in different asymptotic regimes. We consider as well the basis-independent version of the reduction criterion (the absolute reduction criterion), computing thresholds for the corresponding eigenvalue sets. We do the same for other sets relevant in the study of absolute separability, using techniques from random matrix theory. Finally, we gather and compare the known values for the thresholds corresponding to different entanglement criteria, and conclude with a list of open questions.

scholarly journals ALGORITHMIC COMPLEXITY OF QUANTUM STATES

2006 ◽  
Vol 04 (04) ◽  
pp. 715-737 ◽  
Author(s):  
CATERINA E. MORA ◽  
HANS J. BRIEGEL
Keyword(s):  
Quantum State ◽  
Kolmogorov Complexity ◽  
Quantum States ◽  
Algorithmic Complexity ◽  
Experimental Procedure ◽  
Classical Information ◽  
Universal Machine ◽  
Intuitive Idea ◽  
Pure Quantum State ◽  
Classical Information Theory

We give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory, the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the string itself. We define the complexity of a quantum state by means of the classical description complexity of an (abstract) experimental procedure that allows us to prepare the state with a given fidelity. We argue that our definition satisfies the intuitive idea of complexity as a measure of "how difficult" it is to prepare a state. We apply this definition to give an upper bound on the algorithmic complexity of a number of known states. Furthermore, we establish a connection between the entanglement of a quantum state and its algorithmic complexity.

scholarly journals Locally undetermined states, generalized Schmidt decomposition, and application in distributed computing

2009 ◽  
Vol 9 (11&12) ◽  
pp. 997-1012
Author(s):  
Y. Feng ◽  
R. Duan ◽  
M. Ying
Keyword(s):  
Distributed Computing ◽  
Quantum State ◽  
Fault Tolerant ◽  
A Priori ◽  
Sufficient Conditions ◽  
Quantum States ◽  
Consensus Problem ◽  
Schmidt Decomposition ◽  
Pure States ◽  
Necessary And Sufficient

Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient conditions for a pure multipartite state to be locally undetermined, and moreover, characterizing precisely all the pure states sharing the same set of reduced states with it. Interestingly, local determinability of pure states is closely related to a generalized notion of Schmidt decomposition. Furthermore, we find that locally undetermined states have some applications to the well-known consensus problem in distributed computing. To be specific, given some physically separated agents, when communication between them, either classical or quantum, is unreliable, then there exists a totally correct and completely fault-tolerant protocol for them to reach a consensus if and only if they share a priori a locally undetermined quantum state.

AN EFFICIENT SEPARABILITY CRITERION FOR n-PARTITE ARBITRARILY DIMENSIONAL QUANTUM STATES

2011 ◽  
Vol 09 (04) ◽  
pp. 1101-1112
Author(s):  
YINXIANG LONG ◽  
DAOWEN QIU ◽  
DONGYANG LONG
Keyword(s):  
Hilbert Space ◽  
Quantum State ◽  
Pure State ◽  
Coefficient Matrix ◽  
Quantum States ◽  
Mixed States ◽  
Density Matrices ◽  
Separability Criterion ◽  
Dimensional Hilbert Space ◽  
Pure States

In this paper, we obtain an efficient separability criterion for bipartite quantum pure state systems, which is based on the two-order minors of the coefficient matrix corresponding to quantum state. Then, we generalize this criterion to multipartite arbitrarily dimensional pure states. Our criterion is directly built upon coefficient matrices, but not density matrices or observables, so it has the advantage of being computed easily. Indeed, to judge separability for an arbitrary n-partite pure state in a d-dimensional Hilbert space, it only needs at most O(d) times operations of multiplication and comparison. Our criterion can be extended to mixed states. Compared with Yu's criteria, our methods are faster, and can be applied to any quantum state.

scholarly journals QUANTUM KOLMOGOROV COMPLEXITY AND ITS APPLICATIONS

2007 ◽  
Vol 05 (05) ◽  
pp. 729-750 ◽  
Author(s):  
CATERINA E. MORA ◽  
HANS J. BRIEGEL ◽  
BARBARA KRAUS
Keyword(s):  
Quantum Computation ◽  
Quantum State ◽  
Kolmogorov Complexity ◽  
Communication Complexity ◽  
Quantum States ◽  
Qubit State ◽  
Binary String ◽  
Classical Communication ◽  
Pure Quantum State ◽  
Definition Of

Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity. Furthermore, we give some examples of how quantum Kolmogorov complexity can be applied to prove results in different fields, such as quantum computation and thermodynamics, and we generalize it to the case of mixed quantum states.

QUANTUM NANOTECHNOLOGY

2009 ◽  
Vol 08 (04n05) ◽  
pp. 337-344 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Quantum Computer ◽  
Quantum States ◽  
Atoms And Molecules ◽  
Atomic Structures ◽  
Broad Concept ◽  
Unknown Quantum State

Nanotechnology is based on manipulations of individual atoms and molecules to build complex atomic structures. Quantum nanotechnology is a broad concept that deals with a manipulation of individual quantum states of atoms and molecules. Quantum nanotechnology differs from nanotechnology as a quantum computer differs from a classical molecular computer. The nanotechnology deals with a manipulation of quantum states in bulk rather than individually. In this paper, we define the main notions of quantum nanotechnology. Quantum analogs of assemblers, replicators and self-reproducing machines are discussed. We prove the possibility of realizing these analogs. A self-cloning (self-reproducing) quantum machine is a quantum machine which can make a copy of itself. The impossibility of ideally cloning an unknown quantum state is one of the basic rules of quantum theory. We prove that quantum machines cannot be self-cloning if they are Hamiltonian. There exist quantum non-Hamiltonian machines that are self-cloning machines. Quantum nanotechnology allows us to build quantum nanomachines. These nanomachines are not only small machines of nanosize. Quantum nanomachines should use new (quantum) principles of work.

Probability and Explanation

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Causal Explanation ◽  
Born Rule ◽  
Correct Application

We can use quantum theory to explain an enormous variety of phenomena by showing why they were to be expected and what they depend on. These explanations of probabilistic phenomena involve applications of the Born rule: to accept quantum theory is to let relevant Born probabilities guide one’s credences about presently inaccessible events. We use quantum theory to explain a probabilistic phenomenon by showing how its probabilities follow from a correct application of the Born rule, thereby exhibiting the phenomenon’s dependence on the quantum state to be assigned in circumstances of that type. This is not a causal explanation since a probabilistic phenomenon is not constituted by events that may manifest it: but each of those events does depend causally on events that actually occur in those circumstances. Born probabilities are objective and sui generis, but not all Born probabilities are chances.

“Non-locality”

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum Entanglement ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Quantum States ◽  
Action At A Distance ◽  
Insight Into ◽  
Non Locality

Quantum entanglement is popularly believed to give rise to spooky action at a distance of a kind that Einstein decisively rejected. Indeed, important recent experiments on systems assigned entangled states have been claimed to refute Einstein by exhibiting such spooky action. After reviewing two considerations in favor of this view I argue that quantum theory can be used to explain puzzling correlations correctly predicted by assignment of entangled quantum states with no such instantaneous action at a distance. We owe both considerations in favor of the view to arguments of John Bell. I present simplified forms of these arguments as well as a game that provides insight into the situation. The argument I give in response turns on a prescriptive view of quantum states that differs both from Dirac’s (as stated in Chapter 2) and Einstein’s.

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

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