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Quantum coherence and geometric quantum discord

Ming-Liang Hu, Xueyuan Hu, Jie-Ci Wang, Yi Peng, Yu-Ran Zhang, Heng Fan

arXiv:1703.01852v3quant-ph

TL;DR

The paper addresses the need for physically meaningful and rigorous quantifiers of quantum coherence and quantum correlations. It reviews geometric and resource-theoretic measures, their operational interrelations, and behavior across many-body, noisy, and relativistic settings. The review concludes that coherence and discordlike correlations are intimately related and can be connected through geometric and operational frameworks.

  • Problem

    Quantum coherence and quantum correlations are fundamental resources, but their rigorous quantification and intrinsic relationship require systematic treatment.

  • Method

    The paper reviews geometric quantum correlations, quantum coherence measures, resource theories, operational interconversions, and their properties across physical settings.

  • Results

    The review identifies a unified geometric framework in which quantumness measures are optimal distances from states lacking the relevant quantum property, alongside operational connections between coherence and correlations.

  • Takeaways & Limitations

    Quantum coherence and discordlike correlations can be transformed into each other operationally and quantified through related geometric distance constructions.

Abstract

from arXiv · show

Quantum coherence and quantum correlations are of fundamental and practical significance for the development of quantum mechanics.They are also cornerstones of quantum computation and quantum communication theory. Searching physically meaningful and mathematically rigorous quantifiers of them are long-standing concerns of the community of quantum information science, and various faithful measures have been introduced so far. We review in this paper the measures of discordlike quantum correlations for bipartite and multipartite systems, the measures of quantum coherence for any single quantum system, and their relationship in different settings. Our aim is to provide a full review about the resource theory of quantum coherence, including its application in many-body systems, and the discordlike quantum correlations which were defined based on the various distance measures of states. We discuss the interrelations between quantum coherence and quantum correlations established in an operational way, and the fundamental characteristics of quantum coherence such as their complementarity under different basis sets, their duality with path information of an interference experiment, their distillation and dilution under different operations, and some new viewpoints of the superiority of the quantum algorithms from the perspective of quantum coherence. Additionally, we review properties of geometric quantum correlations and quantum coherence under noisy quantum channels. Finally, the main progresses for the study of quantum correlations and quantum coherence in the relativistic settings are reviewed. All these results provide an overview for the conceptual implications and basic connections of quantum coherence, quantum correlations, and their potential applications in various related subjects of physics.

I. INTRODUCTION

The paper reviews quantum coherence and discordlike quantum correlations as related quantum resources, emphasizing geometric distance-based measures and operational connections. It surveys their definitions, properties, applications, and limitations across bipartite, multipartite, many-body, and noisy settings.

  • Quantum correlations describe bipartite or multipartite quantum features, whereas coherence concerns a single system, yet the two notions are intimately related.
  • Geometric quantum correlation measures: Distance-based measures quantify a state's quantum property by its distance from states lacking that property, providing a geometric interpretation.
  • Several measures connect coherence, discord, entanglement, path distinguishability, and many-body phenomena through operational transformations and resource-theoretic analyses.
  • Geometric quantum correlation measures: Geometric discordlike measures can simplify multipartite generalization because they do not rely on quantum mutual information.
  • Geometric quantum correlation measures: Hellinger distance discord is locally unitary invariant, vanishes exactly for classical-quantum states, and remains unchanged under adding an unmeasured local ancilla.
  • Geometric quantum correlation measures: Local quantum uncertainty has a geometric interpretation through its direct connection to Hellinger distance discord, but this relation applies only to (2 × n)-dimensional states.

UMAB EM:AB

The reviewed approach defines discordlike quantumness through measurement-induced entanglement between a system and apparatus, extending the construction to selected subsystems of multipartite states. For qubit systems, related minimizations and analytic expressions simplify evaluation.

