Distributed Entanglement and

1
Distributed Entanglement and Quantum Clock
Synchronization (QCS)
ULVI YURTSEVER
2
JPL Contributors

• Chris Adami
• Jonathan Dowling
• Robert Gingrich
• George Hockney
• Pieter Kok
• Hwang Lee
• Colin Williams
• Ulvi Yurtsever
• Quantum Computing Technologies Group
• JPL

3
Overview of Objectives
Overall Objective
Understanding the foundations (including a fully
relativistic theory of quantum information) and
possible applications of new sensor algorithms
(including, but not limited to the QCS) based on
distributed quantum entanglement
4
Objective and Significance
Quantum Positioning System
Relativistic Quantum Information Theory
Entanglement Enhanced Time Frequency Transfer
Entanglement Enhanced Clocks
QCS Protocols
ROADMAP
5
Objective and Significance
SYNCHRONIZATION PROBLEM AND THE QUANTUM APPROACH
A
B
Invariant Phase
Noisy Classical Channel
Local Operations
Shared Entangle- ment
Quantum Channel
6
THE ROSETTA STONE
Entangled (Frozen) Ramsey Atomic Clocks
7
The Preskill Phase Problem

• JPLs QCS protocol needs pure non-degenerate
  (energy-separated qubit states) entanglement
  distribution
• However, distributing entanglement to distant
  parties leads to a relative phase error f due to
  the energy difference W between qubits
• These phase errors either need to be purified,
  or prevented prior to entanglement distribution,
  for the JPL protocol to work. Otherwise protocol
  equivalent to slow clock transport.
• Efforts within the last 12 months of activity
  concentrated on
• Purification protocols (to measure and correct
  the phase error f after distribution)
• Methods of pure nondegenerate entanglement
  distribution (to prevent phase errors from
  forming during distribution)

8
Asynchronous Entanglement Purification is
Impossible

• One of our major results is the proof, via a
  Lorentz-invariant analysis of the QCS protocol,
  that it is not possible to purify the phase f
  asynchronously, i.e. without already established
  time synchrony between the parties
  (http//xxx.lanl.gov/abs/quant-ph/0010097 to
  appear in Phys Rev A).
• Accordingly, our current efforts to solve the
  Preskill phase problem are focused on
  investigating methods of pure entanglement
  distribution
• Using multi (greater than two)-particle
  entanglement as a distribution medium from which
  the required QCS states might later be
  distillable
• (Example four-particle
• entangled state immune
• to Preskill phase errors
• during transport)
• This investigation is ongoing however
  early results (Bob Gingrich) point towards a
  general proof that such purification schemes
  wont work.
• Exploring novel methods of (binary) entanglement
  distribution which inherently avoid the onset of
  relative phase errors. Two ideas are currently
  under investigation

9
Entanglement Swapping in A Cavity

• Start with a cavity into which two atoms enter
  one after the other
• The initial state is
• After the two-level atom B is in the cavity,
  apply a p/2-pulse (on B)
• After both atoms A and B are in the cavity,
  apply a p-pulse on atom A

Since at each step the overall quantum state (of
atoms plus the EM field) is dark, no relative
phase errors can creep in
10
Entanglement Swapping in A Cavity

• Start with two cavities in each of which a pair
  of atoms A,B and C,D are (independently)
  entangled as above
• The initial state is
• After (locally) synchronizing the nearby atoms B
  and C, perform a Bell measurement on the B-C
  system in the Bell basis
• and select only those instances where the Bell
  measurement outcome is the state (with a
  constant yield of 25).

11
Entanglement Swapping in A Cavity

• After this Bell measurement, the A-D systems
  state collapses to
• thereby extending pure entanglement distribution
  to a distance twice that covered by each cavity.
• This scheme can be carried out iteratively
• To transfer entanglement from A to Z, separated
  by distance L, need order NL/d single-cavity
  entanglement transfers followed by order N-1 Bell
  measurements resources required grow only
  linearly with distance.
• A deeper study of this new nondegenerate (pure)
  entanglement-transfer protocol is currently
  ongoing.

12
The Unruh Effect

• The idea in exploring the Unruh effect is to ask
  the following question
• Can purified entanglement be created
  directly out of the
• Poincare vacuum state of a relativistic
  field in Minkowski spacetime?

