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Implementation of Practically Secure Quantum Bit Commitment Protocol Ariel Danan School of Physics Tel Aviv University September 2008

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Project Members: Ariel Danan, Yoav Linzon Ariel Danan, Yoav Linzon (With a lot of help from Ezra Shaked- electronic workshop) Academic supervisors: Lev Vaidman and Shimshon Barad Lev Vaidman and Shimshon Barad

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Outline Introduction Introduction Bit Commitment Bit Commitment Practically Secure Quantum Bit Commitment Practically Secure Quantum Bit Commitment Phase Encoding with Optical Fibers Phase Encoding with Optical Fibers Experimental Setup Experimental Setup Demonstration (Q.O. lab) Demonstration (Q.O. lab) Security Discussion Security Discussion Final Results Final Results Future Prospects Future Prospects

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Introduction Quantum Information → Quantum computers Quantum Information → Quantum computers ( Grover's quantum search, Shor's quantum factoring ….) Quantum Key Distribution ↔ ‘No Cloning Theorem’ Quantum Key Distribution ↔ ‘No Cloning Theorem’ Unconditionally Secure Quantum Bit Commitment → ‘No Go Theorem’ Unconditionally Secure Quantum Bit Commitment → ‘No Go Theorem’ Practically Secure Quantum Bit Commitment Practically Secure Quantum Bit Commitment Based on the limitation of current technologies (Non-demolition measurement and long quantum memory)

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Introduction Lev’s Practically Secure Quantum Bit Commitment Protocol Lev’s Practically Secure Quantum Bit Commitment Protocol Patent Pending → The term Non Demolition measurement was not used in the thesis Implementation of Practically Secure Quantum Bit Commitment using low cost quantum optics devices Implementation of Practically Secure Quantum Bit Commitment using low cost quantum optics devices

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What is Bit Commitment? Committing phase: Committing phase: Alice select a bit, put it in a strong box and sends it to Bob Alice select a bit, put it in a strong box and sends it to Bob 01or Bob Alice Opening Phase: Opening Phase: Alice sends the key to Bob and he reveals her commitment Alice sends the key to Bob and he reveals her commitment Alice 1 0 or Bob Both Classical and Quantum Unconditionally Secure bit commitment is impossible! Both Classical and Quantum Unconditionally Secure bit commitment is impossible!

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Applications Secure Commercial Biding Secure Commercial Biding User Authentication User Authentication Lon distance coin Tossing Lon distance coin Tossing Oblivious Transfer (Two party secure computation) Oblivious Transfer (Two party secure computation) רק לא גיידאמק!@ # אתמול היה לי יותר

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Conjugate observables Photon has 2 bases of polarization that don’t commute. Photon has 2 bases of polarization that don’t commute. Rectilinear basis: eigenstates of σ z Diagonal basis: eigenstates of σ x

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Practical secure QBC protocol Committing phase: Bob sends photons prepared randomly in one of the 4 polarization Bob sends photons prepared randomly in one of the 4 polarization { } to Alice. { } to Alice. Bob keeps the record of when and what he sent to Alice. Bob keeps the record of when and what he sent to Alice. Alice measures all photons in one of two bases which manifests her commitment { } = 0 { } = 1. Alice measures all photons in one of two bases which manifests her commitment { } = 0 { } = 1. She announces immediately the time of detection of the photons. She announces immediately the time of detection of the photons. Bob Alice b =0 or b =1 Pulse No. 1045 Pulse No. 1045 (1,1) Pulse No. 1044 (0,1) Pulse No. 1043 (1,1) Pulse No. 1042 (0,0)

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Opening Phase: Alice reveals her commitment (measurement base) and the measurements outcomes. -Bob checks Alice’s answers. Opening Phase: - Alice reveals her commitment (measurement base) and the measurements outcomes. -Bob checks Alice’s answers. BobAlice

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Advantages 1. Cheating tasks (long-time Qubit memory, Perfect Non- demolition Measurement) are beyond current technology 2. No need for high fidelity (the security increase exponential with the number of Qubits per commitment). 3. Short distances possibility (unlike Classical bit commitment) 4. Since Alice don’t control the information she gets, it’s more difficult for her to cheat. 5. Bob cannot gain information about Alice's commitment or measurements outcomes before she announces them.

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Phase Encoding with Optical Fibers D1D1 D0D0 Meas. Basis Φ2Φ2 Φ1Φ1 Sent Qubit 0%25%00,00,0 12.5% 01,0 25%0%00,1 12.5% 01,1 12.5% 10,00,0 0%25%11,0 12.5% 10,1 25%0%11,1 Phase Encoding Principle. Two pulses exit Bob apparatus, and interfere on Alice’s side.

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Experimental Setup Single photon detector (~25% efficiency ) 2X2 fiber coupler (Beam splitter) Polarization controller Phase shifter (Piezoelectric mount) Nanosecond pulse laser

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Optical line performance Visibility S-S pulse L-S + S-L interference pulse L-L pulse Classical regime Quantum regime

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Low Fidelity Source Michelson interferometer measurement with short pulses: (a) without interference; (b) & (c) interference with two different phase shifts Let’s Go To The Q.O. Lab For a Demonstration The system's Stability - ~0.3s Photon losses – path transmissivity

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Security Discussion Bob’s Cheating: Bob’s Cheating: 1. Look for correlations between detection efficiency and sent qubit base. 2. Alice has different setting time for different measurement base. 3. Trojan Horse Attack

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Alice’s Cheating: Alice’s Cheating: 1. Non Demolition and Quantum Memory Attack ('no go theorem' ); not feasible with today's technological limit. 2. Random Base Attack Imposes 25% quantum bit error rate (QBER) 3. Photon Number Split Attack To prevent this kind of attack the ratio of the probability for having two photon (or more) in a pulse and Alice's supposed detection probability must be smaller than one. 4. Combined Attack Imposes

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Security Discussion with Low Fidelity source Bob has a low fidelity output which imposes an additional QBER ( ) Bob has a low fidelity output which imposes an additional QBER ( ) 1. Random Base Attack: Imposes 3. Photon Number Split Attack: Will not effect PNS like attack 4. Combined Attack: Imposes

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Final Results Opening stage results (1 photon per pulse ) Each protocol took about two hours to be complete All QBC protocol results do not exceed the standard deviation range and are acceptable commitments.

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Final Results Each protocol took about a day to be complete. All QBC protocol results do not exceed the standard deviation range and are acceptable commitments. Probably the first practically secure QBC system in the world Opening stage results(0.2 photon per pulse ) Fragile Security- to increase security the number of sent qubits per commitment must be increased (2000) commitment must be increased (2000)

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Future Prospects Improve Quantum Bit Error Rate Improve Quantum Bit Error Rate 1. Single photon source (Spontaneous parametric Down-Conversion) (Spontaneous parametric Down-Conversion) 2. Improve pulse coherence Faster Faster 1. Real time Labview \ Design DSP circuits 2. Change Piezo with Crystal for E-O modulation (LiNbO3)

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What did he say? You don ’ t say! Q&A

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