  • The measurement-interaction construction establishes a quantitative connection between discordlike quantum correlation and entanglement.
  • Negativity of quantumness is the minimum entanglement created between a system and measurement apparatus over choices of measurement basis.
  • For multipartite states, measuring a chosen subsystem set defines partial negativity of quantumness, which vanishes exactly when the measured subsystems are classical.
  • Measuring all subsystems yields total negativity of quantumness, while measuring a proper subset yields partial negativity.
  • For a qubit subsystem, minimization over all classical-quantum states can be reduced to minimization over postmeasurement states.
  • For two-qubit states with maximally mixed subsystem A, negativity of quantumness is int{s1, s2, s3}/2, where si are singular values of the correlation matrix.

B. Measurement-induced nonlocality

Measurement-induced nonlocality (MIN) quantifies the maximal state disturbance caused by locally invariant measurements, with variants defined through different distance measures. The review compares their analytical properties, operational meanings, and contractivity limitations.

  • Definition: MIN is defined as the maximal distance between a state and the set of locally invariant postmeasurement states.For the Hilbert-Schmidt version, it quantifies the maximal global disturbance caused by locally invariant measurements.
  • Hilbert-Schmidt MIN: Hilbert-Schmidt MIN is analytically available for pure states, qubit-sided bipartite states, symmetric higher-dimensional states, and several special state families.The review also summarizes matrix-eigenvalue formulas and bounds for these cases.
  • Dynamics: For zero-MIN states, the review identifies channel classes that cannot create MIN, while also noting that MIN can be created under LOCC.The stated characterization depends on the dimension of the measured subsystem and channel properties.
  • Limitations: Hilbert-Schmidt MIN is noncontractive under local operations on the unmeasured party and can decrease after adding an uncorrelated local ancilla.This flaw motivates alternative MIN measures based on other distance functions.
  • Trace-norm MIN: Trace-norm MIN avoids the Hilbert-Schmidt noncontractivity problem because it is nonincreasing under any CPTP map on the unmeasured party.For the reviewed states, trace-norm and Hilbert-Schmidt MIN give qualitatively similar descriptions of nonlocality.
  • Other MIN measures: Entropy-, fidelity-, skew-information-, and related MIN variants provide additional interpretations and contractivity properties under CPTP maps.Examples include maximal losses of total correlations, entropy increases, and uncertainty-induced nonlocality.

C. Applications of geometric quantum discord

Geometric quantum discord connects distance-based correlation measures with operational tasks including remote state preparation, phase estimation, and teleportation. These connections provide task-specific interpretations but do not yield a universal quantitative relation across discord measures and protocol performance.

  • Overview: Geometric discord measures capture different state features and may have distinct physical implications across quantum-information protocols.The review emphasizes that no single geometric measure is uniformly more useful in every context.
  • Teleportation: Geometric discord bounds average teleportation fidelity, but the review states that no direct quantitative connection exists between the various discord measures and fidelity.Teleportation quality also depends on channel purity and is not determined solely by entanglement.
  • Remote state preparation: In remote state preparation, the protocol payoff is averaged over target states and optimized over measurement directions to define RSP fidelity.The target state is prepared through LOCC using a shared two-qubit channel.
  • Remote state preparation: RSP fidelity vanishes exactly when the second and third eigenvalues of R^TR are zero, corresponding to a zero-discord state.Thus, the spectrum of the channel correlation matrix identifies the zero-fidelity condition in the reviewed setting.
  • Remote state preparation: Nonzero geometric discord is necessary but not sufficient for remote state preparation, because some discordant states have zero RSP fidelity.The review gives a family of two-qubit states exhibiting this separation.
  • Phase estimation: For phase estimation, the inverse of the local quantum uncertainty limits the achievable precision of the estimated phase.This result supplies an operational interpretation of local quantum uncertainty.

III. QUANTUM COHERENCE MEASURES

The review develops quantum coherence as a resource defined relative to incoherent states and operations, then surveys coherence measures based on distances, entanglement, entropy, robustness, and related constructions. It also compares their axiomatic validity, operational meaning, and limitations.