13
The Unruh Effect
When an accelerating detector detects a Rindler
particle in Rindler wedge I, inertial observers
see a Minkowski particle being emitted in the
spacelike-separated Rindler wedge II the
responses of the two detectors are strongly
correlated.
Inertial particle detector.
I
II

• Can this Rindler entanglement be harnessed to
  transfer time and phase synch information between
  distant observers communicating via a classical
  channel?

14
Large photon-number path entanglement with
applications to metrology
Objective

• Create entangled photon-number states of
• the form N,0? 0,N? with linear optics
• These states are important for metrology
• applications as quantum lithography and
• quantum gyroscopes.
• It was previously believed that this
• needed nonlinear optical elements.

Ingredients
Approach

• Two beam-splitters split off photons from
• the two incoming modes.
• The deflected beams are sent into a 5050
• beam-splitter.
• A detector coincidence will now be due to
• two photons coming from either the left or
• the right mode.

• We first create an N,N? input state and
• then successively strip away photons with
• the device shown in the top right corner.
• Application of one such box yields the
• state N,N-2? ei? N-2,N? , with a suitably
• chosen phase ?.

15
Parallel transport of geometric structures using
shared prior entanglement
Objective
Classical Link
Alice
Bob

• Understand what can be accomplished with the
• resource of distributed noisyentanglement
• of the form
• for two-level atoms, or the form
• for entangled spinors, where R is an unknown
• spin rotation.

Entangled Spinors
Spin-Singlet Source
Status
Approach

• Transfer of acceleration information over the
• quantum channel possible via the QCS protocol.
• Transport of direction and three-frame
• information over the quantum channel via local
• interactions of entangled comoving spinors...
• Transport of Lorentz frame and relative velocity
• information over the quantum channel via local
• interactions of entangled relativistic
  spinors...

• Study entanglement of relativistic Dirac
• spinors, understand the role of Lorentz
• invariance.
• Exploit classical communications and local
• operations to transfer useful geometric or
• kinematical information from Alice to Bob over
• the quantum channel.

16
Fundamental-Physics Implications
Quantum Information Theory
Quantum Optics Quantum Atomics
Quantum Computing Communications
BEC Coherent Atom Optics, Collective Excitations
Quantum Interferometry Metrology Applications
Fundamental Tests, GW Detectors, Sonic Black
Holes in Superfluids
Relativistic Quantum Information Theory
Advanced Sensors Gradiometers, Gyroscopes, .
17
Relativistic QIT via Thermodynamics
relativistic
quantum
non-relativistic
classical
Relativistic QIT
Relativistic Quantum Thermodynamics
?
equilibrium
non-equilibrium
?
?
Quantum Thermodynamics
QIT
?
Relativistic Thermodynamics
?
Relativistic Info Theory
Classical Information Theory (Shannon)
Thermodynamics
18
Using Entangled Light to Probe Quantum
Mechanics in Interiors of Black Holes

• Complete evaporation of black
• holes may violate unitarity.
• Quantum evolution beyond
• evaporation can be probed by states
• of the form
• where is a controlled phase
• (coherent light), and the B-particle
• is allowed to fall into the black hole.
• Linear evolution (Hawking proposal)
• has no detectable effect on A.
• Nonlinear evolution may give rise to
• a (acausal) signal (interference
• fringes) at A detectable by terrestrial
• experiments.

S
Conformal (Penrose) diagram depicting the causal
structure of a spacetime with an evaporating
black hole.
19
First-Year Scorecard

• Progress on last years objectives
• - Clarified the status of asynchronous
  entanglement purification
• Investigated entanglement distribution
  protocols that use entangled states involving
• three or more particles
• Explored other applications of
  quantum-entanglement to metrology
• Continued the study of relativistic quantum
  information theory
• Investigated the fundamental relationships
  between spacetime structure, linearity of
• quantum mechanics, and relativistic causality
• Research plan for the next 12 months
• - Detailed investigation of new protocols for
  nondegenerate entanglement distribution
• Help with designing experimental tests of
  entanglement distribution and QCS protocols
• Further investigation of entanglement-enhanced
  metrology applications
• Extend information theory to relativistic
  quantum fields
• Long term objectives

A
B