  • Resource framework: Quantum coherence is characterized relative to incoherent states diagonal in a chosen reference basis and operations that preserve the free-state set.This resource-theoretic framework parallels entanglement theory while applying to a single integral system.
  • Free operations: Incoherent operations are represented by Kraus operators with at most one nonzero entry in each column, imposing strong structural restrictions.The review distinguishes trace-preserving operations from operations with subselection of measurement outcomes.
  • State transformations: Pure-state transformations under incoherent operations are possible if and only if the input probability vector is majorized by the output probability vector.This gives a complete criterion for general pure-state conversion under IO.
  • Reference basis: The reference-basis dependence can raise concerns because any density operator is diagonal in its eigenbasis, although practical bases are usually selected according to the physical problem.The review presents this basis choice as an important scope condition for coherence measures.
  • Entropic coherence: The relative-entropy coherence equals the optimal asymptotic rate of distilled maximally coherent states under incoherent operations.This provides a direct operational interpretation of the entropic measure.
  • Distance-based measures: The l1-norm coherence equals the sum of absolute off-diagonal elements and, for bipartite pure states, equals twice the negativity.The review also summarizes bounds and partial results comparing l1-norm and relative-entropy coherence.
  • Axiomatic validity: Hilbert-Schmidt coherence fails selective monotonicity, and every lp or Schatten-p construction with p ≥2 violates that condition.The trace-norm construction satisfies several axioms but is not a proper general coherence measure because one required condition can fail.

B. Entanglement-based measure of coherence

Entanglement activation provides an operational route to quantify coherence: incoherent operations cannot create system–ancilla entanglement from an incoherent state, while suitable operations can saturate the coherence bound. The section also reviews convex-roof, fidelity-based, rank-based, and intrinsic-randomness coherence measures.

  • Entanglement activation: Incoherent operations cannot generate system–ancilla entanglement when the initial system state is incoherent.
  • Entanglement activation: For relative entropy and ancilla dimension dA ≥ dS, a generalized controlled-NOT operation saturates the entanglement–coherence bound.The operation maps the system and vacuum ancilla to a state achieving equality in the bound.
  • Entanglement activation: An operational coherence measure is defined as the maximal entanglement generated between a system and an incoherent ancilla by incoherent operations.The entanglement measure is distance-based, and the construction satisfies the coherence axioms when the entanglement measure is convex.
  • Convex-roof measures: Intrinsic randomness equals relative entropy of coherence for pure states under projective measurements in the reference basis.For mixed states, intrinsic randomness is defined through a convex-roof construction.
  • Convex-roof measures: The coherence concurrence is a convex-roof measure satisfying the coherence axioms and obeying Ccon(ρ) ≥ Cl1(ρ).
  • Convex-roof measures: Fidelity-based coherence has a convex-roof extension and for single-qubit mixed states satisfies CF(ρ) = Cg(ρ)^1/2.
  • Rank measures: The coherence number is a convex-roof measure based on coherence rank and is a coherence monotone under incoherent operations.

D. Robustness of coherence

Robustness-based and related generalized coherence measures quantify how much mixing, distinguishability, or operational resource is required to account for coherence. The review records their monotonicity properties, bounds, special-state formulas, and experimentally accessible variants.

  • Robustness of coherence: Robustness of coherence is defined by the minimum mixing with a state that makes the resulting state incoherent.It is a full coherence monotone and is analytically computable for pure, one-qubit, and X states.
  • Robustness of coherence: For one-qubit, pure, and X states, robustness equals the l1 norm of coherence, CR(ρ) = Cl1(ρ).
  • Robustness of coherence: CR(ρ) reaches its maximum d−1 only for a maximally coherent pure state.
  • Operational resource measures: The coherence weight is the minimal number of coherent states needed, together with maximally many incoherent states, to prepare ρ on average.It satisfies all four coherence-measure conditions; for pure states, Cw(ρ) = 1.
  • Divergence-based measures: Tsallis α-relative-entropy coherence is convex for α ∈ (0, 2] but may violate monotonicity condition (C2b) when α ≠ 1.
  • Skew-information measures: The skew information I(ρ, K) is not a faithful coherence measure because phase-sensitive incoherent operations can increase it.Its asymmetry interpretation is therefore insufficient when incoherent operations are not translationally invariant.
  • Experimental evaluation: Some coherence measures can be evaluated experimentally without reconstructing the full density matrix, with high agreement against state tomography.

H. Generalized coherence measures

Generalized coherence measures connect single-system coherence to purity, superposition, entanglement, discord, steering, and multipartite coherence distribution. The reviewed results establish operational bounds, equivalences, and state-dependent tradeoffs across these settings.

  • Purity and maximal coherence: MIO-based maximal-coherence analysis uses mutually unbiased bases and bounds achievable unitary coherence by distance from the maximally mixed state.
  • Coherence generation: Nonlocal unitaries in the Cartan-decomposed kernel cannot outperform local unitaries in creating coherence, although the general nonlocal case remains open.
  • Generalized free operations: The l1 norm, relative entropy, and intrinsic randomness are genuine coherence monotones under genuinely incoherent operations, as is robustness of coherence.
  • Coherence and correlations: Generated entanglement with an incoherent ancilla is upper bounded by the system’s coherence, with saturation possible for certain contractive distances.
  • Coherence and nonlocality: For two-qubit states, achieving a nonlocal advantage of quantum coherence implies quantum entanglement.
  • Coherence and discord: Relative-entropy coherence equals relative-entropy quantum discord when both are defined through distance to the corresponding free-state sets.
  • Coherence and discord: Coherence consumption under incoherent operations bounds the global discord generated across multipartite subsystems.

B. Complementarity of quantum coherence

Quantum coherence is basis dependent, so the review studies complementarity across incompatible and mutually unbiased bases, as well as tradeoffs between coherence and mixedness or purity. These relations bound how coherence can be distributed among bases and identify states that saturate the bounds.

  • Mutually unbiased bases: Mutually unbiased bases yield complementarity relations that constrain the total coherence across a complete basis set.For the l1 norm, the relation connects coherence with purity and is tight for specified saturating states.
  • Measure dependence: Relative-entropy complementarity relations extend the study beyond the l1 norm, while generalization to other equally suitable coherence measures remains challenging.
  • Incompatible bases: For two incompatible observables, entropic uncertainty relations provide lower bounds on sums of coherence, with bounds depending on basis overlap and the state.
  • Bipartite complementarity: For bipartite states, quantum-memory-assisted uncertainty relations provide coherence bounds that can be tightened using quantum discord.
  • Coherence and mixedness: Fixed mixedness limits the coherence that can be extracted, and fixed coherence conversely limits the mixedness attainable.
  • Coherence and mixedness: Maximally coherent mixed states saturate the coherence–mixedness upper bound and maximize mixedness at fixed coherence.
  • Purity and coherence: Purity measures based on Rényi entropies quantify related purity–coherence tradeoffs, with the Rényi-2 form linked to linear purity.

C. Duality of coherence and path distinguishability

The review connects quantum coherence with wave-like behavior and path distinguishability in interference experiments. It presents duality relations based on coherence measures and distinguishability tasks, while noting limitations for general mult path states.

  • Quantum coherence represents the wave nature of a particle, while path distinguishability represents its particle nature.Their quantitative connection can be studied through unambiguous or ambiguous quantum state discrimination.
  • Bera et al. relate l1 coherence to the upper bound on successful unambiguous path discrimination.The detector states may be nonorthogonal, and the discrimination bound need not be achievable experimentally.
  • For two paths, normalized l1 coherence equals fringe visibility; for three paths, it equals 2V/(3 −V).These relations assume uniform path amplitudes.
  • Mixed particle or detector states can weaken the equality in the coherence–distinguishability relation to an inequality.This extends the duality analysis beyond pure initial states.
  • Relative entropy of coherence also has a duality relation with path distinguishability, including accessible information defined through optimized detector measurements.Accessible information quantifies how well the detector states can be inferred.
  • For N ≥3 general pure states, the upper bound may not be saturated, and wave and particle terms may change simultaneously.This qualifies the direct interpretation of the duality relation as a universal trade-off.

D. Distillation and dilution of quantum coherence

The review treats coherence distillation, formation, assistance, and remote creation as operational resource-conversion tasks. It summarizes rate formulas, asymptotic equivalences, and trade-offs among coherence and entanglement under different operation classes.

  • Standard coherence distillation and dilution: Coherence distillation converts a general state into a maximally coherent state, while coherence formation performs the reverse transformation under incoherent operations.The corresponding optimal rates serve as operational coherence measures.
  • Standard coherence distillation and dilution: Distillable coherence equals relative entropy of coherence, coherence cost equals coherence of formation, and both quantities are additive.These are asymptotic resource-theoretic identities.
  • Standard coherence distillation and dilution: There is no bound coherence: every quantum state has coherence that can be distilled.Unlike bound entanglement, no state requires coherence consumption while yielding no distillable coherence.
  • Assisted coherence distillation: In assisted coherence distillation, LQICC allows general operations on Alice and incoherent operations on Bob, with classical communication between them.The resulting rates define coherence of collaboration for two-way communication and coherence of assistance for one-way communication.
  • Assisted coherence distillation: With N ≥2 assistants and a qubit Bob, local operations plus classical communication can localize maximum coherence on Bob without global auxiliary operations outperforming them.This result concerns the specified pure initial state setting.
  • Assisted coherence distillation: For pure states, coherence of collaboration equals regularized coherence of assistance, and Alice’s assistance can add Bob’s local coherence by S(ρB).The comparison is with the standard distillation protocol.
  • Coherence–entanglement trade-offs: Under LIOCC, simultaneously distillable coherence at Alice and Bob is constrained by their shared entanglement.The review characterizes achievable formation and distillation resource triples.
  • Remote creation of coherence: Remote creation of coherence links subsystem coherence to entanglement, but the stated equality holds only for qubit cases or particular pure-state settings.The operational connection is explicitly limited to initial pure states.

E. Average coherence of randomly sampled states

The review compares coherence statistics for Haar-random pure states and induced random mixed states. Relative entropy and scaled l1 coherence concentrate in high dimensions, whereas unscaled l1 coherence does not, and algorithmic examples connect coherence to performance.

  • Random pure states: Unscaled l1 coherence lacks concentration around its typical value, while scaled l1 coherence concentrates around π/4 for large d.The reported deviation probabilities distinguish the two behaviors.
  • Random pure states: Most Haar-random pure states have relative entropy of coherence close to H_d −1, with deviations exponentially unlikely.The typical amount depends only on the dimension d.
  • Random pure states: The mean classical purity for Haar-random pure states is 2/(d+1), with exponentially small deviation probability.This result supports concentration of a quantity used to bound l1 coherence.
  • Random pure states: Most Haar-random pure states are not maximally coherent, because their optimal diagonal state is typically not maximally mixed.The average trace distance approaches 2/e as d →∞.
  • Random mixed states: For induced mixed states from partial traces, average relative entropy of coherence is (d −1)/2d′, with concentration for d ≥3.The concentration bound applies to the specified induced-measure construction.
  • Quantum algorithms: In the Deutsch–Jozsa setting, coherence limits distinguishability between constant and balanced cases, while sufficiently large detector-state overlap lets the quantum algorithm outperform classical counterparts.The performance comparison is conditioned on the overlap exceeding a critical value.
  • Quantum algorithms: For Grover search, greater coherence depletion leaves less coherence and increases success probability, but may increase the optimal search time.Entanglement and quantum discord are not directly related to the reported success probability or optimal search time.
  • Quantum algorithms: DQC1 speedup corresponds to coherence consumption in the ancilla, while NDQC2 advantage can occur without entanglement or quantum discord.Net global coherence is introduced to interpret the latter advantage.

E. Quantum metrology

The review examines freezing phenomena and resource creation in quantum discord and coherence under quantum channels, identifying conditions, channel classes, and state families governing these behaviors.

  • Resource-independent freezing occurs for geometric quantum correlations when the relevant local channels are invertible.
  • For Bell-diagonal states, geometric quantum correlations remain frozen under independent phase-flip channels until t < t∗= −(1/2γ) ln(|c3(0)|/|c1(0)|).
  • All bona fide distance-based coherence measures can remain permanently frozen under local bit-flip channels, including relative entropy for even N and trace norm for N = 2.
  • Under strictly incoherent channels, every coherence measure freezes if and only if relative entropy of coherence freezes.
  • For qubits, a local channel creates quantum correlations precisely when it is neither completely decohering nor unital.
  • For dimensions d ≥3, even unital channels can create quantum correlations, unlike the qubit case.

C. Resource creating and breaking power

The review characterizes channels by their ability to create, enhance, or destroy quantum coherence and correlations, and summarizes analytical results, additivity properties, and dimensional limitations.

  • Quantum correlating power is the maximum quantum correlation a channel can create when acting locally on one party.
  • Two zero-QCP channels can combine into a positive-QCP channel, demonstrating superadditivity of quantum correlating power.
  • Cohering and decohering power quantify a channel’s maximum ability to produce or destroy coherence.
  • For unitary channels, cohering and decohering power are equal in any basis under the l1 norm and skew-information measures.
  • For N independent unitary channels, decohering power approaches 2^N − 1 as N →∞, except in the special case DP(U_i) = 0 for every U_i.
  • The Hadamard gate H⊗N has maximum cohering power for N-qubit systems under the l1 norm.
  • The coherence-breaking index measures iterative applications of an incoherent channel until coherence is eliminated.

D. Evolution equation of quantum correlation and coherence

The section reviews factorization-type evolution laws for geometric quantum correlations and l1 coherence under noisy channels, then connects coherence to many-body and localization phenomena.

  • Evolution equation of geometric quantum correlation: Geometric quantum discord can exhibit factorization decay when a bipartite system passes through a local quantum channel.The decay is discussed in analogy with concurrence evolution.
  • Evolution equation of geometric quantum correlation: Under specified channel conditions, Dp(E[ρ]) is determined by the initial Dp(ρ) multiplied by a channel-dependent factor |q(t)|.The conditions include a channel action of the form E(̺)=q(t)̺ on the relevant component.
  • Evolution equation of quantum coherence: For l1 coherence, the evolution obeys a factorization relation when Tk0=0 for k∈{1,2,…,d2−d}.The included channels comprise Pauli, Gell-Mann, and generalized amplitude damping channels; a constructed channel works for arbitrary initial states.
  • Noisy-channel behavior: In non-Markovian reservoirs, information backflow can produce damped oscillations of geometric quantum discord.Studies considered two-qubit systems coupled to bosonic structured reservoirs with Lorentzian and Ohmic-like spectra.
  • Noisy-channel behavior: Initial system-bath correlations can prolong coherence in super-Ohmic baths, while boundary proximity and transverse polarization can trap atomic coherence.The reported coherence behavior depends on system-bath correlations, position, and polarization.
  • Quantum coherence and correlations of localized and thermalized states: Thermalized states have diagonal reduced density matrices and therefore possess neither quantum coherence nor quantum correlations, whereas many-body-localized entropy grows slowly rather than following a volume law.Many-body-localized entanglement entropy is described as logarithmic in time, or algebraic for power-law interactions.

D. Quantum coherence and quantum phase transitions

The review examines how coherence and discordlike measures characterize quantum phase transitions across many-body models. Results show that derivatives, extrema, and susceptibilities can identify several critical points, although effectiveness depends on the model and transition type.

  • Quantum phase transitions arise from quantum fluctuations driven by changes in Hamiltonian parameters such as spin coupling and magnetic field.
  • The review places these studies within broader work linking quantum coherence and quantum correlations to quantum-information phenomena and relativistic settings.
  • Coherence susceptibility, defined as the first derivative of relative entropy of coherence, pinpoints exact transition points through singularities and identifies the temperature frame of quantum criticality.
  • Coherence measures and their lower bounds can locate critical points in XY-type models through extrema, derivative singularities, and scaling behavior.For γc = 0, several single- and two-spin measures are extremal; other derivatives show size-dependent behavior near second-order transitions.
  • Discordlike measures detect quantum phase transitions at finite temperature in several spin models, including transitions that entanglement of formation cannot detect.For one model, QD detects Δ = ±1 while entanglement of formation does not; trace-norm discord also identifies λc = 1 and other critical regions.
  • Geometric and coherence-based measures are not universally reliable: trace-norm discord and total correlation detect a first-order transition at Δ = 1, but fail for the infinite-order transition at Δ = −1.The cited results indicate that detection performance varies with both the measure and the many-body model.

B. Free field modes beyond the single-mode approximation

Relativistic motion, gravitational fields, and cosmological expansion reshape accessible quantum correlations and coherence. The reviewed studies report degradation, redistribution, or generation of correlations depending on the field, observer motion, spacetime, and encoding.

  • Hawking radiation reduces entanglement and teleportation fidelity for states prepared in inertial frames, with behavior depending on black-hole and field parameters.
  • Hawking radiation redistributes correlations: physically accessible correlations decrease while inaccessible correlations increase in Schwarzschild spacetime.
  • Unruh-Hawking noise removes quantum coherence at infinite acceleration while leaving a finite classical channel capacity and surviving classical correlation.
  • In dilation black-hole settings, increasing dilation charge destroys discord-type correlations, while accessible measurement-induced nonlocality decreases monotonically but remains nonzero at infinite Hawking temperature for Dirac fields.
  • Curved and expanding spacetimes can generate entanglement between field modes, with fermionic entanglement encoding more information about spacetime history than bosonic entanglement under some conditions.
  • Cosmological-horizon effects degrade teleportation fidelity for scalar and cavity modes, with Planck-scale cutoffs producing additional modifications.

E. Unruh-DeWitt detectors

The reviewed studies examine how acceleration, thermal noise, field modes, and relativistic motion affect quantum correlations, coherence, and teleportation. Results distinguish the degradation patterns of different quantum resources and identify mode mismatch and horizon leakage as important mechanisms.

  • Quantum correlations under acceleration: Unruh thermal noise can completely destroy discord at infinite acceleration while leaving classical correlation nonzero for every acceleration.Unlike entanglement, discord-type correlations do not necessarily exhibit sudden death at finite acceleration in this setting.
  • Quantum correlations under acceleration: Mode mismatch between the squeezed-state mode and the accelerated-frame detectable mode dominates entanglement degradation more than Unruh thermal noise.Leakage through the Rindler horizon also limits complete state measurement and causes irreversible entanglement loss.
  • Quantum correlations under acceleration: Finite acceleration can cause sudden death of entanglement, whereas discord may vanish only asymptotically at large acceleration.Localized modes produce qualitatively different behavior from Unruh modes in the two-mode squeezed-state setting.
  • Relativistic teleportation: Teleportation fidelity can fall below the best classical value before the detector pair becomes disentangled.Detector-state distortion can substantially suppress fidelity even when the detectors remain strongly entangled, so entanglement dynamics are not directly tied to teleportation fidelity.
  • Quantum coherence and acceleration: Coherence approaches zero only at infinite acceleration, while entanglement reaches zero at finite acceleration under Unruh thermal noise.The detector-state decoherence is reported as irreversible without a boundary, and a frozen-coherence condition is discussed.
  • Relativistic field effects: The Unruh effect produces short-distance thermal-like and long-distance nonthermal Casimir-Polder behavior between uniformly accelerated atoms.The long-distance behavior is associated with the breakdown of local inertial descriptions.
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